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Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If n and y are positive integers and 450y = n^3, which of the following must be an integer?
options: A)y/(3*2^2*5) B)y/(3^2*2*5) C)y/(3*2*5^2) D)y/(5^3*2^2) E)y/(5*3*2)
SOLUTION:Solution:
As y and n are both integers so y is of the form of 3*5*2*2*K
where K= an integer.
to make n as an integer and 450y to be a cube of a number.
Now checking with the answers we get only 1 as K.
So the answer is (1). #### A
QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
options: A)40 sec B)42 sec C)45 sec D)48 sec E)58 sec
SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
ANSWER:A #### A
QUESTION:Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
options: A)326 B)372 C)375 D)381 E)312
SOLUTION:A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C #### C
QUESTION:In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
options: A)c/e B)e/c C)e/(c-e) D)c/(c-e) E)1- (e/c)
SOLUTION:We're given a couple of facts to work with:
1) There were a total of c earthquakes
2) Of those earthquakes, e of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Let's TEST VALUES
c = 5 total earthquakes
e = 2 occurred in Asia
Thus, there were 3 earthquakes that DID NOT occur in Asia....
The answer to the question is 2:3
We just need to plug in the values for c and e and find the match...
Answer A: c/e = 5/2 NOT a match
Answer B: e/c = 2/5 NOT a match
Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match
Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match
Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match
C #### C
QUESTION:A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible?
options: A)230 B)360 C)420 D)840 E)5,040
SOLUTION:we have 6 letters out of which 3 are of one kind, 2 are of another kind..
so total ways = 6!/2!1!=360
ans B #### B
QUESTION:If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10?
options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5
SOLUTION:92p × 5p+w + 11w × 6pw--1=B #### B
QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495
SOLUTION:22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15 = 1485
ANSWER:D #### D
QUESTION:A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5
SOLUTION:The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 4/16 = 1/4.
The answer is B. #### B
QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
options: A)22 B)80 C)40 D)77 E)12
SOLUTION:800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C #### C
QUESTION:A soccer coach is preparing his starting lineup of 11 players chosen from 15 players. He considers 8 of his players good at defense and 7 of his players good at offense. If he wants to pick 6 players best at defense and 5 players best at offense, how many different ways can he do this?
options: A)264 B)328 C)460 D)588 E)642
SOLUTION:(8c6)*(7c5)
[8!/(6!*2!)]*[7!/(5!*2!)]
28*21
588
D #### D
QUESTION:what is the integer among the following that represents a sum of 3 consecutive even integers?
options: A)200 B)303 C)400 D)554 E)588
SOLUTION:Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers)
Divisibility of 3: Sum of the digits of the number must be divisible by 3
Divisibility of 2: Unit digit of the number must be divisible by 2
A. 200NOT A MULTIPLE OF 3 SO RULED OUT
B. 303NOT A MULTIPLE OF 2 SO RULED OUT
C. 400NOT A MULTIPLE OF 3 SO RULED OUT
D. 554NOT A MULTIPLE OF 3 SO RULED OUT
E. 588A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!! #### E
QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins
SOLUTION:The pool was 1/5 full initially.
In 6/5 hrs, it was filled to 8/9 of its capacity.
Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled.
So, 6/5 hrs = 8/9 - 1/5 = 31/45
Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins.
Hence D #### D
QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 6:30:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 150 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
options: A)1200 B)1300 C)1500 D)1800 E)1900
SOLUTION:soap:alcohol
Initial ratio soap:alcohol: water --> 6:30:90
Initial soap:alcohol = 6/30 =6:30
after doubled soap:alcohol =2* 6/30 = 12/30=12:30
Initial soap:water = 6/90=6:90
after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360
After soap: alcohol:water --> 12:30:360
given alcohol 150 cubic centimeter.
ratio is 60:150:1800 (12:30:360)
For 150 cubic centimeter of Alcohol ---1800 cu cm water is required.
Answer-D #### D
QUESTION:The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
options: A)12.5% B)13% C)13.15% D)14% E)15%
SOLUTION:Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
A) #### A
QUESTION:A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long?
options: A)17 B)18 C)19 D)20 E)21
SOLUTION:Speed = 99 * 5/18 = 55/2 m/sec
Total distance covered = 300 + 195 = 495 m
Required time = 495 * 2/55 = 18 sec
Answer: B #### B
QUESTION:Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
options: A)173 m B)200 m C)273 m D)300 m E)None of these
SOLUTION:xplanation:
Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, <ACB = 30º and <ADB = 45º.
AB/AC=tan30
Answer: C #### C
QUESTION:How many multiples of 5 are there between 50 and 500 ?
options: A)128 B)91 C)89 D)61 E)60
SOLUTION:It should be mentioned whether 50 and 500 are inclusive.
If 50 and 500 are inclusive, then the answer is (500-50)/5+1=91.
If 50 and 500 are NOT inclusive, then the answer is (495-55)/5+1=89.
Since OA is C, then we have NOT inclusive case. #### C
QUESTION:Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets.
options: A)4 B)6 C)8 D)10 E)24
SOLUTION:I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets.
Answer : E #### E
QUESTION:What is the remainder when 103 * 505 * 607 is divided by 9
options: A)6 B)18 C)2 D)4 E)7
SOLUTION:103/9==> Remainder=4
505/9==> Remainder=1
607/9==> Remainder=4
=4*4*1=16/9==> Remainder=7
Answer: E #### E
QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B?
options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these
SOLUTION:Explanation :
Assume that investment of C = x
Then, investment of A =2x
A receive 48000
Then C will receive = 48000/2 = 24000
And B receive = 180000 - (24000+48000) = 108000
Ratio of investment between A and B = 48000 : 108000 = 4 : 9
Answer : Option A #### A
QUESTION:In boring a well 50 m deep, the cost is
Rs.4/– for the first meter. The cost of each successive meter
increases by Rs.2/–. What is the cost of boring the entire well?
options: A)1650 B)2650 C)3650 D)4650 E)2850
SOLUTION:For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2
So Sum=(n/2)[2a+(n-1)d]= Total cost of boring
=(50/2)[2*4+(50-1)*2]=25(8+98)
= 2650
ANSWER:B #### B
QUESTION:A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent?
options: A)70% B)45% C)48% D)30% E)40%
SOLUTION:Explanation:
840 ---- 380
100 ---- ? => 45%
Answer: B #### B
QUESTION:John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
options: A)6 days B)8 days C)10 days D)12 days E)14 days
SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days
B) #### B
QUESTION:The fourth proportional to 12, 16 and 18 is?
options: A)21 B)24 C)88 D)99 E)26
SOLUTION:(16*18)/12 = 24
Answer: B #### B
QUESTION:If |x| = 4x - 1, then x = ?
options: A)3 B)1/2 C)1 and 1/2 D)-1/2 E)-1
SOLUTION:Answer: A
Approach:
Substituted option A i.e x=1. Inequality satisfied. #### A
QUESTION:A train covers a distance of 100km in 1 hour. If its speed is decreased by 25km/hr, the time taken by the car to cover the same distance will be?
options: A)1hr B)1hr 20min C)50min D)1hr 30min E)1hr 45min
SOLUTION:Speed = 100/1 = 100km/hr
New speed = 100-25 = 75 km/hr
Time taken = 100/75 = 1hr 20min
Answer is B #### B
QUESTION:A reduction of 5% in the price of sugar enables a lady to obtain 5kgs more for Rs.500, find the original price per kg?
options: A)5.26 B)5.0 C)5.52 D)6.2 E)5.8
SOLUTION:Answer: 500*(5/100) = 25 --- 5
? --- 1 => Rs.5
500 --- 475
? --- 5 => Rs.5.26.Answer: A #### A
QUESTION:A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
options: A)22 B)20 C)88 D)71 E)10
SOLUTION:x ------- 12
(x + 10) ---- 6
x * 12 = (x + 10)6
x = 10
\Answer: E #### E
QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour?
options: A)E982 B)27 C)12 D)14.6 E)28
SOLUTION:Explanation:
T = 11/45 * 60 = 14.6
Answer: Option D #### D
QUESTION:In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground?
options: A)70 B)52 C)62 D)59 E)50
SOLUTION:total number of players= 16+12+18+13= 59
Answer is D #### D
QUESTION:Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Taking the prices of products in ascending order(already arranged)
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239
we see that median value is the 6th value as there in total 11 values given
Arithmetic mean = total/number of entries = 1428/11 =129.8181
We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price
as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit
Correct Answer - B #### B
QUESTION:The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
options: A)(a) remain the same B)(b) decrease by 13.64% C)(c) decrease by 15% D)(d) decrease by 18.75% E)(e) decrease by 30%
SOLUTION:Length (L) = 12
Breadth (B) = 4
Height (H) = 4
Total Area of Walls = 2(BH + LH) = 2*(4*4 + 12*4) = 2*(16+48) = 128
Then, Finally
Length (L) = 2*12 = 24
Breadth (B) = 4/2 = 2
Height (H) = 4/2 = 2
Total Area of Walls = 2(BH + LH) = 2*(2*2 + 24*2) = 2*(4+48) = 104
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (104-128)*100 /128=- 18.75% (Decrease)
Answer: Option D #### D
QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
options: A)23 B)24 C)25 D)26 E)27
SOLUTION:Solution:
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Answer C #### C
QUESTION:3^b + 3^b + 3^b =
options: A)7^b B)7^(b + 1) C)7^(7b) D)3^(b + 1) E)49^B
SOLUTION:Easy one.
3*3^b = 3^(b+1)
Ans. D #### D
QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095
SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 600 + 495 = 1095.
E) #### E
QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book?
options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20
SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = 2p
p = p
Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.
With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E
QUESTION:How much is 80% of 40 is greater than 4/5 of 25?
options: A)15 B)57 C)16 D)12 E)73
SOLUTION:(80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D #### D
QUESTION:Set A: {1, 3, 4, 6, 9, 12, 16}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 4?
options: A)3/14 B)2/7 C)9/14 D)5/7 E)1/35
SOLUTION:using probability you can solve: 3/7*2/6*1/5=1/35.
Ans E #### E
QUESTION:A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent?
options: A)25% B)5% C)10% D)15% E)20%
SOLUTION:3000 --- 600
100 --- ? => 20%
Answer: E #### E
QUESTION:A cube has a volume of 343 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
options: A)24 B)48 C)64 D)2744 E)100
SOLUTION:Volume = 343 = side^3
i.e. Side of Cube = 7
New Cube has dimensions 14, 14, and 14 as all sides are twice of teh side of first cube
Volume = 14*14*14 = 2744 square feet
Answer: option D #### D
QUESTION:A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
options: A)9:1 B)4:7 C)7:1 D)2:5 E)5:6
SOLUTION:Explanation:
Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
ANSWER IS A #### A
QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women?
options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35
SOLUTION:METHOD- 1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A #### A
QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
options: A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)58 km/hr
SOLUTION:Speed of the train relative to man = 125/10 m/sec
= 25/2 m/sec.
2
= 25/2 x 18/5 km/hr
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 x = 50 km/hr.
Option B #### B
QUESTION:Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
options: A)s.10 B)s.2 C)s.5 D)s.3 E)s.4
SOLUTION:2500 = D(100/4)2
D = 4
ANSWER:E #### E
QUESTION:A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
options: A)30 B)39 C)87 D)27 E)91
SOLUTION:Let the side of the square(ABCD) be x meters.
Then, AB + BC = 2x metres.
AC = = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = = 30% (approx)
Answer:A #### A
QUESTION:Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age?
options: A)12 years B)13 years C)15 years D)14 years E)18 years
SOLUTION:Let MTomy's present age be 'x' years.
x+ 16 = 3(x- 4)
=> 2x = 28 => x = 14 years.
D #### D
QUESTION:A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
options: A) 16 B) 20 C) 32 D) 44 E) 48
SOLUTION:lets say x ounces of P is mixed with Q.
=> 67-x ounces of Q is present in the mixture (as the total = 67 ounces)
given total almond weight = 15 ounces
(20x/100)+(25/100)(67-x) = 15
=> x = 35
=> 67-35 = 32 ounces of Q is present in the mixture.
Answer is C. #### C
QUESTION:x =1 2 3
y= 4 5 18 then what is the relation between x and y
options: A)1*X)^1 B)1*X)^6 C)1*X)^7 D)1*X)^4 E)1*X)^2
SOLUTION:Y=(1*X)^2
4=(1*2)^2
4=4
ANSWER:E #### E
QUESTION:9, 35, 91, 189, 341, ?
options: A)502 B)521 C)559 D)611 E)712
SOLUTION:Explanation :
13 + 23 = 9
23 + 33 = 35
33 + 43 = 91
43 + 53 = 189
53 + 63 = 341
63 + 73 = 559
Answer : Option C #### C
QUESTION:A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
options: A)27 B)29 C)40 D)89 E)22
SOLUTION:1/8 - 1/x = 1/10
x = 40
Answer: C #### C
QUESTION:There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
options: A)90 B)120 C)675 D)180 E)200
SOLUTION:Number of ways of selecting 2 fiction books = 10C2
Number of ways of selecting 2 non fiction books = 6C2
10C2 * 6C2 = 45 * 15 = 675
Answer: C #### C
QUESTION:How many integers between 263,205and 658,805 have tens digit 1 and units digit 3?
options: A)3,955 B)3,925 C)3,956 D)3,926 E)3,915
SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 263,205 and is 658,805 -263205=395,600 - one number per each hundred gives 133,900/100=3,956
Answer:C. #### C
QUESTION:In how many different number of ways 4 boys and 2 girls can sit on a bench?
options: A)700 B)710 C)720 D)800 E)820
SOLUTION:npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
C) #### C
QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
options: A)15 B)19 C)20 D)21 E)22
SOLUTION:A's 1day work=1/10;
B's 1day work=1/30;
(A+B) 1day work=(1/10+1/30)=2/15;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 2/15 work in 1 day...
They did 2/3 w in 5 days.
Total days=(5+10) = 15
ANSWER:A #### A
QUESTION:There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
options: A)Rs. 30 B)Rs. 34 C)Rs. 42 D)Rs. 48 E)Rs. 50
SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C #### C
QUESTION:The mean of 1^3,2^3,3^3,4^3,5^3 is?
options: A)30 B)45 C)50 D)60 E)75
SOLUTION:1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2
1^3+2^3+3^3+-----+5^3 = (5*6/2)^2 = 225
Required average is = 225/5 = 45
Answer is B #### B
QUESTION:Two representatives must be selected from each of two groups of students. One group consists of two men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?
options: A)1/6 B)1/4 C)5/9 D)1/3 E)1/2
SOLUTION:Group 1: 2 Men and 1 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 2C2*2C2 = 1 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 2*1*1*2 = 4 ways
Total Favorable cases = 1+4 = 5
Total Possible ways of selecting students 2 from each group = 3C2*3C2 = 3*3 = 9
Probability = 5/9
Answer : Option C #### C
QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet?
options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec
SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (36 + 36)*5/18 = 4*5 = 20 mps.
The time required = d/s = 100/20 = 5 sec.
Answer : C #### C
QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him?
options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7
SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E
QUESTION:The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer?
options: A)1500 B)1600 C)1750 D)1900 E)2000
SOLUTION:Let the price of basic computer be C and the price of the printer be P: C+P=$2,500.
The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750.
Plug this value in the first equation: C+750=$2,500 --> C=$1,750
Answer: C. #### C
QUESTION:The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers?
options: A)87 B)42 C)78 D)76 E)26
SOLUTION:5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x =42
Answer: B #### B
QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result?
options: A)132 B)127 C)125 D)152 E)112
SOLUTION:C
125
96 passes out of 125 give an average of 76.8% #### C
QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5
SOLUTION:The sum of three greatest should be more than sum of two lowest.
The total sum is; 5z
A. 6z; 6z is more than 5z. Not possible.
B. 4z; 5z-4z=z(Possible)
C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible
D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible
E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible.
Ans:B #### B
QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 1/4 %, then the amount invested at 11% was?
options: A)12500 B)37500 C)29977 D)26777 E)19871
SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 37/4 * 1/100)
(9x + 1100000 - 11x) = 37000/4 = 925000
x = 87500
Sum invested at 9% = Rs. 87500
Sum invested at 11% = Rs. (100000 - 87500) = Rs. 12500.
Answer: A #### A
<<<Examples ends
QUESTION:What is the maximum number of points that 10 circles of different radii intersect?
options: A)24 B)26 C)33 D)90 E)100
SOLUTION:the maximum number of points that two circles intersect is two.
therefore, each of these 10 circles intersect two point with each of the other 9 circles.
as a consequence, the number of these points is equal to two times the number of combination of the 10 circles.
2∗(10!)/(2!∗10!)=90
Answer: D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If 3 women can color 180 m long cloth in 2 days, then 5 women can color 300 m long cloth in?
options: A)2 days B)3 days C)5 days D)1 day E)4 days
SOLUTION:The length of cloth painted by one woman in one day = 180/ 3× 2 = 30 m
No. of days required to paint 300 m cloth by 5 women = 300/ 5 × 30 = 2 days
Answer : A #### A
QUESTION:Find the greatest number that will divide 48, 210 and 136 leaving 4, 12 and 4 as remainders respectively
options: A)19 B)17 C)13 D)22 E)21
SOLUTION:Explanation:
Answer will be HCF of (48-4, 210-12, 136-4)
HCF of (44, 198, 132) = 22
Option D #### D
QUESTION:Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
options: A)1245 B)1345 C)1455 D)1577 E)1671
SOLUTION:Let the smaller number be x. Then larger number = (x + 1395).
x + 1395 = 6x + 15
5x = 1380
x = 276
Large number = 276+1395 = 1671
E #### E
QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
options: A)227 B)177 C)120 D)288 E)271
SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.Answer:C #### C
QUESTION:The ratio Q , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres
SOLUTION:I guess it should be
the ratio Q, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C) #### C
QUESTION:A toy train started on a 12-feet loop trail at a rate of 4 feet per minute. One minute afterwards, a toy scooter from the same starting point on the loop trail at 6 feet per minute. What is the shortest time that the scooter would take on the trail in order to catch up with the train?
options: A)4 minutes B)3 minutes C)2 minutes D)1 minutes E)0.8 minutes
SOLUTION:we don't need to assume here the direction.we need to find which will take less time
so there are 2 cases
1)both moving in same direction...then time would be 2 minutes
2)both moving in opp direction then time would be 0.8 minutes
as we need the shortest time it would be the second case
Answer:E #### E
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)267 B)240 C)166 D)111 E)121
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300
= 540 ==> x
= 240 m.
Answer: B #### B
QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.
options: A)20% B)21% C)21.33% D)22.109% E)23%
SOLUTION:Lets say the indicated weight is x for $10
but the trader actually get 1.1x for $10
now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1
so profit % = (12.1-10)/ 10 = 0.21 = 21%
ANSWER:B #### B
QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 11?
options: A)44 B)88 C)45 D)176 E)352
SOLUTION:Solution: sequence of 11 lets say sequence is 11n, 11(n+1), 11(n+2), 11(n+3), 11(n+4)
so range is 11n+44-11n = 44
if we put the different values of n we will get different but the range will be multiple of 44
and only 45 is not multiple of 44
Answer : C #### C
QUESTION:There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
options: A)11 B)12 C)15 D)13 E)17
SOLUTION:Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D #### D
QUESTION:Today is Monday. After 61 days, it will be:
options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY
SOLUTION:Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer: Option B #### B
QUESTION:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue?
options: A)25/153 B)28/153 C)5/17 D)E=4/9 E)E=12/17
SOLUTION:P(at least one blue) = 1 - P(0 blue) = 1 - 10/18*9/17 = 12/17.
Answer: E. #### E
QUESTION:The moon revolves around the earth at a speed of approximately 0.9 kilometers per second. This approximate speed is how many kilometers per hour?
options: A)60 B)61.2 C)3240 D)3,600 E)3,672
SOLUTION:moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600seconds.
so one hour, speed= 0.9*3600=3240kilometers per hour.
Option C is correct #### C
QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads?
options: A)3/4 B)1/4 C)3/8 D)7/8 E)None of these
SOLUTION:Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) = n(E) / n(S) =7/8.
ANSWER IS D #### D
QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is?
options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400
SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4
Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C
QUESTION:What is the sum of all the even numbers between 31 and 99, inclusive?
options: A)3,000 B)2,562 C)2,500 D)2,180 E)2,766
SOLUTION:To figure this problem out, you just have to add all the even numbers, starting with 32.
32+34+36+38 and so on, all the way up to 98. You'll get 2,180, so
Final Answer:
D #### D
QUESTION:During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.6 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?
options: A)$2.5 B)$2.55 C)$1.51 D)$3.25 E)$3.0
SOLUTION:finding the Harmonic mean here.
HM = 4/(1/12 + 1/14 + 1/16 + 1/21) = 15.1
C #### C
QUESTION:If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
.
options: A)√n + 1 B)n + 1 C)n^2 + 1 D)n + 2√n + 1 E)n^2 + 2n + 1
SOLUTION:Let a= +ve integer such that
n= a^2
(a+1)= next +ve integer
(a+1)^2 = a^2 + 1 + 2a
and a=n^(1/2)
Therefore ,
(a+1)^2=n+1+2*n^(1/2)
Answer D #### D
QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed?
options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr
SOLUTION:Let the speed be x km/hr
50x-50* 9/10 *x = 450
50x - 45x = 450
x = 90km/hr
Answer is E #### E
QUESTION:If you roll one fair six-sided die, what is the probability that the number is even or less than 4?
options: A)1/6 B)1/3 C)2/ 3 D)3/4 E)5/6
SOLUTION:Total favourable outcomes: 1,2,3 (less than 4), 4,6(even) = 5
Total possible outcome= 6
Probability=5/6.
Answer: Option E #### E
QUESTION:Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?
options: A) 87 B) 89 C) 90 D) 92 E) 95
SOLUTION:Set X = {11, 13, 17,............., 83, 89, 97}
Set Y = {10, 20, 30,..............., 70, 80, 90}
Combining two sets, say Set Z
Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97}
Range = Max Value - Min Value
Range (Z) = 97 - 10 = 87
OA A is the answer. #### A
QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the
second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take
both the punctures together to make it flat ?
options: A)315min B)325min C)335min D)345min E)None of these
SOLUTION:Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st
puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(19+16)=(518)
So both punctures will make the type flat in
(185)mins=335mins
Answer: C #### C
QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it?
options: A)12 days B)18 days C)15 days D)21 days E)22 days
SOLUTION:Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/10 work in 1 day
B alone can do (1/6 -1/10) =1/15 work in 1 day
=> complete work can be done in 15 days by B
Answer: Option C #### C
QUESTION:A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work?
options: A)10 B)12 C)22 D)28 E)20
SOLUTION:A can do the work in 60/4 i.e., 15 days.
A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12
So A and B together can do the work in 12 days.
Answer: B #### B
QUESTION:A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
options: A)35 B)45 C)25 D)15 E)55
SOLUTION:A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=175×9/35=5×9=45
Answer is B. #### B
QUESTION:a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase?
options: A)50 % B)60 % C)70 % D)80 % E)40 %
SOLUTION:let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit.
Nw he adds 10% milk ie total milk z 110 lit.
Now he will get 132 rs. by selling 110 lit f milk (120*110/100)
total profit = 32 rs
increased profit =12 rs
%age increase= 12/20= 60 %
ANSWER:B #### B
QUESTION:List R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?
options: A)12 B)16 C)20 D)24 E)28
SOLUTION:The middle number is 40.
Let the smallest number be x. Then the largest number is 2x+20.
To make x as small as possible, let's make the remaining numbers as large as possible.
So the second largest = the largest = 2x+20.
The second smallest should be equal to the median.
The numbers are x, 40, 40, 2x+20, 2x+20.
x + 40 + 40 + 2x + 20 + 2x + 20 = 5*40 = 200
5x = 80
x = 16
The answer is B. #### B
QUESTION:Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ?
options: A)6000 B)5400 C)6200 D)7200 E)8200
SOLUTION:Investment Ratio = Profit Sharing Ratio.
Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6.
Giri share =
13200
× 6 / 11 = Rs.7200
Hari share =
13200 × 5 / 11 = Rs.6000
Option A #### A
QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8
SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in 5(5/11) min.
ANSWER:D #### D
QUESTION:A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %?
options: A)62 2/3% B)64 2/3% C)66 2/3% D)66 5/3% E)68 2/3%
SOLUTION:Gain=40 lemons
Total 100 lemons
CP 100-40=60
(40/60)*100
=66 2/3%
Ans C #### C
QUESTION:The inverse ratio of 4: 2: 1 is?
options: A)2:4:8 B)2:3:9 C)2:3:2 D)2:3:6 E)2:3:1
SOLUTION:1/4: 1/2: 1/1 = 2:4:8
Answer:A #### A
QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India.
Action:
I. Pollution committee should immediately take certain measures to control the pollution levels in India.
II. Licenses of polluting industries should be cancelled and owners should be put behind the bars.
options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow
SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided.
ANSWER IS A #### A
QUESTION:If pq = p^3 + q^2 – 2pq, for what value of q is pq equal to p^3 for all values of p?
options: A)-2 B)-1 C)0 D)1 E)2
SOLUTION:C
p3 + q2 – 2pq = p3
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI
C #### C
QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.2200, then what is the income of P1?
options: A)s.800 B)s.2400 C)s.4000 D)s.5500 E)s.4200
SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 2200 …(i) and 4x – 2y = 2200 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 2200 -> x = 1100
P1’s income = Rs 5*1100 = Rs.5500
ANSWER:D #### D
QUESTION:Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756
options: A)16 B)33 C)105 D)424 E)2124
SOLUTION:2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
3th term should 34 instead of 33.
B #### B
QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full?
options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes
SOLUTION:1/20 - 1/40 = 1/40
40 minutes
Answer:C #### C
QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is?
options: A)36.7 B)36.1 C)36.5 D)36.9 E)36.3
SOLUTION:Correct sum
= (36 * 50 + 48 - 23)
= 1825.
Correct mean = 1825/50
= 36.5
Answer:C #### C
QUESTION:A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
options: A)6.4 days B)4.4 days C)5.4 days D)8.4 days E)2.4 days
SOLUTION:A
6.4 days
1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300
So, all three together will complete the work in 300/47 = 6.4 days.- #### A
QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph
SOLUTION:Speed downstream = 55 + 20
= 75 kmph
Speed upstream = 55 - 20
= 35 kmph
Answer: C #### C
QUESTION:90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?
options: A)125 B)150 C)225 D)250 E)500
SOLUTION:90 = (x/100)*(# boys)
# boys = .4x
substitute and solve:
90 = (x/100)*(.4x)
9000 = .4(x^2)
25000 = x^2
x=150
Answer: B #### B
QUESTION:If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers?
I. x
II. x + y
III. y/x
options: A)I only B)II only C)III only D)I and II E)I ,II and III
SOLUTION:Ans:
from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D). #### D
QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :
options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 5
SOLUTION:Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 495
99c - 99a = 99(c - a) = 495
495 = 99*5 = 99(c - a)
So c - a = 5
Answer (E) #### E
QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day.
options: A)20 B)10 C)25 D)15 E)24
SOLUTION:work completed in a day by one men = 1/25 = (1/5)*(1/5)
So it takes 25 men to complete this job = 25 * (1/25) = 1
Answer: C #### C
QUESTION:A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work ?
options: A)30 days B)15 days C)45 days D)24 days E)None of these
SOLUTION:Let C completes the work in x days.
Work done by (A + B) in 1 day = 1⁄10
Work done by (B + C) in 1 day = 1⁄18
A’s 5 days’ work + B’s 10 days’ work + C’s 15 days’work = 1
or (A + B)’s 5 days’ work + (B + C)’s 5 days’ work + C’s 10 days’ work = 1
or 5⁄10 + 5⁄18 + 10⁄x = 1 or x = 45 days
Answer C #### C
QUESTION:A sum is divided between A and B in the ratio of 1 : 2. A purchased a car from his part, which depreciates 14 2/7% per annum and B deposited his amount in a bank, which pays him 20% interest per annum compounded annually. By what percentage will the total sum of money increase after two years due to this investment pattern (approximately).
options: A)22.48% B)20.48% C)24.48% D)25.48% E)26.48%
SOLUTION:Let the total money=300
A's part=100
B's part=200
After 2 years A's part=73.46 (As it depreciates by 14.29% per annum)
After 2 years B's part=288 (using the compound interest formula, A=P(1+r/n)^nt), where
P=200,r=0.2,n=1,t=2)
So, After 2 years total amount=361.46
Therefore % increase in money=(361.46-300)*100/300=20.48%
ANSWER:B #### B
QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr?
options: A)4864 B)4854 C)4844 D)4868 E)4866
SOLUTION:p=1000000, r=4% annual , t=3 yr
SI = p*r*t/100 = 1000000*4*3/100 = 120000
CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864
difference = CI - SI = 124864 - 120000 = 4864
ANSWER:A #### A
QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true?
options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t
SOLUTION:the question asks could be!!!!
this means that if at least one option works, it is the answer.
3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C
QUESTION:The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
options: A)12 B)24 C)34 D)48 E)54
SOLUTION:Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.Answer: Option D #### D
QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
options: A)12 B)14 C)15 D)16 E)17
SOLUTION:d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 18
A #### A
QUESTION:A man can row upstream at 10 kmph and downstream at 20 kmph, and then find the speed of the man in still water?
options: A)11 B)77 C)25 D)88 E)34
SOLUTION:US = 20
DS = 30
M = (30 + 20)/2 = 25
Answer:C #### C
QUESTION:If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x?
I. 1/2x
II. -5/x
III. 4/x
options: A)II B)II and III C)I &II D)III E)IV
SOLUTION:x2y2 - xy = 20
x2y2-xy-20 = 0
(xy-4)(xy+5)=0
xy = 4 or xy=-5
y = 4/x or y = -5/x
II and III only
B #### B
QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
options: A)9 B)10 C)11 D)12 E)13
SOLUTION:35 + 30 + 20 = 85
This number includes some people counted twice and some people counted three times.
85 - 66 = 19, and this number represents people counted twice or three times.
8% of the people are counted two extra times.
The percentage of people counted one extra time is 19 - 8(2) = 3.
The percentage of people who liked more than one product is 8% + 3% = 11%.
The answer is C. #### C
QUESTION:If n = 2.0767 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n?
options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0047 E) 0.0033
SOLUTION:n*=2.08
n*-n=2.08-2.0767
0.0033
Answer: E #### E
QUESTION:If it is true that x > -3 and x < 7, which of the following must be true?
options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above.
SOLUTION:the range is -3 < x < 7
A. x > 3 - no because x can be between -3 < x < 3
B. x < -7 - no because the values of x are always >-7
C. x < 3 - no because x can be between 3 < x < 7
D. -7 < x < 3 - no because x can be between 3 < x < 7
E. none of the above.
Answer: E #### E
QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true?
options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6
SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) .
ans B #### B
QUESTION:If xy ≠ 0 and x^2y^2 − 2xy = 24, which of the following could be y in terms of x?
I. 6/x
II. -4/x
III. 1/x
options: A)I only B)II only C)I and II only D)I and III E)II and III
SOLUTION:(x^2)(y^2) –2xy - 24 = 0
(xy – 6)(xy + 4) = 0
xy – 6 = 0 or xy + 4 = 0
xy = 6 or xy = -4
Since we need y in terms of x, we can isolate y in both of our equations.
y = 6/x or y = -4/x
Answer: C #### C
QUESTION:Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
options: A)432 miles B)651 miles C)387 miles D)954 miles E)556 miles
SOLUTION:The number of miles to drive to finish his journey is given by
1200 - 768 = 432 miles
correct answer A #### A
QUESTION:How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 4?
options: A)a. 220 B)b. 249 C)c. 432 D)d. 216 E)e. 288
SOLUTION:Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120
Total Such cases = 120+15 = 135
Case 2: If unit digit is fixed as Five
With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]
With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12
With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40
With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60
Total Such cases = 2+12+40+60 = 114
Total numbers = 135+114 = 216
ANSWER OPTION D #### D
QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is
options: A)3 months B)4 months C)6 months D)8 months E)10 months
SOLUTION:Solution
S.I on Rs. 1600 = T.D on Rs. 1680.
Rs.1600 is the P.W of Rs.1680.
Rs.80 is S.I on Rs.1600 at 15%.
Time = (100x80 / 600x15)
= 1/3 year
= 4 months.
Answer B #### B
QUESTION:what is the radius of a circle that has a circumference of 3.14 meters?
options: A)0.5 mtr B)1.5 mtr C)2.3 mtr D)0.2 mtr E)1.2 mtr
SOLUTION:circumference of a cirlce = 2nr, given circumference= 3.14 mtr.
2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (A) #### A
QUESTION:Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern?
options: A)90 min B)100 min C)110 min D)120 min E)None
SOLUTION:Solution
Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75)
= (1/50 - 3/100)
= -1/100.
Therefore, the third pipe alone can empty the cistern in 100 min.
Answer C #### C
QUESTION:When 12 is divided by the positive integer k, the remainder is 7, for how many different values of k is this true?
options: A)2 B)3 C)4 D)7 E)8
SOLUTION:When 20 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2.
It also means that 18 is completely divisible by k.
Factors of 18 are 1, 2, 3, 6, 9, 18
Out of these, k can be 3, 6, 9 and 18.
Answer (C) #### C
QUESTION:The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is
options: A)3 B)5 C)6 D)8 E)9
SOLUTION:Sol.
By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6.
Answer C #### C
QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 9:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train?
options: A)12:30 B)1:00 C)1:30 D)2:00 E)2:30
SOLUTION:In thirty minutes the first train travels 35 km.
The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h.
The second train will catch the first train in 35/10 = 3.5 hours, so at 1:00 pm.
The answer is B. #### B
<<<Examples ends
QUESTION:If c is 14% of a and 40% of b, what percent of a is b?
options: A) 2.5% B) 15% C) 25% D) 35% E) 250%
SOLUTION:Answer = D
14a/100 = 40b/100
b = 14a/40 = 35a/100 = 35% #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)?
options: A)16 B)20 C)24 D)28 E)32
SOLUTION:The height:length ratio will be equal in both cases.
18 / 45 = x / 50
x = 20
The answer is B. #### B
QUESTION:Health insurance Plan Q requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
options: A)$600 B)$1000 C)$3800 D)$5300 E)$6200
SOLUTION:0.5 * 600 = 300 where Q = B #### B
QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C?
options: A)2250 B)3000 C)3018 D)3019 E)3012
SOLUTION:60*5:36*6:75*3
100: 72: 75
75/247 * 7410 = 2250
Answer: A #### A
QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result?
options: A)132 B)127 C)125 D)152 E)112
SOLUTION:C
125
96 passes out of 125 give an average of 76.8% #### C
QUESTION:In the quadratic equation ax2 - x - 12 = 0, if the sum of two roots is 1, what is the product of the two roots?
options: A)-12 B)-6 C)12 D)6 E)24
SOLUTION:Explanation:
The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 1 and c = -12.
we get, sum of the roots = 1 / a = 1
a = 1
Product of the roots = -12 / 1 =-12
ANSWER: A #### A
QUESTION:A shopkeeper sold an article for 240 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’?
options: A)25% B)50% C)23% D)28% E)None of these
SOLUTION:Cost price = 240×100/120= 200
S.P. at no discount = 240×100/80 = 300
∴ % profit = 100×100/200 = 50 %
Answer B #### B
QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)?
options: A)0 B)20 C)75 D)5 E)10
SOLUTION:Explanation :
Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0
Answer : A #### A
QUESTION:1.14 expressed as a per cent of 1.9 is:
options: A)6% B)10% C)60% D)90% E)None
SOLUTION:Solution: Required percentage = (1.14*100)/1.9 = 60%.
Answer: Option C #### C
QUESTION:The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 50% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 25% less than the number there from 10 a.m. to 11 a.m. If 75 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.?
options: A)10 B)20 C)30 D)40 E)50
SOLUTION:No of people from 10 - 11 is x
No of people from 11 - 12 is 3x/4
No of people from 12 to 1 is (3/2)(3x/4)
Given that 3x/4 + (3/2)(3x/4) = (3x/4)(5/2) = 75
Then x = 40
D #### D
QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest.
options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23
SOLUTION:R = 100 I / PT
=> R = (100 * 7200)/ (15000 * 5) = 9.6%
CI = P{ [1 + R /100]n - 1}
= 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24
Answer:D #### D
QUESTION:Which of the following fractions is the largest?
options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6
SOLUTION:L.C.M of 8, 16, 40 and 80 = 80.
7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80
Since, 70/80 > 63/80 > 65/80 > 62/80,
So, 7/8 > 63/80 > 13/16 > 31/40
So, 7/8 is the largest.
Answer: A #### A
QUESTION:A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 6 minutes. How much time will be take to cover a distance of 6 kilometres?
options: A)48 min. B)50 min. C)66 min. D)55 min. E)None of these
SOLUTION:Rest time = Number of rest × Time for each rest
= 5 × 6 = 30 minutes
Total time to cover 6 km
= (6â„10 × 60)minutes + 30 minutes = 66 minutes
Answer C #### C
QUESTION:A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight?
options: A)20 lb B)11 lb C)10 lb D)15 lb E)5 lb
SOLUTION:Sol.
66÷6 = 11.
Answer : B #### B
QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B?
options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these
SOLUTION:Explanation :
Assume that investment of C = x
Then, investment of A =2x
A receive 48000
Then C will receive = 48000/2 = 24000
And B receive = 180000 - (24000+48000) = 108000
Ratio of investment between A and B = 48000 : 108000 = 4 : 9
Answer : Option A #### A
QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255
options: A)11 B)8 C)27 D)63 E)127
SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong.
B #### B
QUESTION:A train leaves Delhi at 9 a.m. at a speed of 35 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
options: A)229 B)288 C)600 D)888 E)1400
SOLUTION:D = 35 * 5 = 175
RS = 40 – 35 = 5
T = 175/5 = 35
D = 40 * 35 = 1400 km
Answer: E #### E
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter
SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer:A #### A
QUESTION:Two trains of equal are running on parallel lines in the same direction at 44 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
options: A)40 m B)72 m C)80 m D)82 m E)84 m
SOLUTION:Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 44 - 36 = 8 km/hr.
= 8 * 5/18 = 20/9 m/sec.
2x/36 = 20/9 => x = 40.
ANSWER:A #### A
QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive?
options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000
SOLUTION:There are 5 people inheriting the money.
We have to take the total of the inheritance and divide it by 5 for each person receiving money.
$527,500 / 5 = $105,500.
Therefore the correct answer is D. #### D
QUESTION:One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card?
options: A)1/4 B)1/7 C)1/8 D)1/5 E)2/5
SOLUTION:Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = 12/48 = 1/4
A #### A
QUESTION:The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together?
options: A)26 years B)30years C)15years D)24years E)20years
SOLUTION:The required average = (125*23+162*25)/125+162 = 24 years
Answer is D #### D
QUESTION:What percent is 20% of 25%?
options: A)20% B)30% C)50% D)60% E)80%
SOLUTION:Required percentage = 20%/25% * 100 = 20/25 * 100 = 80%
Answer is E #### E
QUESTION:There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
options: A)90 B)120 C)315 D)180 E)200
SOLUTION:Number of ways of selecting 2 fiction books = 7C2
Number of ways of selecting 2 non fiction books = 6C2
7C2 * 6C2 = 21 * 15 = 315
Answer: C #### C
QUESTION:A basket has 6 apples and 6 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
options: A)1/2 B)1/3 C)1/4 D)2/5 E)3/10
SOLUTION:The total possible choices are 12C3 = 220
The ways to choose 3 apples: 6C3 = 20
The ways to choose 2 apples: 6C2 * 6C1 = 90
P(at least 2 apples) = 110/220 = 1/2
The answer is A. #### A
QUESTION:A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.
The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
options: A)981 B)1000 C)1011 D)1101 E)1110
SOLUTION:The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3
The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.=1000
Answer: B. #### B
QUESTION:Each child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total?
options: A)16 B)12 C)18 D)22 E)08
SOLUTION:2*8=16.Answer is A. #### A
QUESTION:A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
options: A)720 B)760 C)680 D)780 E)880
SOLUTION:On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is
10 x 9 x 8 = 720
ANSWER:A #### A
QUESTION:If Jane takes 12 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
options: A)xy/12 B)12x/(60y) C)60xy/12 D)xy/720 E)720x/y
SOLUTION:The answer is B.
She runs x yards in 12x/y seconds =12x/60y minutes. #### B
QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?
options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n
SOLUTION:C is the answer.
To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.
Given
- tank was already 1/3 full.
- When n ltr added, it became 5/9
So 1/3 + n = 5/9
n = 5/9 - 3/9
n = 2/9
capacity of the tank is full fraction . i.e. 1 i.e. 9/9
so the question is 9/9 is how much times n
= 9/9 = 1 = xn
so x = 9/2
and total = 9/2n #### C
QUESTION:If p/q = 5/4 , then 2p+q= ?
options: A)12 B)14 C)13 D)15 E)16
SOLUTION:let p=5, q=4 then 2*5+4=14
so 2p+q=14.
ANSWER:B #### B
QUESTION:The average successfull Search time for sequential search on n items is
options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1
SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison.
Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons.
Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons.
so we can write total search time will be: (1+2+3+........+n)
average search time will be (1+2+3+........+n)/n
NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2
ANSWER: C #### C
QUESTION:How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits?
options: A) 48 B) 52 C) 66 D) 68 E) 84
SOLUTION:Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
2 5 5
Number of possibilities = 3*4*4 = 48.
Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52.
Answer: B #### B
QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
options: A)2000 B)2200 C)3000 D)3400 E)3500
SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C #### C
QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is
options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above
SOLUTION:Let distance be D
10 = D/4 + D/6 Answer : D #### D
QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good.
options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980
SOLUTION:Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6400
1 = 6400/68.4
100 = (6400*100)/68.4 = Rs. 9357.
Answer: Option D #### D
QUESTION:A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used
options: A)12 months B)10 months C)14 months D)16 months E)None of these
SOLUTION:Explanation :
B received 2/3 of the profit
=> A : B = 1 : 2
Let the total capital = x
Then A's capital = x/4
B's capital = x – x/4 = 3x/4
Assume B's money was used for b months
Then A:B = (x/4)*15 : (3x/4)*b = 1 : 2
=> 15/4 : 3b/4 = 1 : 2
=> 15 : 3b = 1 : 2
=> 5 : b = 1 : 2
=> 5/b = 1/ 2
=> b = 5*2 = 10. Answer : Option B #### B
QUESTION:In the city of San Durango, 50 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 30 owned rabbits, and 20 owned exactly two of the three types of pet, how many people owned all three?
options: A)2 B)4 C)8 D)5 E)12
SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR
50 = 20 + 30 + 30 - (20) - 2x
x = 5
So, answer will be D #### D
QUESTION:A man can row his boat with the stream at 19 km/h and against the stream in 11 km/h. The man's rate is?
options: A)4 kmph B)2 kmph C)7 kmph D)8 kmph E)3 kmph
SOLUTION:DS = 19
US = 11
S = ?
S = (19 - 11)/2 = 4 kmph
Answer:A #### A
QUESTION:Which of the following is(are) true for a@b=b@a?
I. a@b=b+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ
SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A
QUESTION:On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled?
options: A)80 B)81 C)82 D)83 E)84
SOLUTION:Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 15 more transactions than Cal.
Jade = 66 + 15
= 81
Jade handled = 81 transactions.
Answer: B #### B
QUESTION:Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
options: A)16 sec B)13 sec C)17 sec D)21 sec E)23 sec
SOLUTION:Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 12 + 6 = 18 m/sec.
Required time = (120 + 120)/18 = 13 sec.
Answer: B #### B
QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
options: A)18% B)20% C)25% D)23% E)Cannot be determined
SOLUTION:Answer: C. #### C
QUESTION:During a trip on an expressway, Son drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
options: A)8.5% B)50% C)x/12% D)60/x% E)500/x%
SOLUTION:so Son drove (x-5) miles at 60mph and 5 miles at 30mph:
(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance
if the entire trip @60mph than time = x/60
so to get percent [(X+5)/60 ]/[x/60] x100
=(x+5)/x *100
=100+500/x
so increase of 500/x%[/u]=E #### E
QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone?
options: A)4 2/3 B)7 C)9 D)24 E)21
SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 6 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/7+6*1/x=1
5x+42=7x
2x=42
x=21 days.
Ans:E #### E
QUESTION:A company pays 20.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?
options: A)25 B)66 C)18 D)19 E)41
SOLUTION:Explanation:
Dividend on 1 share = (20.5 * 50)/100 = Rs.10.25
Rs.25 is income on an investment of Rs.100
Rs.10.25 is income on an investment of Rs. (10.25 * 100)/25 = Rs.41
ANSWER: E #### E
QUESTION:A train covers a distance in 50 min ,if it runs at a speed
of 48kmph on an average.The speed at which the train must run
to reduce the time of journey to 40min will be.
options: A)60kmph B)63kmph C)57kmph D)70kmph E)61kmph
SOLUTION:Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=40/60hr=2/3hr
New speed = 40* 3/2 kmph= 60kmph
Answer is A. #### A
QUESTION:The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :
options: A)144 m2 B)140 m2 C)108 m2 D)158 m2 E)None of these
SOLUTION:Area of the outer rectangle = 23 × 16 = 368 m2
Area of the inner rectangle = 19 × 12 = 228 m2
Required area = (368 – 228) = 140 m2
Answer B #### B
QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state?
options: A)8200 B)7500 C)7000 D)8000 E)8400
SOLUTION:Equal number of candidates appeared in each state.
In state A, 6% candidates got selected.
In state B, 7% candidates got selected.
Given that 80 more candidates got selected in state B than A.
Therefore, 1% of candidates appeared in each state =80
Answer: Option D
= 100% of candidates appeared in each state
=80×100=8000
i.e., number of candidates appeared from each state = 8000 #### D
QUESTION:By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
options: A)20 kmph B)30 kmph C)87 kmph D)99 kmph E)77 kmph
SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance
= 40 * 3x = 120x km
He covered 2/3 * 120x = 80x km in 1/3 * 3x
= x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed
= 40x/2x = 20 kmph.
Answer:A #### A
QUESTION:Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Let x be the number of shelves.
11x - 30 = 7(x-1) + 5
4x = 28
x = 7
The answer is C. #### C
QUESTION:There are three foam generators in the factory, each of the first two can generate 8 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
options: A)120. B)132. C)146. D)154. E)115
SOLUTION:Let the foam generators capacity be -
A = 8 lit/hr
B = 8 lit/hr
C = 18 lit/hr
Total foam generation in 1 hour will be 34 lit ( 8 + 8 + 18 ) ; since in 1 and 1/2 hr they will generate 34 + 17 => 51 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 8 lit/hr
C = 18 lit/hr
Total foam generation in 2 hour will be 52 litres {2 (8+18)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 8 => 12 litres
So, total foam generated will be 115 Litres ( 51 + 52 + 12 ) ; hence answer will be (E) #### E
QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use?
options: A)14 B)47 C)54 D)180 E)64
SOLUTION:Area = Length x Breadth
480 = 40 x Breadth
So, Breadth = 12 Units
Fencing required is -
Breadth + Breadth + Length
12 + 12 + 40 => 64 feet
Answer must be (E) 64 #### E
QUESTION:A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 63 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
options: A)2000 B)2100 C)2200 D)2300 E)2400
SOLUTION:1 percent for 3 years= 63
1 percent for 1 year = 21
=> 100 percent = 2100
ANSWER:B #### B
QUESTION:In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three?
options: A)5 B)7 C)9 D)11 E)13
SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR
40 = 20 + 30 + 10 - (10) - 2x
x = 5
So, answer will be A #### A
QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is:
options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62
SOLUTION:(3x-9):(5x-9) = 3:2
x = 1 => 3x = 3
Answer:A #### A
QUESTION:200 is what percent of 40?
.
options: A)0.2% B)2% C)5% D)20% E)500%
SOLUTION:200= x*40/100
x = 500%
Ans; E #### E
QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n?
options: A)-200 B)-130 C)-104 D)51 E)305
SOLUTION:2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:
-51 < c < 151
-51 < n < 151
-102 < c+n < 302.
Only option D is in this range.
Answer: D. #### D
QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?
options: A)10.5 B)15 C)15.5 D)30 E)60
SOLUTION:The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes
It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10
x=15.5 minutes
Answer: C #### C
QUESTION:Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
options: A)87 B)89 C)90 D)93 E)95
SOLUTION:Total score on 3 tests = 81*3 = 243
Jerry wants the average to be = 83
Hence total score on 4 tests should be = 83*4 = 332
Score required on the fourth test = 332 - 243 = 89
Option B #### B
QUESTION:Which of the following numbers is a perfect square?
options: A)1266 B)1444 C)2022 D)4034 E)8122
SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022.
38*38 = 1444
ANSWER:B #### B
QUESTION:Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 55
options: A)55 B)6 C)15 D)31 E)91
SOLUTION:1(result) + (1*1) = 2.
2(result) + (2*2) = 6.
6(result) + (3*3) = 15.
15(result) + (4*4) = 31.
31(result) + (5*5) = 56.
Now we are getting 56 not 55.. So 55 is the wrong number of the given.
answer : A #### A
QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip?
options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph
SOLUTION:So The Answer is Plainly A....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles
in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours
so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles
Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A
QUESTION:John found that the average of 15 numbers is 40. If 12 is added to each number then the mean of number is?
options: A)52 B)45 C)65 D)78 E)64
SOLUTION:(x+x1+...x14)/15 = 40
52
Option A #### A
QUESTION:f a < b < c , which of the following must be true?
(I) a < b^2
(II) b − a < c
(III) a^2 < b^2 < c^2
options: A)None B)I only C)II only D)III only E)II and III
SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: A. #### A
<<<Examples ends
QUESTION:A man divides $8600 Among 5 Sons, 4 Daughters and 1 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
options: A)A)$200 B)B)$1000 C)C)$819 D)D)$1200 E)E)$400
SOLUTION:Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 5*5X+4*4X+1*X=8600
25X+16X+X=8600
42X=8600, X=204.76.
Daughter receives four times of nephew so 4 * 204.76= 819.
So Each Daughter receives $800. answer is option C) $819. #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A straight pipe 5 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
options: A) 1/6 and 1/4 only B) 1/4 and 1/3 only C) 1/6, 1/4, and 1/3 D) 1/12, 1/6 and 1/4 E) 1/12, 1/6, and 1/3
SOLUTION:Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/4, 6-4=2=2/12=1/6meters long pieces.
Answer: A. #### A
QUESTION:Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day?
options: A)Rs. 120 B)Rs. 150 C)Rs. 250 D)Rs. 400 E)None of these
SOLUTION:Solution: Ratio of number of men, women and children,
= (18/6): (10/5):(12/3) = 3:2:4
Total (Men +Women +Children) = 18
3X +2X +4X = 18
9X = 18
X = 2
Hence, number of women = 2X = 2*2 = 4
Share of all women = (10*4000)/40 = Rs. 1000 [18+10+12 =40]
Thus, share of each woman = 1000/4 = Rs. 250.
Answer: Option C #### C
QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?
options: A)3 B)16 C)75 D)24 E)26
SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.
2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).
3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.
4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!
6) Answer choice E. #### E
QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches?
options: A)24 B)26 C)28 D)30 E)32
SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x
x=30
answer is D #### D
QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2
options: A)I only B)I,II only C)II only D)I,III only E)III only
SOLUTION:12=2*2*3
16=2*2*2*2
GCF =2*2=4
Answer : C #### C
QUESTION:3x^2 + 5x - 2 =
options: A)(3x-1)(x+2) B)(3x-4)(x+2) C)(3x-4)(x-2) D)(3x-2)(x+4) E)none of above
SOLUTION:3x^2 + 5x - 2
= 3x^2 + 6x - x - 2
= 3x (x + 2) - (x+2)
= (3x-1) (x+2)
Option A #### A
QUESTION:The workforce of Company Samsung is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers?
options: A)180 B)170 C)160 D)150 E)145
SOLUTION:let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added
06x/(0.4x +20) = 50/100 or 60x = 50*( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125
total worker = 125+20= 145
E #### E
QUESTION:Sum of the squares of three numbers is 363 and the sum of their products taken two at a time is 131. Find the sum?
options: A)20 B)22 C)25 D)27 E)29
SOLUTION:(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 363 + 2* 131
a + b + c = √625 = 25
C #### C
QUESTION:Find the odd man out. 18, 7, 12, 24, 48, 34, 46
options: A)16 B)46 C)24 D)11 E)7
SOLUTION:Explanation :
7 is the only odd number in the given series
Answer : Option E #### E
QUESTION:The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product
(n − 1)(n − 2)...3.2.1 is not divisible by n is
options: A)5 B)7 C)13 D)14 E)16
SOLUTION:Explanation :
(n-1)! is always divisible by n unless and untill n is a prime number
e.g.(5-1)!=4! which is not divisible by 5 bcuz 5 is a prime number
Therefore, find all prime numbers in the range of 12 to 40 i.e
13, 17, 19, 23, 29, 31 and 37
Hence, the number of positive integers n is 7.
Answer : B #### B
QUESTION:Solve for x: 2x – y = (3/4)x + 6.
options: A)(y + 6)/5 B)4(y + 6)/5 C)(y + 6) D)4(y - 6)/5 E)6(y-4)/5
SOLUTION:2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5
correct answer B #### B
QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price?
options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/-
SOLUTION:100 % ------> 400 (100 * 4 = 400)
140 % ------> 560 (140 * 4 = 560)
Selling price = Rs.560/-
A #### A
QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
.
options: A)Rs. 650 B)Rs. 690 C)Rs. 698 D)Rs. 700 E)Rs. 720
SOLUTION:S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698. Answer: Option C #### C
QUESTION:The ratio 25:50 expressed as percent equals to
options: A)50 % B)85 % C)25 % D)75 % E)None of above
SOLUTION:Explanation:
Actually it means 25 is what percent of 50, which can be calculated as,
(25/50)*100 = 25 * 2 = 50
Answer: Option A #### A
QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour?
options: A)181 B)211 C)241 D)271 E)301
SOLUTION:In 2/5 of an hour there are 24*60 = 1440 seconds
The number of 6-second intervals = 1440/6 = 240
After the first flash, there will be 240 more flashes for a total of 241.
The answer is C. #### C
QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
options: A)800 B)840 C)864 D)900 E)1,080
SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B
QUESTION:There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf?
options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5!
SOLUTION:There are 4 copies of 5 different pencils.20!/((4!)^5)
Answer - C #### C
QUESTION:For 15 people each has to pay Rs.20.For 20 people each has to pay Rs.18. For 40 people--how much has each to pay?
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:15-->20
20-->18
25-->16
30-->14
35-->12
40-->10
ANSWER:B #### B
QUESTION:John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish?
options: A) 24 B) 34.8 C) 37.8 D) 40 E) 84
SOLUTION:The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40.
Answer: D. #### D
QUESTION:Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time?
options: A)9 B)8 C)10 D)8.5 E)21
SOLUTION:63/3=21
Answer : E #### E
QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
options: A)508 B)500 C)800 D)570 E)503
SOLUTION:We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.
Answer:B #### B
QUESTION:Find all integers x NOT EQUAL TO 3 such that X-3|X^3-3
options: A)1,2,3,4,5 B)-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 C)1 D)6 E)-1,0,1
SOLUTION:Let x-3=t. Thus, t is an integer not equal to such'that t|(t+3)^2-3,
which is equivalent to the condition t|3^3-3, or t|24. Therefore, it is necessary
and sufficient for t to be an integer divisor of 24, hence t must be equal
to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x
= t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7,
9, 11, 15, and 27.
Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 #### B
QUESTION:Ram works in a bakery. He made cookies that cost $1.75 and made $325. How many customer did he have?
options: A)200 customers B)186 customers C)250 customers D)100customers E)170 customers
SOLUTION:A cookie costs $1.75 adding another one is $3.5. 325 divided by 3.5 is 92.86 x 2 is 186. He had 186 customers. The correct answer is B. #### B
QUESTION:Today is Monday.After 61 days,it will be
options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)None of these
SOLUTION:Solution
Each day of the week is repeated after 7 days
So,after 63 days,it will be Monday.
∴ After 61 days,it will be Saturday. Answer B #### B
QUESTION:A student committee on academic integrity has 42 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
options: A)7 B)8 C)9 D)10 E)11
SOLUTION:xC1 * (x-1)C1=42
x^2 -x -42 =0
(X-7 (X+6) = 0
X= 7 , -6
-6 can't possible.
Hence 7 should be the answer
A #### A
QUESTION:In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N?
options: A)(N-M) B)MN/(M + N) C)(NM) D)(N-M)/(M+N) E)NONE OF THESE
SOLUTION:The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N).
Answer: B #### B
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
options: A)120 metres B)180 metres C)324 metres D)150 metres E)180 metres
SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec.
Length of the train = (Speed x Time).
Length of the train = 50 x 9/3 m = 150 m.
ANSWER : OPTION D #### D
QUESTION:A car covers a distance of 1080 km in10 hrs. What is its speed in mps.
options: A)40 m/s B)25 m/s C)20 m/s D)15 m/s E)30 m/s
SOLUTION:Explanation:
Distance = Speed x Time
Speed = (1080/10) = 108 kmph
Spees in mps = 108 x 5/18 = 6 x 5 = 30 mps.
Answer: Option E #### E
QUESTION:What is the units digit of (12^3)(15^4)(31^7)?
options: A)0 B)2 C)4 D)6 E)8
SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8.
The units digit of 15^4 is the units digit of 5^4 which is 5.
The units digit of 31^7 is the units digit of 1^7 which is 1.
The units digit of 8*5*1 is 0.
The answer is A. #### A
QUESTION:1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
options: A)10.5 B)12.5 C)13.5 D)11.5 E)11
SOLUTION:1000*15 = 1200*x
x = 12.5
ANSWER B #### B
QUESTION:How many factors of 2475 are odd numbers greater than 1?
options: A)3 B)4 C)17 D)6 E)7
SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18
since we need odd divisors other than 1 =>18-1 = 17 odd divisors
C is the answer #### C
QUESTION:A man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack?
options: A)106 B)301 C)309 D)400 E)450
SOLUTION:Explanation:
Clearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (L.C.M of 3, 4, 5, 6) x + 1 i.e., (60x + 1 ) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So the number is 301.
Answer: B) 301 #### B
QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds?
options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these
SOLUTION:First cart speed will be 24/3=8
Second cart speed is 120/2=60
So, ratio is 8/60=2/15
ANSWER:A #### A
QUESTION:If m and n are positive integers, and m=2n and k=9m, then -
options: A)k is a factor of m. B)2m is a factor of k. C)3m is a factor of k/2. D)m/2 is a factor of k. E)k is a factor of m/2.
SOLUTION:m=2n --> m is even.
k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k.
Answer: D. #### D
QUESTION:What is the remainder when 3990990900032 is divided by 32 ?
options: A)0 B)8 C)4 D)2 E)3
SOLUTION:Though i was unaware of the divisibility test for 32 but i guessed the pattern!!
divisibility rule for 4- last two digits must be divisible by 4
divisibility rule for 8- last three digits must be divisible by 8
similarly, divisibility rule for 32 - last five digits must be divisible by 32
Hence, Ans A #### A
QUESTION:2+2^2+2^+......+2^9=?
options: A)2044 B)1022 C)1056 D)1065 E)None of them
SOLUTION:This is a G.P. in which a=2, r=2^2/2=2 and n=9
S^n=a(r^n -1)/(r-1)
=2x(2^9-1)/(2-1)
=2x(512-1)=2x511
=1022
Answer is B #### B
QUESTION:Simple interest on a certain sum at a certain annual rate of interest is 1/3 of the sum. If the numbers representing Time is three times the Rate percent , then the Rate is:
options: A)1 1/3 %. B)2 1/3 %. C)3 1/3 %. D)4 1/3 %. E)5 1/3 %.
SOLUTION:Explanation :
Let sum = x. Then, S.I. = x/3
Let N =3R
[x * 3R * R / 100] = x/3? R^2 = 100/9
R = 10/3 = 3 1/3%.
Hence, Rate = 3 1/3 %.
Answer : C #### C
QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he
can cover?
options: A)20km B)40km C)60km D)80km E)160km
SOLUTION:t=d/s, so
36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)
36=x(18/80)
x=160km
ANSWER:E #### E
QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 25 years and that for 40 years?
options: A)5:8 B)7:5 C)3:8 D)Data inadequate E)None of these
SOLUTION:Let the principal be P and rate of interest be R%.
∴ Required Ratio = [(P×R×25/100) /(P×R×40/100)]=25PR/40PR=25/40=5:8
Answer A #### A
QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions?
options: A)2112 m B)2704 m C)2278 m D)2288 m E)2378 m
SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions.
= 1500 * 2 * 22/7 * 22.4 = 211200 cm
= 2112 m
Answer: A #### A
QUESTION:What is greatest positive integer n such that 2^n is a factor of 12^11?
options: A)a)10 B)b)12 C)c)22 D)d)20 E)e)60
SOLUTION:The given number is 12^11
=(2*2*3)^11
=(2^22)*(3^11)
So the greatest possible value for n such that 2^n can be factor of given number is 22.
Answer C #### C
QUESTION:A cab driver 5 days income was $250, $400, $750, $400 , $500. Then his average income is?
options: A)$440 B)$450 C)$460 D)$470 E)$480
SOLUTION:avg = sum of observations/number of observations
avg income=(250+400+750+400+500)/5 = 460
Answer is C #### C
QUESTION:The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
options: A)72 B)83 C)45 D)53 E)64
SOLUTION:Sum of all the 13 numbers = 13 * 58 = 754
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 754 = 72.
Answer:A #### A
QUESTION:By selling an article at Rs.600, a profit of 30% is made. Find its cost price?
options: A)400 B)267 C)287 D)480 E)811
SOLUTION:SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+50)]
= 600 * [100/150] = Rs.400
Answer: A #### A
QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr.
SOLUTION:Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=24 or x=12.
Rate upstream=12 km/hr,rate downstream=36 km/hr.
Hence,rate of stream=1/2(36-12)km/hr=12 km/hr.
Answer is B. #### B
QUESTION:In a group of 70 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
options: A)1140 B)1160 C)1180 D)1200 E)1040
SOLUTION:Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 70 * 12 = 840.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 10 * 20 = 200.
Total number of sweets = 840 + 200 = 1040.
E) #### E
QUESTION:A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:
options: A)1.8h B)3h C)4h D)5h E)None of these
SOLUTION:Explanation:
Upstream speed = B-S
Downstream speed = B + s
B - S = 15/5 = 3 km/h
Again B = 4S
Therefore B - S = 3 = 3S
=> S = 1 and B = 4 km/h
Therefore B + S = 5km/h
Therefore, Time during downstream = 15/5 = 3h
Answer: B #### B
QUESTION:A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long?
options: A)17 B)18 C)19 D)20 E)21
SOLUTION:Speed = 99 * 5/18 = 55/2 m/sec
Total distance covered = 300 + 195 = 495 m
Required time = 495 * 2/55 = 18 sec
Answer: B #### B
QUESTION:One woman and one man can build a wall together in four hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them eight hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
options: A)5/7 B)1 C)10/7 D)12/7 E)24/7
SOLUTION:Solution:Let work done by man, women and girl per hour be m,w,g respectively.
Then, m+w = 1/4-->(1) , w + 2g = 1/4-->(2) and m + g =1/8-->(3).
No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g
From (1) and (2), m=2g and from (3) g=1/24,m=1/12 and w=1/6.
So, n = 1/(7/24) = 24/7
Option, E #### E
QUESTION:If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,711 minutes earlier? (Assume standard time in one location.)
options: A)6:22 B)6:24 C)6:27 D)6:36 E)6:32
SOLUTION:6:27minus 2,880,711in any way must end with 6, the only answer choice which ends with 6 is D.
Answer: D. #### D
QUESTION:A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident?
options: A)35 B)30 C)25 D)20 E)None of these
SOLUTION:Let the truth spoken by A and B be pl and p2
respectively, i.e., pl = 3⁄4 and p2 = 4⁄5
They will contradict each other only when one speaks truth and the other is lying.
i.e., 3⁄4 × 1⁄5 + 4⁄5 × 1⁄4 = 3⁄20 + 4⁄20 = 7⁄20 = 35⁄100 i.e, 35%
Answer A #### A
QUESTION:Find the greatest number of five digits to which if 7143 is added, the final number becomes exactly divisible by 18, 24, 30, 32 and 36.
options: A)22391 B)81111 C)27999 D)27711 E)99417
SOLUTION:LCM of 18, 24, 30, 32 and 36 is 1440. 99999 + 7143 = 107142. Dividing 107142 by 1440, the remainder is 582. ∴ Required number = 99999 – 582 = 99417 Alternate Method: Cross check with options.
Answer:E #### E
QUESTION:There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks?
options: A)5,15 B)4,15 C)5,10 D)4,10 E)5,20
SOLUTION:Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D #### D
QUESTION:Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive?
options: A)$444 B)$445 C)$446 D)$447 E)$448
SOLUTION:A+B+C = 1200
Given ratio 10:12:13
Let us say the shares of A,B,C deducting 10,20,15 be a,b,c
a+b+c = 1200-45= 1155 = 35K
c share = (1155X13)/35 = 429
C = chandran share = 429+15 = 444
Option A #### A
QUESTION:A certain quantity of 45% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
options: A)1/4 B)1/3 C)1/2 D)2/3 E)3/4
SOLUTION:Let's say that the total original mixture A is 100 ml
The original mixture A thus has 45 ml of alcohol out of 100 ml of solution
You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 45 ml and 25 ml is 20 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 20%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 10%. Therefore, 10 out of 20 is 1/2 and C is the answer. #### C
QUESTION:The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago?
options: A)1: 3 B)2: 3 C)3:3 D)4: 3 E)5: 4
SOLUTION:3x-25/2x-25 = 4/3
Therefore x=-25
Age cannot be negative.
Answer: D #### D
QUESTION:In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
options: A)-4/3 B)1/4 C)-4 D)3/4 E)4/3
SOLUTION:The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A. #### A
QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11
SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10
Answer: D #### D
QUESTION:A shopkeeper sold an article at $100 with 30% profit. Then find its cost price?
options: A)$120 B)$100 C)$91 D)$77 E)$69
SOLUTION:cost price = selling price *100/(100+profit)
C.P. = 100*100/130 = $77(approximately)
Answer is D #### D
QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere?
options: A) 6/π B) 9/π C) 6 D) 9 E) 12
SOLUTION:Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4*PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !! #### D
QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
options: A)270 B)252 C)272 D)292 E)285
SOLUTION:number of astronauts with previous experience = 7
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group
(7C1)*(9C2)
=7*36= 252
Answer : B #### B
QUESTION:find value for x from below equation? x + 1 = 3
options: A)-5 B)-4 C)4 D)3 E)2
SOLUTION:1. Subtract 1 from both sides:
x + 1 - 1 = 3 - 1
2. Simplify both sides:
x = 2
E #### E
QUESTION:There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems
options: A)36 minutes B)60 minutes C)72 minutes D)100 minutes E)None of these
SOLUTION:Explanation :
Let x = minutes spent on a non-math problem
then 2x = minutes spent on a math problem
x(200-50) + 2x(50) = 180
x(150) + 2x(50) = 180
150x + 100x = 180
250x = 180
x = 0.72 minutes
Time to spend on math problems:
2x(50)=100x = 100(0.72) = 72 minutes
Answer : C #### C
QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola
y = x2 + x + 4 at exactly one point. Compute the intersection point.
options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10)
SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution
in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4.
Therefore, k = -3 or k = 5.
Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection
point is (2, 10) .
correct answer A #### A
<<<Examples ends
QUESTION:A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food.
options: A)$400 B)$1400 C)$3400 D)$2400 E)$4400
SOLUTION:Part of salary left =1-(2/5+3/10+1/8)
=7/40
Let the monthly salary be $x
Then (7/40) of x=1400
X=8000
Expenditure on food=$2400
Option D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If
BAT = 58
HAT = 52
CAT = 57
then
whats RAT = ?
options: A)42 B)45 C)34 D)76 E)25
SOLUTION:A
42 #### A
QUESTION:The average (arithmetic mean) of four numbers is 5x + 3. If one of the numbers is 2x, what is the average of the other three numbers?
options: A)x + 1 B)3x + 3 C)4x + 1 D)5x + 3 E)6x + 4
SOLUTION:The sum of all four numbers is 4 * (5x + 3) = 20x + 12.
If one of the numbers is 2x, the sum of the other 3 numbers is 18x+12.
The average of the remaining three numbers is (18x+12)/3 = 6x+4.
The answer is E. #### E
QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:Solution
Start with 11 coins.
Sharon takes 3 coins from you: 11 - 3 = 8 coins.
Steven takes 4 coins from you: 8 - 4 = 4 coins.
So you have 4 at the end.
Correct answer : C #### C
QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 10 years?
options: A)3 : 2 B)1 : 3 C)2 : 3 D)1 : 5 E)2 : 1
SOLUTION:Explanation :
Simple Interest = PRT/100
Here Principal(P) and Rate of Interest (R) are constants
Hence, Simple Interest ∝ T
Required Ratio = Simple Interest for 2 years/Simple Interest for 10 years
=T1/T2
=2/10
=1/5
=1:5
Answer : Option D #### D
QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P?
options: A)20% B)40% C)50% D)60% E)80%
SOLUTION:65% is 15%-points below 80% and 10%-points above 55%.
So the ratio of solution P to solution Q is 2:3.
Mixture P is 2/5 = 40% of the volume of mixture PQ.
The answer is B. #### B
QUESTION:Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36,
find P (E|F) and P(F|E)
options: A)5 B)8 C)2 D)6 E)12
SOLUTION:Here, E and F are events
P(E|F) = P(EnF)/P(F) = 36/36 = 1
P(F|E) = P(EnF)/P(E) = 36/24 = 2.
C) #### C
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train?
options: A)500 m B)620 m C)872 m D)150 m E)765 m
SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 30) m
= 500 m.
Answer: A #### A
QUESTION:The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %?
options: A)18% B)20.5% C)30% D)45% E)12%
SOLUTION:1800 ---- 370
100 ---- ? => 20.5%
Answer:B #### B
QUESTION:A man starts walking at 3 pm . he walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way?
options: A)12 B)66 C)77 D)88 E)91
SOLUTION:lets us consider t1 = time taken on level road. t2 = uphill. t3 = down hill; the distance traveled uphill and down hill same so t2*3 = 6*t3; => t2 = 2t3;---> (1) total time = 2*t1 + t2 + t3 = 6 hours ---> (2) 2t1+3t3 = 6 -->(3) total distance = 2*(4t1) + 3*t2+ 6*t3 ---> (4) substitute (1) in (4) 8t1 + 12t3 => 4(2t1+3t3) then from (3) the total distance will become 4*6= 24 => one way distance = 12km
Answer: A #### A
QUESTION:A 470 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
options: A)41.1 sec B)64.8 sec C)31.8 sec D)50.4 sec E)none of the above
SOLUTION:Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 470 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 990 m
Time = Distance / Speed
= 990 x 18 / (5 x 55)
= 64.8 sec
Ans is :B #### B
QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true?
I. h = y
II. y = 1
III. h and y are prime integers.
options: A) None B) I only C) II only D) III only E) I and II
SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2).
I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2);
II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2);
III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2).
Answer: A. #### A
QUESTION:What proximate value should come in place of the question mark (?) in the following question?
6.795 × 1084 + 2568.34 – 1708.34 = ?
options: A)6,000 B)12,000 C)10,340 D)8,204 E)9,000
SOLUTION:? ≈ 6.8 × 1080 + 2560 – 1700 ≈ 7344 + 860 ≈ 8204
Answer D #### D
QUESTION:21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
options: A)7/41 B)3/41 C)9/42 D)4/51 E)5/13
SOLUTION:The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C #### C
QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c?
options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12
SOLUTION:6a/100 = 12
a = 200
12b/100 = 6
b = 50
c = b/a = 50 / 200 = 1/4
The answer is C. #### C
QUESTION:Convert 2/5 to a decimal
options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5
SOLUTION:Divide 2 by 5: 2 / 5 = 0.4
Answer: 2/5 = 0.4 (D) #### D
QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
options: A)13.5 B)14 C)15 D)12.5 E)None
SOLUTION:Solution:
At present the total age of the family = 5*20 =100.
The total age of the family at the time of the birth of the youngest member,
=[100−10−(10*4)]=50.
Therefore, average age of the family at the time of birth of the youngest member,
= 50/4 = 12.5.
Answer: Option D #### D
QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have?
options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these
SOLUTION:Explanatory Answer
Step 1: Compute sum of all interior and exterior angles
The sum of an exterior angle and an interior angle of a polygon = 180o.
The sum of all the exterior angles of a polygon = 360o.
From the question stem: sum of all interior angles of the given polygon = 1440o.
Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o.
Step 2: Compute number of sides
If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o.
Therefore, n = 10.
Alternative Approach : Using formula
Sum of all interior angles of a convex polygon = (n - 2)* 180
So, (n - 2) * 180 = 1440
n - 2 = 8
n = 10
Choice A #### A
QUESTION:A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
options: A)287 B)27 C)28 D)25 E)28
SOLUTION:[50/x + 50/(x/2)] – 100/x = 2
x = 25
Answer: D #### D
QUESTION:How many numbers from 10 to 1000 are exactly divisible by 9?
options: A)100 B)10 C)11 D)12 E)14
SOLUTION:10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100
Answer : A #### A
QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed?
options: A)104 B)190 C)109 D)278 E)211
SOLUTION:Explanation:
624/6 = 104 kmph
Answer:C #### C
QUESTION:How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible?
options: A)4C3+4 B)4C3+9 C)4C3+2 D)4C3 E)4C3+6
SOLUTION:So 4C3 for abcd - 4 choices
3 more for dd(b,c or a)
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 4C3+9
Ans : B #### B
QUESTION:How many quarters are equal to 4 dollars?
options: A)16 B)8 C)12 D)9 E)7
SOLUTION:4*4 = 16 quarters
Answer : A #### A
QUESTION:The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is
options: A)3 B)5 C)6 D)8 E)9
SOLUTION:Sol.
By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6.
Answer C #### C
QUESTION:If 40% of a number is 16, then the number is
options: A)number is 60 B)number is 70 C)number is 90 D)number is 40 E)None of these
SOLUTION:Solution:
Let "a" be the number we seek. We get
40% × a = 16
2 × 40% × a = 2 × 16 = 32
80% × a = 32
10% × a = 32 : 8 = 4
100% × a = 4 × 10 = 40
a = 40
Answer D #### D
QUESTION:If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle.
options: A)127 cm^2 B)125 cm^2 C)120 cm^2 D)102 cm^2 E)None of them
SOLUTION:Let length = x and breadth = y. Then,
2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289.
Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120
Area = xy = 120 cm^2
Answer is C. #### C
QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km
SOLUTION:Explanation:
Speed in still water = 6 kmph
Speed of the current = 1 kmph
Speed downstream = (6+1) = 7 kmph
Speed upstream = (6-1) = 5 kmph
Let the required distance be x km
Total time taken = 1 hour
⇒ x/7+x/5=1
⇒5x+7x=35
⇒12x=35
⇒x=2.9 km
Answer: Option C #### C
QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss?
options: A)25 % B)50 % C)75 % D)85 % E)None of these
SOLUTION:Explanation :
Let the original expenditure = Rs. 100.
New final expenditure = 150% of (50% of Rs. 100)
= Rs.(150/10050/100100)
= Rs. 75.
Decrease = 100- 75 = 25 %
Answer : A #### A
QUESTION:An old priest fell on a bottom of the well of a church.
The well is 16 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
options: A)12-days B)14-days C)11-days D)19-days E)10-days
SOLUTION:A
12-days
In 11-days, he will climb 11-inch and when he climbs 5 inch more, he will be out of the well :-) #### A
QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50
SOLUTION:Others equal 5650.
Answer D #### D
QUESTION:There are two inlets and one outlet to a cistern. One of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
options: A)2 hours B)2.5 hours C)3 hours D)3.5 hours E)8 hours
SOLUTION:The combined inflow rate of the two inlets is 1/4 + 1/8 = 3/8 cistern/hour. Thus, working together, it takes 8/3 hours (time is reciprocal of rate) to fill the cistern.
From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) =2*3/8 = 3/4 th of the cistern .
Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour.
Letting x to be the rate of the outlet, we would have: 3/8 - x = 1/4 --> x = 1/8 cistern/hour, which means that it takes 8 hours the outlet working alone to empty the cistern.
Answer: E. #### E
QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph.
SOLUTION:DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A #### A
QUESTION:If y exceeds x by 22%, then x is less than y by?
options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3%
SOLUTION:X=100 y=122
122------22
100-------? => 18 2/61%
Answer:C #### C
QUESTION:Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
options: A)6 B)7 C)8 D)10 E)11
SOLUTION:It's a simple geometry problem. Look at the diagram below:
Answer: E. #### E
QUESTION:Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?
options: A) $24 million B) $120 million C) $144 million D) $240 million E) $888 million
SOLUTION:Convert units to millions as answer is in millions
1996 Imports = $1.44 bill = $1440 mill
i.e. 1440/12 = $120 mill/month
1997 Imports = $388 mill/2 month
i.e. $194 mill/month
Difference/month = 194-120 = 74
Difference/year = $74 mill * 12 = $988 mill
ANSWER: E #### E
QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24?
options: A)101 B)187 C)191 D)201 E)287
SOLUTION:here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 24 = t 3 + 3 + 4 + 5 + 6....+ 23
the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 23 sequence is equal to n*(n+1)/2 with n being 23, so equal to 23 * 24 / 2 = 276
so :
t 20 = t 3 + 276 - 3
t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E
QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
6 – 9 + 8 × 3 ÷ 15 =
options: A)6 B)10 C)12 D)-2 E)15
SOLUTION:E 15 #### E
QUESTION:You roll two six sided dices together.
Can you calculate the probability that the first dice gives the number 2 while the second dice gives the number 5?
options: A)2/23 B)1/33 C)1/36 D)3/54 E)6/35
SOLUTION:C
1/36
The number of possibilities for the first as well as the second dice are 6 and 6 respectively. Therefore the total possibilities or outcome are 6 * 6 = 36.
Out of 36 outcomes, we need only one case i.e. the first gives 2 and the second gives 5.
Therefore, the probability will be 1 on 36 or 1/36. #### C
QUESTION:Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10?
options: A)2140 B)2520 C)2980 D)3260 E)3680
SOLUTION:The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520
The answer is B. #### B
QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
options: A)2007 B)2008 C)2002 D)2000 E)2001
SOLUTION:(10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: D #### D
QUESTION:The sum of money will be double itself in 30years and simple interest find rate of interest?
options: A)A)2.33% B)B)3.33% C)C)4.33% D)D)5.33% E)E)6.33%
SOLUTION:T = 30 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/30x =3.33%
Answer is B #### B
QUESTION:A and B invests Rs.4000 and Rs.6000 in a business. After 4 months, A withdraws three-fourth of his capital and 4 months later, B withdraws half of his capital. In what ratio should they share the profits at the end of the year?
options: A)2:5 B)3:5 C)4:5 D)3:7 E)5:7
SOLUTION:A : B
(4000*4)+(1000*8) : (6000*8)+(3000*4)
24000 : 60000
2 : 5
Answer: A #### A
QUESTION:A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
options: A)8 B)9 C)4 D)18 E)None
SOLUTION:Ratio of rates of working of A and B = 2 : 1
So, ratio of times taken = 1 : 2
B's 1 day's work = 1/12
Therefore A's 1 day's work = 1/6
(A + B)'s 1 day's work = (1/6 + 1/12)= 1/4
So, A and B together can finish the work in 4 days.
Answer: C #### C
QUESTION:Andrew started saving at the beginning of the year and had saved $180 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
options: A)11% B)25% C)44% D)56% E)100%
SOLUTION:Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 540
Saving in 2nd year + 180 = 540
Saving in 2nd year = 540 - 180 = 360
Change in Value = 360 - 180 = 180
Original Value = 180
Percentage Increase = (180 / 180 ) * 100 = 100%..... Answer E...... #### E
QUESTION:Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these
SOLUTION:Explanation:
Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260
Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260
Therefore, Total amount = Rs.260+Rs.260 = Rs.520.
Answer: Option A #### A
QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
options: A)24 B)21 C)20 D)17 E)15
SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E
QUESTION:A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
options: A)4/19 B)7/19 C)12/19 D)21/99 E)26/77
SOLUTION:Solution
P( None is defective)
= 18C2 / 22C2
= 51/77
P( at least one is defective)
= (1- 51/77)
= 26/77.
Answer E #### E
QUESTION:Two pipes P and Q can fill a cistern in 12 and 13 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
options: A)1/8 B)1/4 C)2/4 D)1/4 E)3/4
SOLUTION:3/12 + x/13
= 1
x= 7 3/4
Answer: E #### E
QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years.
options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these
SOLUTION:Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗4/100) /(P∗R∗12/100)]
=4PR /12PR=1:3
Option C #### C
QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
options: A)22 B)80 C)40 D)77 E)12
SOLUTION:800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C #### C
QUESTION:If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite?
options: A)x^2 B)x^2 – y^2 C)y^2 D)(y + x)^2 E)(x – y)^2
SOLUTION:(y^2 − xy)/x=y-x
=> y^2 − xy = xy -x^2
=> x^2 - 2xy + y^2 = 0
=> (x-y)^2 = 0
Answer E #### E
QUESTION:A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
options: A)102 B)60 C)75 D)90 E)95
SOLUTION:Let number of notes of each denomination be x.
Then x + 5x + 10x = 544
16x = 544
x = 34.
Hence, total number of notes = 3x = 102
Answer: Option A #### A
QUESTION:At 12:10 o'clock Bill leaves point A towards point B at a speed of 30 Km/h. At 13:40 o'clock Richi leaves from the same point towards point B also, but at a speed of 60 Km/h. At what time will Richi passes over Bill?
options: A)14:40. B)15:10. C)16:10 D)15:40 E)15:30
SOLUTION:Distance travelled by Bill in 1hr 30min ( 12:10 to 13:40) = 30kmph*(90/60)hr = 45km
Relative speed = Richi's speed ~ Bill's speed = 30kmph
Time taken by Richi to cross Bill = 45/30 = 1.5 hrs
Time at which Richi will cross Bill = 13:40 + 1:30 = 14:70 = 15:10 hrs
Ans. B #### B
QUESTION:The watch store down the street from Wendy's house has 2 leather watches, 1 gold watch, and 1 silver watch. How many watches does the store have in all?
options: A)10 B)19 C)04 D)12 E)07
SOLUTION:Add the numbers of watches.
2 + 1 + 1 =4.
Answer is C. #### C
QUESTION:A train 120 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
options: A)11 s B)10 s C)8 s D)12 s E)None of these
SOLUTION:We know from the formula Time = Distance/ Speed
Thus, Time = 120/ 54 x 5/18
or, Time = 8 sec.
ANSWER:C #### C
QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0
options: A)-1 B)1 C)2 D)3 E)4
SOLUTION:a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A #### A
QUESTION:In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ?
options: A)13/40 B)13/80 C)2/13 D)Data inadequate E)None
SOLUTION:Answer
Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp.
∴ 2/13 of total number of students took part in the camp.
Correct Option: C #### C
QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt?
options: A)16.67 B)30 C)50 D)60.33 E)150
SOLUTION:let x=ounces of 60% salt solution to be added
.2*50+.6x=.5(50+x)
x=150
Answer E #### E
QUESTION:Find the average of first 4 multiples of 11?
options: A)10 B)12.6 C)27.5 D)31.3 E)40.8
SOLUTION:average = (11+22+33+44)/4 = 27.5
Answer is C #### C
QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
options: A)8 B)twelve (12) C)14 D)16 E)18
SOLUTION:Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B #### B
QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
options: A)4 B)16 C)25 D)36 E)100
SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number.
The answer is C. #### C
QUESTION:If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I. x > y> z
II. x = z
III. x > y
options: A)I and II B)I only C)II only D)III only E)None
SOLUTION:3x-3y=-3z
x-y=-z
Since z<0; -z>0
x-y>0
x>y
III correct.
We can't say much about z though;
x=-5; y=-100; z=-95
I and II incorrect.
Ans:D #### D
QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?
options: A)Rs. 120,002 B)Rs. 1,20,000 C)Rs. 1,20,00 D)Rs. 1,20,028 E)Rs. 1,20,011
SOLUTION:Explanation:
The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000
Answer: B #### B
QUESTION:If the average (arithmetic mean) of x + 2, x + 3, and x + 4 is 0, then x =
options: A)–4 B)–3 C)–2 D)–1 E)0
SOLUTION:(x+2 + x+3 + x+4)/3 = 0
=>3x + 9 = 0
=>x = -3
Answer B #### B
QUESTION:Find the invalid no.from the following series 15 46 63 71 75 77 78
options: A)32 B)35 C)46 D)49 E)67
SOLUTION:In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
46
C #### C
<<<Examples ends
QUESTION:A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5
SOLUTION:The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 4/16 = 1/4.
The answer is B. #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92
SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9
Answer: C. #### C
QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her
options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger
SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1997 has to be the ring finger
Answer is (D) #### D
QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
options: A)2777 B)2999 C)2799 D)2781 E)10500
SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7 = Rs. 10500.Answer: E #### E
QUESTION:A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5760. What is the average monthly balance maintained by John in his
account during the year?
options: A) 2840 B) 28800 C) 6840 D) 7540 E) 28400
SOLUTION:bank balance is doubled with accumulation of interest tp 5760..
this means INTEREST is 5760/2=2880 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 28800..
B #### B
QUESTION:9log9(5) = ?
options: A)1 B)2 C)3 D)5 E)8
SOLUTION:Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
9log9(5) = 5
correct answer D #### D
QUESTION:A started a business with 4500 and another person B joined after some period with 3000. Determine this period after B joined the business if the profit at the end of the year is divided in the ratio 2 : 1
options: A)After 3 months B)After 4 months C)After 6 months D)After 2 1⁄2 months E)None of these
SOLUTION:Let B joined after x months.
Then, 4500 × 12 : 3000 (12 – x) = 2 : 1
Ratio of their investments
4500×12/3000(12−x)=2/1 ⇒ x = 3
Answer A #### A
QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres
SOLUTION:I guess it should be
the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C) #### C
QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?
options: A)57% B)60% C)58% D)50% E)20%
SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years
=> C.I - S.I
=> 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100
=> 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5
=> 16r/100 + 8r2/(100)2 = 20r/100
=> 4r/10 = 8r2/(100)2
=> 8[r/100]2 - 4r/100 = 0
=> r/100 {8r/100 -4} = 0
=> r = 0% of 50%
Since r!= 0%, r =50%
Answer:D #### D
QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are
options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44
SOLUTION:A
11, 42
Let the age of Priya = x years
Then, the age of her father = (x+ 31) years
ATQ,
(x+ 8) + (x+ 31 + 8) = 69
2x+ 47 = 69
2x= 69 – 47 = 22
x= 11
The age of Priya = 11 years
The age of her father = 11 + 31 = 42 years #### A
QUESTION:If
1 = 3
2 = 6
3 = 9
4 = 12
5 = 15
Then 9 = ?
Hint: Its a logic Riddle not a mathematical riddle
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:C
3
As stated
3=9 => 9=3
Answer is C #### C
QUESTION:One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish.
options: A)10 B)11 C)12 D)13 E)14
SOLUTION:Fast's 1 hr work = 1/2
slow's 1 hr work = 1/3
1/2 + 1/3 = 5/6
they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins
ANSWER:C #### C
QUESTION:I. m-14, m, m, m, m+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c
The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?
options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I
SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end.
A. #### A
QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
options: A)80% B)105% C)120% D)124.2% E)138%
SOLUTION:x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,15 = 15/100
x= 80*15/100
x= 12
12/10 = 1,2 = 120%, Answer C #### C
QUESTION:A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the president?
options: A) 1/720 B) 1/5 C) 1/10 D) 1/9 E) 1/6
SOLUTION:This question is much easier than it appears.
Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the president is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the president is 1/10+1/10=2/10.
Answer: B #### B
QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?
options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10
SOLUTION:(p-2)(p-4) = q
p = 3 for this to be true, so
1/10
Ans :B #### B
QUESTION:A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
options: A)3 B)4 C)5 D)8 E)9
SOLUTION:Explanation:
50 + 25 = 75/15 = 5 (Remainder)
C #### C
QUESTION:A dishonest dealer professes to sell his goods at Cost Price but still gets 30% profit by using a false weight. What weight does he substitute for a kilogram?
options: A)769 1/7 grams B)769 3/13 grams C)769 8/3 grams D)769 1/3 grams E)769 1/13 grams
SOLUTION:If the cost price is Rs.100, then to get a profit of 30%, the selling price should be Rs.130.
If 130kg are to be sold, and the dealer gives only 100kg, to get a profit of 30%.
How many grams he has to give instead of one kilogram(1000 gm).
130 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/130 = 769 3/13 grams.
Answer:B #### B
QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
options: A)42 6/9% B)42 3/7% C)42 7/7% D)42 6/7% E)22 6/7%
SOLUTION:SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D #### D
QUESTION:If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number?
options: A)20 B)22 C)27 D)28 E)30
SOLUTION:Given Ratio => 2:3
2x - 10 : 3x - 10 = 2 : 4
4[2x - 10] = 2[3x - 10]
8x - 40 = 6x - 20
8x - 6x = 40 - 20
x = 10
Then biggest number is = 3x
3x = 30
Ans = E #### E
QUESTION:In the formula V = 1/(4r)^2, if r is halved, then V is multiplied by
options: A)64 B)8 C)4 D)64 E)1/64
SOLUTION:Say r=2 => V1 = 1/64
when r=1; V2 = 1/16
V2 = 4*V1.
Answer=C=4 #### C
QUESTION:If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K?
options: A)30 B)4 C)5 D)66 E)All of these
SOLUTION:The first term divisible by 3, so any term could be the third term.
Answer =(E) #### E
QUESTION:A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.
The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
options: A)981 B)1000 C)1011 D)1101 E)1110
SOLUTION:The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3
The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.=1000
Answer: B. #### B
QUESTION:In the xy-plane, line k passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line k?
options: A)3x+2y-5=0 B)3x+2y+5=0 C)2x-3y-12=0 D)2x+3y=0 E)4x+3y-6=0
SOLUTION:If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line k should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A. #### A
QUESTION:What is x if x + 3y = 33 and y = 10?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:Substitute y by 10 in x + 3y = 33
x + 3(10) = 33
x + 30 = 33
If we substitute x by 3 in x + 30 = 33, we have 3 + 30 = 33. Hence
x = 3 correct answer C #### C
QUESTION:Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
options: A)65 B)69 C)72 D)75 E)NOne
SOLUTION:Sol.
Average
= 66 + 65 + 77 + 62 + 75 / 5)
= (345 / 5)
= 69.
Answer B #### B
QUESTION:131,95,70,54, ?
options: A)42 B)45 C)44 D)40 E)39
SOLUTION:131 - 95 = 36 = 6^2
95 - 70 = 25 = 5^2
70 - 54 = 16 = 4^2
so we can write
54 - x = 09 = 3^2 , where x is the next number
x = 54 - 9 = 45
so the next number will be 45
ANSWER:B #### B
QUESTION:Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
options: A)17603 B)17608 C)17628 D)17600 E)176023
SOLUTION:Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375
= Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100
= Rs. 17600
Answer: D #### D
QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2
SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer: B #### B
QUESTION:Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes.
How much time will it take Roy to consume all the five tablets?
options: A)60 min B)50 min C)70 min D)65 min E)80 min
SOLUTION:A
60 min
Roy will be able to consume all the five tablets in an hour.
Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min. #### A
QUESTION:Let N = 18p, where p is a prime number greater than 2. How many odd numbers divide N?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:We start by factoring 18. 18 = 2*9 = 6*3 = 2*3*3. Since p is a prime number greater than 2 it must be odd. Therefore 3, 9, and p are the odd numbers that divide N. There are three odd divisors and the answer is therefore C. #### C
QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount?
options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these
SOLUTION:Explanation :
F = Rs. 2360
TD = Rs. 360
PW = F - TD = 2360 - 360 = Rs. 2000
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 2000 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2360 for unexpired time
=360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B
QUESTION:Sixty percent of a number is 21 less than four fifth of that number. What is the number ?
options: A)240 B)140 C)230 D)130 E)105
SOLUTION:Let the number be x.
Then, 4*x/5 –(60% of x) = 21
4x/5 – 60x/100 = 21
x = 105.
Answer E. #### E
QUESTION:A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
options: A)Rs. 64 B)Rs. 69 C)Rs.72 D)Rs.75 E)Rs.90
SOLUTION:C.P. = Rs. (100/122.5)x392
= Rs. (1000/1225)x392
= Rs. 320
Profit = Rs. (392 - 320) = Rs. 72.
Answer:C #### C
QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 40 miles per gallon, and from Town B to Town C, the car averaged 50 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
options: A)42.85 B)40 C)35 D)41 E)39
SOLUTION:step 1) took LCM of 40 and 50.. came as 200.
step 2) 200 distance between B to C... do 200/50 hence 4 gallons used
step 3) twice distance.. hence 200*2= 400... do as above.. 400/40= 10 gallons used
step 4) total gallons.. 4+10= 14 gallons
step ) total miles= 200+400= 600 miles
hence.. average of whole journey = 600/14 which comes to 42.85
Answer : A #### A
QUESTION:What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive?
options: A)90 B)80 C)100 D)105 E)110
SOLUTION:10 and 190 inclusive would mean there are 17 terms.
No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170
The middle term is the average which is the tenth term = 80
B is the answer. #### B
QUESTION:Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $3 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?
options: A)9% B)56.6% C)11% D)12% E)15%
SOLUTION:You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So
3(15) = 45 - Fox
2(18) = 36 - Pony
The total discount discount is $3 and you are asked to find the percent discount of pony jeans,
so 45(18 - X)/100 + 36(X)/100 = 3 or 45*18 -45*x + 36*x =3*100 or 9x = -3*100 +45*18
x= 510/9 = 56.6%
B #### B
QUESTION:How many pieces of 0.85 metres can be cut from a rod 42.5 metres long?
options: A)30 B)40 C)50 D)60 E)70
SOLUTION:Number of pieces = 42.5/0.85
= 42.50/0.85
= 4250/85
= 50.
ANSWER:C #### C
QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
options: A)5 B)8 C)9 D)10 E)11
SOLUTION:Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5
Option A #### A
QUESTION:Find the invalid no.from the following series 15 46 63 71 75 77 78
options: A)32 B)35 C)46 D)49 E)67
SOLUTION:In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
46
C #### C
QUESTION:How many even multiples of 55 are there between 549 and 1101?
options: A)5 B)6 C)9 D)10 E)11
SOLUTION:550 = 10*55
1100 = 20*55
The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B. #### B
QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is
options: A)70 B)71 C)72 D)73 E)74
SOLUTION:Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=264
<=>11x/3=264
=>x=72
Answer: Option C #### C
QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature T in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
options: A)29 B)30 C)30.5 D)31 E)32
SOLUTION:to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median T will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30
hence B #### B
QUESTION:Which of the following is not divisible by 6?
options: A)10032 B)21192 C)47816 D)91232 E)72031
SOLUTION:Divisibility rule of 6: Number must be divisible by both 2 and 3
Option A: 10032, Divisible by 2. Hence divisible by 6
Option B: 21192, Divisible by 2 & 3. Hence divisible by 6
Option C: 47816, Divisible by 2. Hence divisible by 6
Option D: 91232, Divisible by 2. Hence divisible by 6
Option E: 72031, Not divisible by 2 or 3. Hence 72031 is not divisible by 6 #### E
QUESTION:Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
options: A)70 m B)60 m C)80 m D)90 m E)100 m
SOLUTION:Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B #### B
QUESTION:76^77 /7
remainder is ?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1
and 5^3/3 remainder=2 and also 5/3=2
so it does not matter on the power value
so the answer will be 76/7 remainder=6
ANSWER:B #### B
QUESTION:Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
options: A)15:8 B)15:5 C)15:9 D)15:2 E)15:3
SOLUTION:Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8
Answer:A #### A
QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:
options: A)276 B)299 C)322 D)345 E)395
SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12).
Larger number = (23 x 12) = 276.
Answer: Option A #### A
QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 11 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?
options: A)64 B)72 C)80 D)90 E)99
SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k.
After adding gold coins, the number of coins is 3k and 6k.
Thus k = 11 and the total number of coins is 9k = 99.
The answer is E. #### E
QUESTION:Which of the following numbers is a perfect square?
options: A)1266 B)1444 C)2022 D)4034 E)8122
SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022.
38*38 = 1444
ANSWER:B #### B
QUESTION:A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
options: A)metres B)metres C)metres D)metres E)metres
SOLUTION:Explanation:
Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 18 s
Distance Covered, d = vt = (400/36)× 18 = 200 m
Distance covered is equal to the length of the train = 200 m
Answer: Option C #### C
QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.?
options: A)4.5 B)5 C)5.5 D)5.8 E)6
SOLUTION:if $x$ is the number, x/6 * 12 = 11
=> 2x = 11
=> x = 5.5
C #### C
QUESTION:A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.
options: A)200, 360,162 B)200, 460,160 C)200, 360,160 D)200, 360,138 E)200, 360,129
SOLUTION:Explanation:
let ratio be x.
Hence no. of coins be 5x ,9x , 4x respectively
Now given total amount = Rs.206
=> (.50)(5x) + (.25)(9x) + (.10)(4x) = 206
we get x = 40
=> No. of 50p coins = 200
=> No. of 25p coins = 360
=> No. of 10p coins = 160
Answer: C) #### C
QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
a.
b.
c.
d.
e.
options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5)
SOLUTION:no of different stocks for 4-letter code = 26^4
no of different stocks for 4-letter code = 26^5
total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4)
ANS:C #### C
QUESTION:On a two-dimensional coordinate plane, the line s = x^2 - x^3 touches the x-axis in how many places?
options: A) 0 B) 1 C) 2 D) 3 E) 4
SOLUTION:Apparently it's s = x^2 - x^3 instead of s = x^2 - s^3.
In this case: the x-intercept is the value(s) of x for s = 0.
0 = x^2 - x^3;
0 = x^2(1 - x);
x = 0 or x = 1.
Answer: C. #### C
QUESTION:What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.?
options: A)Rs. 8908.42 B)Rs. 9720 C)Rs. 10123.20 D)Rs. 10483.20 E)None
SOLUTION:Amount = [22000 * (1 + 12/100)3]
= 22000 * 28/25 * 28/25 * 28/25 = Rs. 30908.42
C.I. = (30908.42 - 22000) = Rs. 8908.42
ANSWER:A #### A
QUESTION:45 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?
options: A)80 litres B)90 litres C)120 litres D)170 litres E)None of these
SOLUTION:Explanatory Answer
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*45 = 60 litres.
However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.
i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.
Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*60 = 90 litres.
Answer B #### B
QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is?
options: A)75 B)78 C)80 D)82 E)86
SOLUTION:Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86
E) #### E
QUESTION:In a clock (Conventional clock with numbers 1 to 12 in order)is cut into 3 pieces such that the sum of each piece in AP with a common difference of 1. What is the count of numbers in each piece? and what are the numbers?
options: A)25 B)26 C)27 D)28 E)29
SOLUTION:Sum of the 12 numbers=1+2+3+......+12=12*13/2=78
So we have to divide it into 3 slots such that the sum is 78 and sum of each slot is in AP, thus the 3 slots are 25,26,27. So the numbers can be:
3+4+5+6+7=25
8+9+10=27
11+12+1+2=26
ANSWER:B #### B
QUESTION:Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and B is closed after 3 minutes, how much further time would it take for A to fill the bucket?
options: A)5min. 50sec. B)5min. 30 sec. C)6 min 36 sec. D)6mins. 32 sec. E)6 min. 15 sec.
SOLUTION:Explanation:
Part filled in 3 minutes =
3∗(1/12+1/15)=3∗9/60=9/20
Remaining part =1−9/20=11/20
=>1/12:11/20=1:X
=>X=6.6 mins.
=>X=6.6 mins.
So it will take further 6 mins 36 seconds to fill the bucket.
Option C #### C
QUESTION:Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
options: A)8 kmph B)10 kmph C)12 kmph D)16 kmph E)18 kmph
SOLUTION:Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C #### C
QUESTION:If 144/0.144 = 14.4/x, then the value of x is:
options: A)0.144 B)1.44 C)0.0144 D)0.014 E)0.00144
SOLUTION:=144/0.144 = 14.4/x
=144 x 1000/144
=14.4/x
=x = 14.4/1000
= 0.0144
Answer is C. #### C
QUESTION:How many 4 letter words can we make from the letters in an alphabet?
options: A)358800 B)358802 C)358801 D)358809 E)358810
SOLUTION:There are 26 letters in an alphabet
to choose 4 from these 26 would mean
26P4 = 26!/(26-4)!
We take Permutation and not Combination since the arrangement of letters matter in forming a word. Like MAPS and PAMS both are different words.
Therefore the answer is 26!/ 22! = 26*25*24*23 = 358800
Answer:A #### A
QUESTION:At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ?
options: A)Rs.7.50 per kg B)Rs.8.20 per kg C)Rs.8.85 per kg D)Rs.9 per kg. E)None
SOLUTION:Explanation:
Total C.P of 200 kg of sugar
= Rs.(80×6.75+120×8)=Rs.1500
C.P of 1 kg = Rs.[1500/200]=Rs.7.50
Gain required = 20%
S.P of 1 kg = (120% of Rs.7.50)
= Rs.[120/100×7.50]=Rs.9 per kg.
Correct Option : D #### D
QUESTION:2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill?
options: A)1/5 B)1/3 C)2/7 D)3/5 E)3/11
SOLUTION:1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
B #### B
<<<Examples ends
QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ?
options: A)-1 B)-5 C)-2 D)-3 E)-4
SOLUTION:Use answer options to solve this problem -
x is negative integer (-1,-2,-3......)
put x=-1
7x+3y=14
7(-1)+3y=14
-7+3y=14
3y=14+7
3y=21
y=7
Answer will be (A) #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15
SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B
QUESTION:A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
options: A)Rs.3178 B)Rs.3120 C)Rs.3127 D)Rs.3121 E)Rs.3122
SOLUTION:Explanation:
Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B #### B
QUESTION:A shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal?
options: A)18% B)20% C)17% D)18% E)None of these
SOLUTION:Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.130.
SP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117.
Gain = Rs.117 – Rs.100 = Rs.17
Therefore, gain/profit percent = 17%.
Answer: Option C #### C
QUESTION:A bike covers a certain distance at the speed of 68km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
options: A)85 km/h B)85.34 km/h C)87.67 km/h D)90.66 km/h E)90.64 km/h
SOLUTION:Ans.(D)
Sol. Total distance = 68 × 8 = 544 km
Now speed = 544/6 = 90.66 km/h #### D
QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours?
options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44)
SOLUTION:Explanation:
Here clock-wise and anti-clockwise arrangements are same.
Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}}
Answer: C) 18!(6 x 24) #### C
QUESTION:C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used?
options: A)months B)months C)months D)months E)months
SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7
ANSWER:D #### D
QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 70, how many coins of each type are there?
options: A)20 coins B)30 coins C)40 coins D)25 coins E)None of these
SOLUTION:Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 70
⇒ 1.75x = 70 ⇒ x = 40 coins
Answer C #### C
QUESTION:4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
options: A)4 days B)6 days C)7 days D)9 days E)1 days
SOLUTION:1 women's 1 day work = 1/28
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/28 + 10/140) = 1/4
5 women and 10 children will complete the work in 4 days.
Answer: A #### A
QUESTION:From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 40 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009?
options: A)80 B)126 C)95 D)100 E)108
SOLUTION:Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 40% = 90*1.2 = 126
Thus ratio = 126/100 = 1.26 (in % terms = 126%). Thus B is the correct answer. #### B
QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 10 and 100?
options: A)1345 B)1576 C)2475 D)2578 E)1895
SOLUTION:numbers are 11,13,15-------,97,99
Average of the set: (largest+smallest)/2=(99+11)/2=55;
# of terms: (largest-smallest)/2+1=(99-11)/2+1=45
The sum = 45*55= 2475
Answer: C #### C
QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
a.
b.
c.
d.
e.
options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5)
SOLUTION:no of different stocks for 4-letter code = 26^4
no of different stocks for 4-letter code = 26^5
total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4)
ANS:C #### C
QUESTION:In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ?
options: A)64 B)1/8 C)1 D)4 E)1/64
SOLUTION:Say r=2 => V1 = 1/16
when r=1; V2 = 1/4
V2 = 4*V1.
Answer : D #### D
QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box?
options: A)336 B)425 C)275 D)235 E)689
SOLUTION:B
425
(68 ÷ 16) × 100 #### B
QUESTION:Given two fair dice, what is the probability E that the sum of their numbers is 4 if exactly one die shows a 3?
options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5
SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.
E=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A
QUESTION:The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
options: A)3. B)7. C)10. D)16. E)15.
SOLUTION:Time taken by the birds to meet = 20/(4 + 1) = 4 mins
Distance traveled by the bird traveling from West-Town = 4 *4= 16
Answer: D #### D
QUESTION:The area of playground is 6000 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
options: A)a) $144 B)b) $150.50 C)c) $168 D)d) $158.60 E)e) $160.70
SOLUTION:total volume * unit cost = total cost
or, 6000 * 0.01 * 2.8 = total cost = 168=C #### C
QUESTION:There are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
.
options: A)75 Kg B)80 Kg C)85 Kg. D)90 Kg E)92 Kg
SOLUTION:New average weight= 110+60/2= 85 kgs
Since avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85
C is the answer #### C
QUESTION:A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning?
options: A)31 B)32 C)33 D)34 E)35
SOLUTION:14x + 75 = 15(x + 3)
x = 30 + 3 = 33
Answer:C #### C
QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following?
options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2
SOLUTION:initially - did x= 1/y^2
But this yielded the wrong answer,
I then re examined the question and tried y^2/x =1
Which I then got y = SQR(X)
subbing into y/6a I got answer E) #### E
QUESTION:How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
options: A)sec B)sec C)sec D)sec E)sec
SOLUTION:The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A #### A
QUESTION:When 242 is divided by a certain divisor the remainder obtained is 15. When 698 is divided by the same divisor the remainder obtained is 27. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor?
options: A)11 B)17 C)13 D)23 E)37
SOLUTION:let that divisor be x
since remainder is 15 or 27 it means divisor is greater than 27.
now 242-15=227 =kx (k is an integer and 234 is divisble by x)
similarly 698-27=671 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (227+671)+15+27
=x(k+l) + 42
when we divide this number by x then remainder will be equal to remainder of (42 divided by x) = 5 hence x = 42-5 = 37
hence E #### E
QUESTION:Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen
options: A)44/221 B)55/221 C)76/221 D)45/221 E)63/221
SOLUTION:WE HAVE N(S)=52C2=(52*51)/(2*1)=1326.
LET A=EVENT OF GETTING BOTH BLACK CARDS
B=EVENT OF GETTING BOTH QUEENS
AB=EVENT OF GETTING QUEEN OF BLACK CARDS
N(A)=26C2=(26*25)/(2*1)=325,
N(B)=4C2=(4*3)/(2*1)=6 AND
N(AB)=2C2=1
P(A)=N(A)/N(S)=325/1326;
P(B)=N(B)/N(S)=6/1326 AND
P(AB)=N(AB)/N(S)=1/1326
P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221
Option: B #### B
QUESTION:During the months May through October, Teddy the bear triples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
options: A)9m−1300 B)9m−300 C)4m−1200 D)3m−300 E)m−1300
SOLUTION:Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 3m - 300
April' 75 = 3m - 400
Oct' 75 = 9m - 1200
April'76 = 9m - 1300
Hence answer will be (A) 9m - 1300 #### A
QUESTION:If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K?
options: A)30 B)4 C)5 D)66 E)All of these
SOLUTION:The first term divisible by 3, so any term could be the third term.
Answer =(E) #### E
QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
options: A)80% B)107% C)116.7% D)120% E)140%
SOLUTION:Kim purchased 20 gallons of gas. She paid for 5 + 0.9*15 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%.
Isabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%.
8 is 8/7.5*100 = 107% of 7.5.
Answer: B. #### B
QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision?
options: A)2003 B)2009 C)2005 D)2006 E)2007
SOLUTION:She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009.
Answer: B. #### B
QUESTION:The average age of the district level hockey team of eleven is 35 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ?
options: A)43 yrs. B)44 yrs. C)45 yrs. D)47 yrs. E)46 yrs.
SOLUTION:Explanation:
Total age of players in team = 35 x 11 = 385
When coach is included, total members = 12, Avg age increases by one becomes 23
Total age when coach is included = 36x12 = 432
Age of coach = 432-385 = 47 yrs.
Answer:D #### D
QUESTION:In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was:
options: A)2500 B)2520 C)3000 D)3100 E)None of these
SOLUTION:Explanation :
Number of valid votes = 70% of 9000
= 6300.
Valid votes polled by other candidates = 40% of 6300
(40/1006300)
= 2520.
Harsh Mishra a year ago
0 upvotes
Answer : B #### B
QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5
SOLUTION:Rate of flow of water in second hour = 18 gallons per hour
Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour
Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons
Answer B #### B
QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
options: A)587 × 10<10>(exponent) miles B)587 × 10<-12> (exponent) miles C)587 × 10<-10>(exponent) miles D)587 × 10<12>(exponent) miles E)587 × 10<8>(exponent) miles
SOLUTION:The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 ×10<12>(exponent) miles #### D
QUESTION:In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted?
options: A)72% B)47% C)42% D)34% E)28%
SOLUTION:Town A is 40%, therefore town B must be 60%
Town A registered voters:0.70∗0.40=0.28
Town B registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent
ANSWER:B #### B
QUESTION:If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 200 units?
options: A)50 hours B)40 hours C)25 hours D)12 hours E)8 hours
SOLUTION:Here, we're told that 5 machines can produce 20 units in 10 hours....
That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.
20 units/5 machines = 4 units are made by each machine every 10 hours
Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...
10 hours/4 units = 2.5 hours per unit when 1 machine is working.
The prompt asks us how long would it take 20 machines to produce 200 units.
If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 200 units is '10 times' 20, we need '10 times' more TIME.
(2.5 hours)(10 times) = 25 hours
Final Answer:
[Reveal]Spoiler:
C #### C
QUESTION:The true discount on a bill of Rs.4320 is Rs.720.The banker's discount is
options: A)862 B)864 C)866 D)868 E)None of these
SOLUTION:Solution
P.W = Rs.(4320 - 720)
= Rs. 3600
S.I on Rs. 4320 =Rs.(720/3600 x 4320)
= Rs. 864.
Answer B #### B
QUESTION:For any 5 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.
options: A)I only B)II only C)I and II only D)II and III only E)None of the above
SOLUTION:Let the 3 numbers be x, y and z.
Question: Which of the following is equivalent to (x + y + z)/3
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141
II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent
Answer: C #### C
QUESTION:If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is
options: A)not an even B)an even C)a perfect square D)an odd E)a prime
SOLUTION:x^2 - 2x + 2y + 3 = 2x^2 - 3x + y + 1
y = x^2 - x - 2
y = (x-2)(x+1) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B. #### B
QUESTION:If a:b = 3:1, then find (a - 3b)/(2a - b)?
options: A)0 B)1 C)2 D)1/7 E)2/7
SOLUTION:a/b = 3/1 => a = 3b
(a - 3b)/(2a - b) = (3b - 3b)/(6b - b)
= 0/7b => 0
ANSWER:A #### A
QUESTION:Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 16 hours. If all the pipes are open, in how many hours will the tank be filled ?
options: A)2.5 hours B)2 hours C)3.5 hours D)2.3 hours E)None of these
SOLUTION:Explanation:
Part filled by A in 1 hour = 1/4
Part filled by B in 1 hour = 1/8
Part filled by C in 1 hour = 1/16
Part filled by (A+B+C) in 1 hour =
1/4+1/8+1/16=7/16
So all pipes will fill the tank in 2.3 hours.
Option D #### D
QUESTION:Express the ratio 3 2/3 : 7 1/3 in its simplest form.
options: A)1:21 B)1:1 C)2:1 D)1:2 E)2:11
SOLUTION:Solution
We first convert the mixed numbers 3 2/3 and 7 1/3 into fractions
3 2/3 = 3*3 / 3 + 2 / 3 = 11 / 3
7 1/3 = 7*3 / 3 + 1 / 3 = 22 / 3
The ratio 3 2/3 : 7 1/3 can be expressed as
11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22
Simplify
= 11 / 22 = 1 / 2
The ratio is 1 / 2 or 1:2
ANSWER IS D #### D
QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere?
options: A) 6/π B) 9/π C) 6 D) 9 E) 12
SOLUTION:Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4*PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !! #### D
QUESTION:What is the sum of all the multiples of 10 between 0 and 75?
options: A)500 B)620 C)450 D)340 E)280
SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280.
Final Answer:
E #### E
QUESTION:What should come in place of the question mark (‘?) in the following equation?
18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16
options: A)2764.44 B)2864.34 C)1864.44 D)2684.44 E)None of these
SOLUTION:? = 8697.32 – 3058.16 – 92⁄5 × 150.8
= 5639.16 – 2774.72 = 2864.44
Answer E #### E
QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ?
options: A)50 B)30 C)40 D)60 E)80
SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E.
So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km
So, he will have to move 10 + 20 = 30 Km
ANSWER B #### B
QUESTION:Jane makes toy bears. When she works with an assistant, she makes 53 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
options: A)20% B)70% C)100% D)180% E)200%
SOLUTION:Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears/hr ([40 bears * 1.53] / [40 hrs * .90]).
[(1.7 - 1)/1] * 100% = 70%
ANSWER:B #### B
QUESTION:If 2x = 3y = 20, then 12xy = ?
options: A) 1,200 B) 800 C) 120 D) 40 E) 20
SOLUTION:2x = 20;x=10
3y = 20;y=20/3
Multiply: 12xy=12*10*20/3=800.
Answer: B. #### B
QUESTION:A water tank is three-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
options: A)6 min B)8 min C)7 min D)9 min E)1 min
SOLUTION:The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15
Since the rate is negative, the tank will be emptied.
A full tank would take 15 minutes to empty.
Since the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes
The answer is D. #### D
QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
options: A)21 B)36 C)39 D)60 E)65
SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room.
Therefore there are 3/8*96=36 people in the room under the age of 21.
Answer: B. #### B
QUESTION:If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is
options: A)1/2 B)1 C)2 D)4 E)8
SOLUTION:Given: 5/w + 5/x = 5/ywx=y
Find: (w+x)/2 = ?
5(1/w + 1/x) = 5(1/y) - divide both sides by 5
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A #### A
QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price
options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/-
SOLUTION:100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
A #### A
QUESTION:Find the fourth proportional to 2.8 , 3.4 and 5.2?
options: A)5.98 B)6.14 C)6.29 D)6.31 E)5.64
SOLUTION:Formula = fourth proportion =(b x c)/a
a=2.8 , b=3.4 and c=5.2
(3.4 x 5.2)/2.8=6.31
D #### D
QUESTION:Tim and Élan are 120 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
options: A)30 miles. B)35 miles. C)45 miles. D)60 miles. E)80 miles.
SOLUTION:Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.
Plugging in the answer choice Only Answer Choice E meet the 2:1(Tim:Elan=80:40) ratio of maintaining total distance traveled 120 miles
So Correct answer E #### E
QUESTION:Q. How many 9-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6, 6, 7?
options: A)180 B)140 C)210 D)270 E)300
SOLUTION:the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2
i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _
case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6
when the units digit is 2 i.e 1 _ _ _ _ _ 2
number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60
when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30
case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)
number of ways this can be done would be 5! / (2!) for 2 =60
and 5! / 2! for 6 ... = 60
adding all of these ... gives the answer 140 ...
the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat
B #### B
QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3%
SOLUTION:Let 100 is the enrollment in 1990.
Enrollment in 1980= 83.3
% increase= (Increase from 1980 to 1990)/Enrollment in 1983
=>16.7*100/83.3 =20%
ANSWER:C #### C
QUESTION:A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
options: A)$330.00 B)$331.00 C)$332.30 D)$333.30 E)$334.60
SOLUTION:The maximum interest in one month is 10%*$300=$30.
The combined payment (base plus interest) is $300 + $30 = $330.
The greatest possible payment is: 1.01*$330=$333.30.
The answer is D. #### D
QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?
options: A)170 B)185 C)190 D)196 E)200
SOLUTION:185
Answer is B #### B
QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?
options: A)409 B)1636 C)16360 D)16000 E)15360
SOLUTION:terms in this sequence are 7,12,17----402
now since this is an a.p. with a common difference of 5. therefore its sum can be given as
a(f+l)/2----------------1)
a= total no. of terms =80
f= first term=7
l= last term=402
subsituting values in the expression 1 we have
80(7+402)/2
= 40(409)
=16360=C #### C
QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
options: A)227 B)177 C)120 D)288 E)271
SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.Answer:C #### C
QUESTION:Kate and her boyfriend Ben, completed the painting of their new apartment together in 6 days.If they were to work separately, how long will it take each of them to complete it, if Ben can complete the painting 5 days earlier than Kate.
options: A)6 and 11 B)5 and 10 C)10 and 15 D)8 and 13 E)6 and 10
SOLUTION:Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job.
Answers E, A and C are illogical, since the individual times must both be greater than 10 days.
so we can TEST the values for Answers B and D.
Using the values for Answers C and D...
Answer C: (10)(15)/(10+15) = 150/25 = 6 This is a match
Final Answer:
C #### C
QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y
SOLUTION:The answer is B.
She runs x yards in 10x/y seconds =10x/60y minutes. #### B
QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments.
options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3
SOLUTION:The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:21.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6.
ANSWER:A #### A
QUESTION:A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
options: A)17% B)25% C)69% D)31% E)19%
SOLUTION:Let the price be 100.
The price becomes 130 after a 30% markup.
Now a discount of 10% on 130.
Profit=117-100
17%
answer A #### A
QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be?
options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday
SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999.
366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday
Answer: A #### A
QUESTION:What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15
options: A)3 B)5 C)6 D)8 E)9
SOLUTION:Explanation:
On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
Option A #### A
QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour?
options: A)E982 B)27 C)12 D)14.6 E)28
SOLUTION:Explanation:
T = 11/45 * 60 = 14.6
Answer: Option D #### D
QUESTION:The average age of a class of 23 students is 22 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
options: A)40 B)41 C)46 D)42 E)49
SOLUTION:Total age of all students =23×22
Total age of all students + Age of the teacher =24×23
Age of the teacher
=24×23−23×22=23(24−22)=23×2=46
Answer is C. #### C
<<<Examples ends
QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is:
options: A)276 B)299 C)322 D)345 E)355
SOLUTION:Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14) = 322.
ANSWER:C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:How many three letter words are formed using the letters of the word TIME?
options: A)28 B)21 C)26 D)24 E)29
SOLUTION:The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃
= 4 * 3 * 2 = 24.
Answer: D #### D
QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin?
options: A)$110 B)$150 C)$225 D)$54 E)$75
SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices.
110/3 = 36.67
150/3 = 50
225/3 = 75
54/3 = 18
75/3 = 25
A is not an integer amount.
Answer:A #### A
QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is?
options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m
SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
E #### E
QUESTION:For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6?
options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4.
SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6
= 6*0 + 2*7.2 + 8 - 6.6
= 0 +14.4 +1.4
15.8
Answer B #### B
QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day.
options: A)20 B)10 C)25 D)15 E)24
SOLUTION:work completed in a day by one men = 1/25 = (1/5)*(1/5)
So it takes 25 men to complete this job = 25 * (1/25) = 1
Answer: C #### C
QUESTION:A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
options: A)49 B)4 C)12 D)9 E)27
SOLUTION:Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x 14 * x = 6 x 21
x = (6 x 21)/14
x = 9.
Answer is D. #### D
QUESTION:The remainder obtained when a prime number greater than 4 is divided by 4 is
options: A)a) 1 or 3 B)b) 1 or 5 C)c) 3 or 5 D)d) 4 or 5 E)e) 5
SOLUTION:The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 4, i.e. 7 and 5:
7/4 = 1 + remainder of 3
5 / 4 = 1 + remainder of 1
This is already sufficient to see that answer choice a) is correct.
A #### A
QUESTION:if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
options: A)11x/y B)10x/y C)x/11y D)11/xy E)xy/11
SOLUTION:Answer is B.
The rate of running hards: 10 minutes per y hards.
Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y #### B
QUESTION:Find avrg speed if a man travels at speed of 18km/hr up and 24km/hr dawn at an altitude of 300m.
options: A)25.8 B)26.8 C)27.8 D)20.5 E)21.8
SOLUTION:avg speed=2*x*y/(x+y)
=2*18*24/(18+24)=20.5
ANSWER:D #### D
QUESTION:A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 25 hours, 50 percent worked 40 hours, and the rest worked 50 hours?
options: A) $180,000 B) $185,000 C) $180,000 D) $200,000 E) $192,500
SOLUTION:30% of 1000 = 300 worked for 20 hours
Payment @ 5/hr
Total Payment = 300*25*5 = 37500
50 % of 1000 = 500 worked for 40 hours
Payment @ 5/hr
Total payment = 500*40*5 = 100000
Remaining 200 worked for 50 Hours
Payment for first 40 Hours @ 5 /hr
Payment = 200*40*5 = 40000
Payment for next 10 hr @ 7.5/hr
Payment = 200 * 10 * 7.5 = 15000
Total Payment = 37500+100000 + 40000 +15000 = 192500
Hence , answer is E #### E
QUESTION:A and B go around a circular track of length 900m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
options: A)120 sec B)165 sec C)186 sec D)180 sec E)168 sec
SOLUTION:Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 900/ (36 * 5/18) , 900/ (54 * 5 /18) }
= LCM (90, 60)
=180 sec.
Answer:D #### D
QUESTION:Which of the following must be divisible by 4, given that y is a positive integer?
options: A)(y−1)*y*(y+3) B)y^2*(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3)
SOLUTION:option A) (y−1)*y*(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A
QUESTION:100 identical coins each with probability 'pp' showing up heads & tossed.
options: A)13/101 B)11/101 C)51/101 D)53/102 E)54/101
SOLUTION:Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C #### C
QUESTION:In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
options: A)2.5 sec B)4.25 sec C)3.75 sec D)12.5 sec E)6 sec
SOLUTION:Speed = 144 * 5/18 = 40 m/sec
Time taken = 150/40 = 3.75 sec.
ANSWER:C #### C
QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.25000?
options: A)8275 B)1879 C)2779 D)2672 E)2782
SOLUTION:A = 25000(11/10)^3
= 33275
= 25000
----------
8275
Answer: A #### A
QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long?
options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec
SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec
time = (360+140)/25/2
= 500*2/25
=40sec
ANSWER:A #### A
QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
options: A)Rs.64.18 B)Rs.64.67 C)Rs.64.08 D)Rs.64.10 E)Rs.64.22
SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000]
= Rs. 464.10 Difference
= (464.10 - 400)
= Rs. 64.10
Answer: D #### D
QUESTION:Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ?
options: A)30 B)32 C)34 D)36 E)38
SOLUTION:First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 1*2*2*2*2*2 = 32
ANSWER:B #### B
QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
options: A)12 B)14 C)15 D)19 E)10
SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15. Answer:C #### C
QUESTION:If 0.75: x :: 5:9, then x is equal to:
options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these
SOLUTION:Explanation:
(x * 5) = (0.75 *9)
X=6.75/5 = 1.35
Answer: D #### D
QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?
options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150
SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15.
Hence, the probability that at least one light bulb fails is 1-0.94^15.
Answer: A.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A
QUESTION:In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together?
options: A)A)360 B)B)480 C)C)720 D)D)5040 E)of these
SOLUTION:The word 'SINGING' has 7 different letters.
When the vowels II are always together, they can be supposed to form one letter.
Then, we have to arrange the letters SNGNG (II).
Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.
The vowels (II) can be arranged among themselves in 1! = 1 way.
Required number of ways = (720 x 1) = 720.
ANSWER:C #### C
QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are
options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44
SOLUTION:A
11, 42
Let the age of Priya = x years
Then, the age of her father = (x+ 31) years
ATQ,
(x+ 8) + (x+ 31 + 8) = 69
2x+ 47 = 69
2x= 69 – 47 = 22
x= 11
The age of Priya = 11 years
The age of her father = 11 + 31 = 42 years #### A
QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE.
If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE?
options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards
SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question.
1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle.
2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus.
3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle.
4) From (1), we know that x = 202+y2−−−−−−−√202+y2.
5) From (3), we know x = 25 - y.
6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y
7) Solving for y, we get 4.5.
8) 25 - 4.5 = 20.5 = x
9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82.
The answer is B, 82 #### B
QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true?
options: A)35 B)48 C)69 D)70 E)74
SOLUTION:5*a1 + 7*b1 = t
5*a2 + 7*b2 = t
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.
Lets check how it works for our numbers, starting from the largest:
E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad
D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus
D is the answer #### D
QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8
SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.
15 = x y and 16 = 2 x + 2 y
Solve the second equation for x
x = 8 - y
Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as
15 = (8 - y) y
Solve for y to find
y = 3 and y = 5
Use x = 8 - y to find x
when y = 3 , x = 5 and when y = 5 , x = 3.
The dimensions of the rectangle are 3 and 5.
correct answer B #### B
QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
options: A)19 B)18.7 C)19.9 D)21.7 E)22.8
SOLUTION:Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 36 Paise is given as tax
=> Total tax incurred = 36 Paise = Rs.36/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−36/100−x)6/100 = 36/100
⇒ 6(25 −0.36 −x) = 36
⇒ (25 − 0.36 − x) = 6
⇒ x = 25 − 0.36 − 6 = 18.7
B) #### B
QUESTION:39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
options: A)9 B)12 C)10 D)13 E)15
SOLUTION:Explanation:
Let the required number of days be x
More persons, less days (indirect proportion)
More hours, less days (indirect proportion)
Hence we can write as
(persons)39:30
(hours) 5:6}:: x:12
⇒39×5×12=30 × 6 × x
⇒39×5×2=30 × x
⇒39=3×x
⇒x=13
Answer: Option D #### D
QUESTION:12,31,68,129,220,?
options: A)129 B)220 C)387 D)347 E)520
SOLUTION:2*2*2 + 4 = 12
3*3*3 +4 = 31
4*4*4 + 4 = 68
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
ANSWER : D #### D
QUESTION:If a and b are positive integers and a/b=0 then which of the following give positive Numbers and CANNOT be zero?
options: A)ab/ba B)a/b-b/a C)b/a-a/b D)(a^2 -b^2)/ab E)a/b
SOLUTION:(D) (a^2 -b^2)/ab = a/b-b/a gives negative value.
The option C is Answer.
(C)a/b-b/a
If a/b=0, b/a gives positive numbers.(a and b are positive integers) #### C
QUESTION:For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution?
options: A)12 B)9 C)3 D)7.5 E)2.5
SOLUTION:we have 2 equations
1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36
2. kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B #### B
QUESTION:A train 250 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform?
options: A)150m B)200m C)250m D)270m E)300 m
SOLUTION:D = 72 * 5/18 = 20 = 400 – 250 = 150m
ANSWER:A #### A
QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches?
options: A)25 B)23 C)22 D)15 E)18
SOLUTION:Area of Carol's rectangle = 24*5 = 120
Let width of Jordan's rectangle= w
Since , the areas are equal
8w = 120
=>w = 15
Answer D #### D
QUESTION:A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
options: A)229 B)108 C)278 D)72 E)112
SOLUTION:S = 120/6 * 18/5 = 72 kmph
Answer: D #### D
QUESTION:A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A.
options: A)237 B)126 C)971 D)611 E)150
SOLUTION:Explanation:
ANSWER: E #### E
QUESTION:If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.
options: A)5 : 3 B)2 : 5 C)4 : 7 D)5 : 2 E)None of these
SOLUTION:Explanation:
Let the first number is A and second number is B.
As per question
(40/100)A = (2/3)B
A/B = 2/3 x 100/40
A/B = 5/3
=>A:B = 5:3
Answer: Option A #### A
QUESTION:A rectangular field is 20 yards long and 18 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)
options: A)330 ft B)336 ft C)430 ft D)330 ft E)230 ft
SOLUTION:20 + 18 + 20 + 18 = 76 yds. for
outside of field.
18 + 18 = 36 yds. for dividing sections
76 + 36 = 112 yds. of fencing
112 x 3 = 336 ft. of fencing
correct answer B #### B
QUESTION:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar?
options: A) 9 B) 12 C) 15 D) 18 E) 21
SOLUTION:(Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)
í.ẹ. Red*White = Blue*Total Coins
Let, Red = 3a
White = 3b
Blue = 3c
Total Coins = 3(a+b+c)
í.ẹ. 3a * 3b = 3c*3(a+b+c)
í.ẹ. a*b = c*(a+b+c)
For smallest values of a, b and c
2*3 = 1*(1+2+3)
í.ẹ. Minimum Total Coins = 3*(1+2+3) = 15
Answer: Option C #### C
QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?
options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these
SOLUTION:Explanation :
Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30
Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15.
For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number.
So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6
Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24
So total probability = 24/90 = 4/15
Answer : C #### C
QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)285 m B)240 m C)277 m D)765 m E)176 m
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/39 = 15 ==> x + 300 = 585 ==> x
= 285 m.
Answer: A #### A
QUESTION:If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1, then what is the value of abc/def ?
options: A) 27/4 B) 27/8 C) 3/4 D) 3/2 E) 1/4
SOLUTION:Say a = 2. Then:
a/b = 1/3 --> b = 6;
b/c = 2 --> c = 3;
c/d = 1/2 --> d = 6;
d/e = 3 --> e = 2;
e/f = 1 --> f = 2.
abc/def = (2*6*3)/(6*2*2) = 3/2.
Answer: D. #### D
QUESTION:Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ?
options: A)6000 B)5400 C)6200 D)7200 E)8200
SOLUTION:Investment Ratio = Profit Sharing Ratio.
Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6.
Giri share =
13200
× 6 / 11 = Rs.7200
Hari share =
13200 × 5 / 11 = Rs.6000
Option A #### A
QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business?
options: A)$11,000 B)$50,000 C)$16,500 D)$ 6,600 E)$ 3,600
SOLUTION:Total Investment between 5: (x/5)
Total investment including 2200 less between 3 people(x-(2200*3))/3
Set both eq. equal to each other.
16,500
Answer C) #### C
QUESTION:(3x + 2) (2x - 1) = ax^2 + kx + n . What is the value of a - n + k ?
options: A)5 B)8 C)9 D)10 E)11
SOLUTION:Expanding we have 6x^2 - 3x + 4x -2
6x^2 + x - 2
Taking coefficients, a = 6, k= 1, n = -2
Therefore a - n + k = 6 - (-2) +1 = 8 + 1 = 9
The answer is C. #### C
QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
options: A)160 B)170 C)175 D)195 E)180
SOLUTION:Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER :C #### C
QUESTION:Naomi was ordering yarn from a discount web site. If she ordered more than $50 worth of
yarn labeled “discountable”, she could take an extra 10% from the price of that yarn. Only
some of the yarn she ordered was eligible for the discount. Here is what Naomi ordered:
2 skeins at $2.50 per skein (not discountable)
8 skeins at $8.40 per skein (discountable)
7 skeins at $5.99 per skein (discountable)
Tax is 5% and shipping is 8%. How much did Naomi pay for her yarn?
options: A)$116.64 B)$216.64 C)$316.64 D)$416.64 E)$516.64
SOLUTION:8 x $8.40 = $67.20 (All money is rounded to hundredths at each step.)
7 x $5.99 = $41.93
$67.20 + $41.93 = $109.13 discountable
$109.13 x .10 = $10.91 (rounded)
$109.13 - $10.91 = $98.22 for discounted yarn
2 x $2.50 = $5.00 for un-discounted
$98.22 + $5.00 = $103.22 cost of yarn
$103.22 x 1.13 = $116.64 with tax and shipping
(5% + 8% = 13%)
correct answer A #### A
QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)
options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87
SOLUTION:Explanation:
Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer: A #### A
QUESTION:A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
options: A)4 B)5 C)6 D)7 E)8
SOLUTION:The rate of the pump + leak = 5/14
1/2 - leak's rate = 5/14
leak's rate = 1/2 - 5/14 = 1/7
The leak will empty the tank in 7 hours.
The answer is D. #### D
QUESTION:The wages earned by Robin is 50% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
options: A)18.75% B)23% C)30% D)50% E)7%
SOLUTION:Let wage of Erica = 10
Wage of Robin = 1.5*10 = 15
Wage of Charles = 1.6 *10 = 16
Percentage by which wage earned by Charles is more than that earned by Robin = (16-15)/15 * 100%
= 1/15 * 100%
=7%
Answer E #### E
QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 20% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
options: A)40% B)45% C)55% D)60% E)64%
SOLUTION:VERITAS PREPOFFICIAL SOLUTION:
D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 80% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5*(4/5) of the original price, which nets to 0.64 of the original price, or 64%.
E #### E
QUESTION:(0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is:
options: A)0.8 B)0.4 C)0.96 D)0.69 E)0.76
SOLUTION:Given expression
= (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.5 - 0.1)
= 0.4
Answer is B #### B
QUESTION:A can do a piece of work in 10 days and B alone can do it in 15 days. How much time will both take to finish the work ?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 10 x 15 / (10 + 15)
= 150 / 25
= 6 days
Answer: B #### B
QUESTION:Average between two sets of numbers is closer to the set withmore numbers?
options: A)70 B)80 C)90 D)95 E)98
SOLUTION:If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B #### B
QUESTION:The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is
options: A)17.2 km B)7.2 km C)7.6 km D)17.6 km E)27.2 km
SOLUTION:speed of a boat in still water = 15 km/hr
Speed of the current = 3 km/hr
Speed downstream = (15+3) = 18 km/hr
Distance travelled downstream in 24 minutes=(24/60)×18=(2×18)/5 = 7.2 km
Answer is B #### B
QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 37.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans?
options: A)5.5 B)11 C)47.5 D)50.5 E)67.5
SOLUTION:Total price of six cans = 6*37.5 = 225
Total price of 4 cans = 4*31 = 124
Total rice of two cans = 225 - 124 = 101
Average price of two cans = 101/2 = 50.5 c
Another way to do it is this:
Assume that the four leftover cans were of 31c each. The avg was 37.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans.
So cost of the two cans = 2*37.5 + 4*6.5 = 101
Avg cost of the two cans = 101/2 = 50.5c
Answer (D) #### D
QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
options: A)22 B)80 C)40 D)77 E)12
SOLUTION:800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C #### C
QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted?
options: A)3 B)6 C)2 D)12 E)27
SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black.
But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2.
Answer: C. #### C
QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent?
options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3%
SOLUTION:750 ---- 50
50 ---- ? => 6 2/3%
Answer: E #### E
QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
options: A)10 B)99 C)787 D)62 E)22
SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer: A #### A
QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?
options: A)30sec B)45sec C)36sec D)29sec E)52sec
SOLUTION:Speed of the train = 50*5/18 = 250/18 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(250/18) = 500*18/250 = 36sec
Answer is C #### C
QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
options: A)230 B)250 C)260 D)300 E)360
SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360
E #### E
QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
options: A)3999 B)7799 C)2500 D)2772 E)2912
SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500.Answer: C #### C
QUESTION:In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/4.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
options: A)5. B)7. C)9. D)10. E)17.
SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10
Lets take LCM of three balls 4,5 and 10 =20.
The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls.
The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls.
The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS.
Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls.
IMO option C is correct. #### C
QUESTION:Eight years ago, Rhea was half of Rick in age. If the ratio of their present ages is 3:4, what is the total of their present ages?
options: A)25 years B)28 years C)32 years D)26 years E)28 years
SOLUTION:let rhea age be x
rick age be y
given
x-8=1/2(y-8)......a
also given
x/y=(3/4)
=>x=3/4(y).......b
by solving a and b
we get y=16
x=12
then x+y=12+16=28
ANSWER:B #### B
<<<Examples ends
QUESTION:Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg. How much amount did he pay to the shopkeeper?
options: A)A)1040 B)B)1045 C)C)1055 D)D)1190 E)E)1075
SOLUTION:Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 70 × 9 = 630.
Total cost he has to pay = 560 + 630 = 1190.
D) #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 82 unique alphanumeric case sensitive characters.
options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6)
SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password
= 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways )
=82^4(1+ 82)
=82^4 * 83
Answer B #### B
QUESTION:If r and s are positive integers and r-s=6, which of the following has the greatest value J?
options: A)2r B)2s C)r +s D)2r-s E)2s-r
SOLUTION:You can answer this question by using Number Properties and logic or by TESTing VALUES.
We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.
IF....
R = 8
S = 2
Answer A: 2R = 2(8) = 16
Answer B: 2S = 2(2) = 4
Answer C: R+S = 8+2 = 10
Answer D: 2R-S = 2(8) - 2 = 14
Answer E: 2S-R = 2(2) - 8 = -4
Final Answer:
A #### A
QUESTION:The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
options: A)12.5% B)13% C)13.15% D)14% E)15%
SOLUTION:Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
A) #### A
QUESTION:A shop owner sells 56 apples and gains SP of 16 apples. Find the gain %?
options: A)30% B)40% C)50% D)56% E)78%
SOLUTION:Gain=16 apples
Total 56 apples
CP 56-16=40
(16/40)*100
=40%
Ans B #### B
QUESTION:A garrison of 150 men has provisions for 31 days. At the end of 16 days, a reinforcement arrives, and it is now found that the provisions will last only for 5 days more. What is the reinforcement?
options: A)150 B)450 C)400 D)600 E)300
SOLUTION:150 ---- 31
150 ---- 15
x -----5
x*5 = 150*15
x = 450
150
-------
300
Answer: E #### E
QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7
SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7
Answer: B #### B
QUESTION:2 pipes can separately fill a tank in 20hrs and 30hrs respectively. Both the pipes are opened tofill the tank, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
options: A)12 hrs B)14 hrs C)16 hrs D)18 hrs E)20 hrs
SOLUTION:1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
C #### C
QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9
SOLUTION:Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability B= 50/90 = 5/9
Correct answer E #### E
QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159
SOLUTION:46 + 28 + 10 = 84%
100 – 84 = 16%
850 * 16/100 = 136
Answer:A #### A
QUESTION:By selling 99 pens, a trader gains the cost of 11 pens. Find his gain percentage?
options: A)11 1/3% B)11 7/3% C)11 1/8% D)11 1/3% E)11 1/9%
SOLUTION:Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 11 pens
= Rs. 11
Profit% = 11/99 * 100
= 11 1/9%
Answer: E #### E
QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be
options: A)12 B)21 C)16 D)17 E)14
SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21
Ans: B #### B
QUESTION:A and B can do a piece of work in 12 days and 24days. Both starts the work together for some time, but B leaves the job 6 days before the work is completed. Find the time in which work is finished.
options: A)10 days B)12 days C)14 days D)5 days E)6 days
SOLUTION:Explanation:
A & B completes the work in 12*24/12+24 = 12*24/36 = 8 days
2 days work = 2+1/8 = ¼ work
Remaining work = 1-1/4 = ¾
A completes ¾ work in ¾*16 = 12 days
Answer: Option B #### B
QUESTION:which of the following inequalities indicates the set of all values of d for which the lengths R of the three sides of a triangle can be 3,4, and d?
options: A)0<d<1 B)0<d<5 C)0<d<7 D)1<d<5 E)1<d<7
SOLUTION:This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .
Thus,
|a-b| < c < a+b
|b-c| < a < b+c
|c-a| < b < a+c
Thus, if the sides of the triangle are 3,4 and d,
4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer. #### E
QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train?
options: A)278 B)166 C)151 D)240 E)109
SOLUTION:Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 280)/26 = 20
x = 240 m.
Answer:D #### D
QUESTION:Two vessels contains equal number of mixtures milk and water in the ratio 5:2 and 6:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?
options: A)1:3 B)9:13 C)5:11 D)11:3 E)15:4
SOLUTION:The ratio of milk and water in the new vessel is = (5/7 + 6/7) : (2/7 + 1/7)
= 11/7 : 3/7 = 11:3
Answer is D #### D
QUESTION:Jerry, an electrician, worked 5 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 5? 12 months = 1 year
options: A)58.33% B)68.33% C)78.33% D)88.33% E)41.66%
SOLUTION:1. Multiply the opposites
5 x 100 = 500
100=5/12
Divide by the remaining number
41.66% (rounded to hundredth)
correct answer E #### E
QUESTION:A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days G will the work get over?
options: A)60 B)70 C)G=75 D)G=80 E)100
SOLUTION:We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75
Ans: C (75 days) #### C
QUESTION:A furniture manufacturer has two machines, but only one can be used at a time. Machine E is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine E can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
options: A)14 B)13 C)11 D)9 E)7
SOLUTION:machine E finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts
Lets assume total work require 120 shifts
Therefore,
rate of E = 5 shifts/day
rate of B = 4 shifts/day
rate of (E+B) = 9 shifts/day
According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day
Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days=D #### D
QUESTION:A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected?
options: A)1/3 B)2/5 C)2/7 D)3/7 E)3/8
SOLUTION:Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)
= = 2/5
B #### B
QUESTION:When x is multiplied by 3, the result is 4 more than the result of subtracting x from 16. What is the value of x?
options: A)-4 B)-2 C)5 D)13 E)22
SOLUTION:The equation that can be formed is:
3x-4=16-x
or, 4x=20
or, x=5.
Answer : C #### C
QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
options: A)5040 B)2520 C)360 D)120 E)42
SOLUTION:6! = 720
720/2=360 half the time carmelo is in front, vice versa
Answer:
(C) 360 #### C
QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years?
options: A)30 B)35 C)40 D)50 E)60
SOLUTION:Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 20 years = (20 + 20) years =40 years.
Answer : C #### C
QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020
SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10200 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv)
Subtracting (ii) from (iv), we get, P = 4050.
P's monthly income = Rs.4050.
Answer: A #### A
QUESTION:In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥60. The smallest n which fulfills this condition is n = 8.
Answer C #### C
QUESTION:A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed
against the current will be
options: A)11 kmph B)10 kmph C)14 kmph D)17 kmph E)None of these
SOLUTION:Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 5 = 15
Now speed against the current will be
speed of the man - speed of the current
= 15 - 5 = 10 kmph
Answer: B #### B
QUESTION:For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y?
options: A)14 B)12 C)10 D)16 E)18
SOLUTION:we know that : x > 1, y > 1, and x + 3y < 1000,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 =1024 (it exceeds 920, so, x can't be 2^10)
so, max value that X can take is 2^9 , for which has length of integer is 9.
now, since x =512 ,x+3y<920
so, 3y<408
==> y<136
so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7
for 2^7 has length of integer is 7.
SO, combined together : 9+7 = 16.
D #### D
QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers?
options: A)56% B)57% C)58% D)45% E)35%
SOLUTION:let assume he sells 1 buffet daily,
now
then 300*1 = revenue (eq -1)
if he reduced his price by 20% then ,
240*(customer) = 125/100*revenue
customer = 1.25*300/240 = 1.56
means 56 % increase in customer.
ANSWER:A #### A
QUESTION:In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground?
options: A)70 B)52 C)62 D)59 E)50
SOLUTION:total number of players= 16+12+18+13= 59
Answer is D #### D
QUESTION:If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
options: A)7 days B)3 days C)9 days D)8 days E)2 days
SOLUTION:C
9 days
C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C
QUESTION:x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median W of x, y, and z?
I. 9
II. 10
III. 11
options: A)I only B)II only C)III only D)I and II only E)I and III only
SOLUTION:Average gives us an idea that 3 nos. are close to 10.
so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.
Let us see options.
If 9 has to be median W.
1st term has to less than 9 or equal to 9. (also maintain z-x = 3)
9 9 12 --> satisfies all conditions so 9 can be a median value.
If 11 has to be a median
3rd term has to be 11 or more than 11. (also maintain z-x = 3)
8 11 11 -->satisfies all conditions so 9 can be a median value.
Now for 10 to be median.
z+ x = 20 and z-x = 3, we wont have integer values of z.
10 cannot be a median
E is the answer. #### E
QUESTION:Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
options: A)4328 B)5382 C)6174 D)7690 E)8436
SOLUTION:The number of ways for the ships to go to the ports is 3! = 6.
At Port A, the number of ways to choose two winners is 7C2 = 21.
At Port B, the number of ways to choose one winner is 7.
At Port C, the number of ways to choose one winner is 7.
The total number of ways to give out gift certificates is 6*21*7*7 = 6174
The answer is C. #### C
QUESTION:A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
options: A)6.4 days B)4.4 days C)5.4 days D)8.4 days E)2.4 days
SOLUTION:A
6.4 days
1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300
So, all three together will complete the work in 300/47 = 6.4 days.- #### A
QUESTION:A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is:
options: A)90 cm B)6 dm C)1 m D)1.1 cm E)None of these
SOLUTION:Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (160 - x)] = 8000 × 1000
=> 320 × 250 × (160 - x) = 8000 × 1000
=> (160 - x) = 8000×1000/320=
100
=> x = 60 cm = 6 dm.
Answer: B #### B
QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head?
options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8
SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {HHT,HHH,THH,HTH,TTT}
5/8
E #### E
QUESTION:If n ≠ 0, which of the following must be greater than n?
I. 2n
II. 2 - n
III. n^2
options: A)I only B)II only C)I and II only D)II and III only E)None
SOLUTION:n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)
but if n = positive:
n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=> only III
=>answer is E #### E
QUESTION:The number of female students in a college in the previous year was 400. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year?
options: A)200 B)600 C)900 D)1600 E)2000
SOLUTION:Let x be the number of male students last year. The number of male students this year is 2x.
Let y be the number of female students this year.
x/400 = 2(2x/y)
y = 1600
The answer is D. #### D
QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females?
options: A)16% B)45% C)32% D)40% E)28%
SOLUTION:answer b
male-employed - 64%
female-employed-19%
Total employed 64%
means total unemployed = 36%
therefore d and e are not correct because female unemployed has to be less than 36%
female-unemployed = 32% male unemployed = 4%
48% + 4% = 52%
16% + 32% = 48%
plug in a and b in place of 32% and the sum is not 100%
19/64 =28 E #### E
QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?
options: A)4 B)5 C)6 D)9 E)7
SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even.
1) 2(6 times)
2) 2(3 times) + 3(2 times)
3) 2(2 times) + 3 + 5
4) 2 + 3 + 7
5) 2 + 5 + 5
6) 3(4 times)
7) 5 + 7
Answer: E #### E
QUESTION:There are 680 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
options: A)425 B)345 C)375 D)380 E)400
SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 680. Hence
3x + 5x = 680
Solve for x
8x = 680
x = 85
Number of boys
3x = 3 × 85 = 255
Number of girls
5x = 5 × 85 = 425
A #### A
QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2.
options: A)Cannot be determined B)1 C)2 D)3 E)4
SOLUTION:take square of any prime number
remainder will be 1
Ans B #### B
QUESTION:A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
options: A)299m B)287m C)279m D)100m E)277m
SOLUTION:A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D #### D
QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true?
options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11
SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E
QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test.
You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it?
options: A)48% B)55% C)60% D)71% E)80%
SOLUTION:C
60%
In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability.
In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already.
Therefore, P(Second/First) = P (First and Second)/ P (First)
= 0.25/0.42
=0.60
=60 % #### C
QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
options: A)10 B)12 C)15 D)20 E)25
SOLUTION:Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
ANSWER:B #### B
QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time?
options: A)s. 53.30 B)s. 53.22 C)s. 51.219 D)s. 53.18 E)s. 51.10
SOLUTION:Explanation:
Sum = (52 * 100) / (2 * 5) = Rs. 520
Amount = [520 * (1 + 5/100)2] = Rs. 573.3
C.I. = (573.3 - 520) = Rs. 53.30.
Answer:A #### A
QUESTION:A sum of money becomes triple itself in 5 years at simple interest. How many years will it become nine times at the same rate?
options: A)12 ½ years B)62 ½ years C)18 ½ years D)72 ½ years E)12 ½ years
SOLUTION:100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
900 ---- 18 ½ years
Answer:C #### C
QUESTION:The ratio of spinsters to cats is 2 to 7. If there are 40 more cats than spinsters, how many spinsters are there?
options: A)14 B)16 C)18 D)20 E)22
SOLUTION:Let 2x be the number of spinsters. Then 7x is the number of cats.
7x-2x=40
x=8 and the number of spinsters is 2(8)=16.
The answer is B. #### B
QUESTION:The cost of raw material of a product increases by 30, the manufacturing cost increases by 20 and the selling price of the product increases by 60. The raw material and the manufacturing cost, originally, formed 40 and 60 of the total cost respectively. If the original profit was one-fourth the original manufacturing cost, find the approximation new profit percentage.
options: A)48.38% B)54.68% C)62.48% D)42.36% E)None of these
SOLUTION:Explanation :
Let, the total initial cost of the product be Rs 100.
Manufacturing cost = Rs 60
Raw materials cost = Rs 40
Also, original selling price
=> Rs100+(60/4)= Rs 115.
New raw material cost
=>Rs 40+30% of 40= Rs 52.
New manufacturing cost
=>Rs 60+20% of 60= Rs 72
New cost of the product = Rs124
New selling price
=>115+60% of 115=Rs 184
New profit percentage
=>60/124×100
=>48.38%.
Answer : A #### A
QUESTION:How many digits are in (8×10^10)(10×10^5)?
options: A)17 B)25 C)26 D)27 E)28
SOLUTION:The question simplfies to (8×10^10)(10^6)
=> 8*10^16
=> Will contain 16 zeros +1 digit 8
=>17
Ans A #### A
QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
options: A)160 B)175 C)180 D)195 E)205
SOLUTION:Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 * 8 * 4) = 160.
Therefore, 160 * 2.40 + x * 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER:B #### B
QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper?
options: A)30 B)40 C)42 D)44 E)46
SOLUTION:here two cases are possible.
case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3
case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2
thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30
ANS:A #### A
QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month?
options: A)20 B)30 C)35 D)40 E)55
SOLUTION:Total = 75 books.
65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned.
Now, there are 66 books, thus 76-68=7 books are NOT returned.
{loaned out}*0.30=7 --> {loaned out}=30.
Answer: B. #### B
QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8?
I. x^2
II. y^2
III. xy
options: A)I only B)II only C)III only D)I and II only E)I, II and III
SOLUTION:4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is C #### C
QUESTION:If w is a positive integer and 10^w – 74 in decimal notation has digits whose sum is 440, what is the value of w?
options: A)40 B)44 C)45 D)46 E)50
SOLUTION:Answer E = 50
We have (10^w)-74, where the sum of the digits is 440.
100-74 = 26, so we already have 2+6 = 8 from the 440.
Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.
So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.
So we have 48 + 2 as an w = 50 #### E
QUESTION:Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (p,c). If c = 2, which of the following could be the equation of line m, which is perpendicular to line L?
options: A) 2x + y = px + 7 B) 2x + y = –px C) x + 2y = px + 7 D) y – 7 = x ÷ (p – 2) E) 2x + y = 7 – px
SOLUTION:So we need m=p-2, so we should get y=mx+b form in answer choices
(A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need
(B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong
(C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong
(E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong
A #### A
QUESTION:Which of the following must be divisible by 4, given that y is a positive integer?
options: A)(y−1)*y*(y+3) B)y^2*(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3)
SOLUTION:option A) (y−1)*y*(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A
QUESTION:Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in six hours, what fraction of the room can Joseph paint in 20 minutes?
options: A)1/6x B)x/(x-3) C)(x-6)/18x D)x/(x-6) E)(x-6)/x
SOLUTION:Let J be Joseph's rate per hour.
1/x + J = 1/6 of a room per hour
J = 1/6 - 1/x, of a room per hour
In 20 minutes, Joseph can paint 1/3*(1/6-1/x) = 1/18-1/3x = (x-6)/18x
The answer is C. #### C
QUESTION:A division of a company consists of five men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
options: A)2/5 B)2/7 C)2/9 D)2/11 E)2/13
SOLUTION:Total number of ways to select 2 members = 10C2 = 45
Total number of ways to select 2 females = 5C2 = 10
P(two females) = 10/45 = 2/9
The answer is C. #### C
QUESTION:If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)?
options: A)9. B)12. C)15. D)16 E)18.
SOLUTION:Expand this to get: (2X + Y)(2Z + W) = 4XZ + 2XW + 2YZ + YW
= 4 XZ + YW + 2XW + 2YZ [I rearranged the terms]
= 3 + 2XW + 2YZ [replaced 4XZ + YW with 3]
= 3 + 2(XW + YZ) factored out a 2
= 3 + 2(6)
= 3 + 12
= 15
ANSWER:C #### C
QUESTION:there is four light.all light glow in blue,white,yellow and red.
all glow together and take different color.every time each light change its color in given four of the color.but at same time no two light have same color then tell how many design will form?
options: A)20 B)24 C)18 D)16 E)22
SOLUTION:it is so simple,it is just permutation of 4 item.
4P4=4!=24
answer B #### B
QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 7.
options: A)18 B)20 C)17.5 D)30 E)32
SOLUTION:Solution
Average = (7+14+21+28)/4)
= 70 / 4
= 17.5.
Answer C #### C
QUESTION:What is the minimum number of square marbles required to tile a floor of length 3 metres 39cm and width 2 metres 26 cm?
options: A)176 B)187 C)540 D)748 E)6
SOLUTION:The marbles used to tile the floor are square marbles.
Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble.
As we have to use whole number of marbles, the side of the square should a factor of both 3 m 39 cm and 2m 26. And it should be the highest factor of 3 m 39 cm and 2m 26.
3 m 39 cm = 339 cm and 2 m 26 cm = 226 cm.
The HCF of 339 and 226 = 113.
Hence, the side of the square is 113.
The number of such square marbles required,
=339×226/113×113
=6 marbles
Option(E) #### E
QUESTION:If four coins are tossed, the probability of getting two heads and two tails is ?
options: A)3/8 B)3/6 C)3/1 D)3/2 E)3/4
SOLUTION:Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A #### A
QUESTION:In how many ways can 4 men & 3 women can be made from a gang of 6 men & 7 women ?
options: A)10 hr B)50 C)20 D)250 E)260
SOLUTION:Explanation:
6C4 * 7C3 = 50
B #### B
<<<Examples ends
QUESTION:A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income?
options: A)A)452000 B)B)200000 C)C)800000 D)D)500000 E)E)652000
SOLUTION:3 children got = 3*15% = 45%
wife got = 30%
orphan house = 5%
total = 45+30+5 = 80%
remaining = 100-80 = 20%
20% = 40000
100% = 40000*100/20 = $200000
Answer is B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg?
options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these
SOLUTION:Solution
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg
Answer D #### D
QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A - B is also a Even number.
(3) A^B is also a prime number.
options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3.
SOLUTION:Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A - B is also a Even number. : True
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans : C #### C
QUESTION:In a certain neighborhood, there are half as many beige houses as white houses, and 3 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?
options: A)4:1 B)3:5 C)2:3 D)1:3 E)1:4
SOLUTION:The ratio of beige:white:brown = 3:6:2
The answer is C. #### C
QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5
options: A)45 B)20 C)25 D)27 E)22
SOLUTION:Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5 = 20.
Answer:B #### B
QUESTION:Sum of 53 odd numbers is?
options: A)2709 B)2809 C)2909 D)3009 E)3109
SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 53 odd numbers = 53^2 = 2809
ANSWER:B #### B
QUESTION:The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there?
options: A)24 B)30 C)36 D)42 E)48
SOLUTION:Let the number of pens be 5x and the number of pencils be 6x.
6x - 5x = 5
x = 5
The number of pencils is 30.
The answer is B. #### B
QUESTION:A certain ski shop sells pairs of gloves in 11 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?
options: A)1/144 B)1/143 C)1/21 D)1/23 E)1/12
SOLUTION:there are 11 different colours sothere are 11 pairs of gloves dropped..
first can be any of 22..so 22/22..
second has to be its pair, which will be just one out of remaining 21.. 1/21..
overall prob=22/22*1/21= 1/21..
C #### C
QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
options: A)3 1/5 Km B)4 Km C)4 1/5 Km D)3 2/5 Km E)3 3/5 Km
SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A #### A
QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.
options: A)13 B)14 C)15 D)16 E)17
SOLUTION:Length of longest pole = Length of the diagonal of the room
= sqrt(12^2+8^2+9^2= sqrt(289)= 17 m.
Answer is E. #### E
QUESTION:In a coconut grove, (x + 3) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 3) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
options: A)3 B)4 C)5 D)6 E)None of the above
SOLUTION:(x+3)×60+x×120+(x−3)×180/(x+3)+x+(x−3)=100
⇒ 360x−360/3x = 100
⇒ 60x = 360 ⇒ x = 6
Answer D #### D
QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350
SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C #### C
QUESTION:After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 200 billion gallons, the reservoir was approximately what percentage full before the storm?
options: A)45% B)48% C)50% D)58% E)65%
SOLUTION:When the storm deposited 120 billion gallons, volume of water in the reservoir = 200 + 120 = 320 billion gallons
If this is only 80% of the capacity of the reservoir, the total capacity of the reservoir = 320/0.8 = 400 billion gallons
Therefore percentage of reservoir that was full before the storm = (200/400)*100 = 50%
Option C #### C
QUESTION:Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm.
options: A)227 B)299 C)300 D)161 E)212
SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (22 + 18) * (15)
= 300 cm2
Answer: C #### C
QUESTION:Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
options: A)456 B)234 C)285 D)342 E)213
SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
Answer: Option C #### C
QUESTION:A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight?
options: A)20 lb B)11 lb C)10 lb D)15 lb E)5 lb
SOLUTION:Sol.
66÷6 = 11.
Answer : B #### B
QUESTION:What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10?
options: A)5 B)7 C)4 D)9 E)3
SOLUTION:30,40,50,60,70
total 5
Answer is A #### A
QUESTION:Joe has a total of $200 in his two pockets. He takes one fourth of the
money in his left pocket and puts it in his right pocket. He then takes
$20 from his left pocket and puts it in his right pocket. If he now has
an equal amount of money in each pocket, then how much money did he
originally have in his left pocket?
options: A)$120 B)$130 C)$140 D)$150 E)$160
SOLUTION:Joe had $100 in his left and $100 in his right pocket at the end. So, he had $120
in his left pocket (and $80 in his right pocket) before moving $20 from his left to his
right pocket. Thus, he had $160 in his left pocket originally (solve x − x/4 = 120).
correct answer E #### E
QUESTION:Set L is composed of nine numbers, labeled L1 through L9. Set M is also composed of nine numbers, labeled M1 through M9. Set M is defined as follows: M1 = 1 + L1; M2 = 2 + L2; and so on, including M9 = 9 + L9. How much larger is the sum of set M's mean and range than the sum of set L's mean and range?
options: A)3 B)4 C)cannot be determined D)6 E)8
SOLUTION:Yes, the correct answer is C #### C
QUESTION:Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day A on which the buses leave at the same time.
options: A)A=Tuesday B)Wednesday C)Thursday D)Sunday E)A=The busses will never leave at the same time
SOLUTION:The answer is E.
I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.
Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E #### E
QUESTION:How many 3-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same?
options: A)1236 B)504 C)4096 D)4608 E)6561
SOLUTION:First digit.. 9 posibilities
Second digit, 8 possibilities
third digit, 7 possibilities
9*8*7 = 504.
B #### B
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)240 B)377 C)2908 D)287 E)201
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: A #### A
QUESTION:The sum of the non-prime numbers between 10 and 20, non-inclusive, is
options: A)60 B)75 C)90 D)105 E)120
SOLUTION:sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 * # of terms = (11 + 19)/2 * 9 = 15 *9 = 135
sum of non-prime numbers b/w 10 and 20, non inclusive ===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75
Answer: B #### B
QUESTION:(1+0.0001)/(0.04+10000)
The value of the expression above is closet to which of the following?
options: A)0.0001 B)0.001 C)0.1 D)1 E)10
SOLUTION:Notice that we need approximate value of the fraction.
Now, the nominator is very close to 1 and the denominator is very close to 10, hence the value of the fraction is very close to 1/10000=0.0001.
Answer: A #### A
QUESTION:10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day?
options: A)4 days B)10 days C)20 days D)25 days E)26 days
SOLUTION:Explanation:
10*12*15/20 = 24*20*x/32
X=4
Answer: Option A #### A
QUESTION:The average of first ten prime numbers which are odd is?
options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5
SOLUTION:Sum of first 10 prime no. which are odd = 158
Average = 158/10
= 15.8
Answer:D #### D
QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr.
SOLUTION:Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=24 or x=12.
Rate upstream=12 km/hr,rate downstream=36 km/hr.
Hence,rate of stream=1/2(36-12)km/hr=12 km/hr.
Answer is B. #### B
QUESTION:Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
options: A) 3 B) 6 C) 7.2 D) 5 E) 9
SOLUTION:Answer is D.
x/x+36=1/5
x=9
14-9=5 #### D
QUESTION:A = {0, 1, -3, 6, -8, -10}
B = {-1, 2, -4, 7, 6, -9}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0?
options: A)1/4 B)1/3 C)5/13 D)5/12 E)1/2
SOLUTION:For the product of 2 numbers to be negative either of them must be positive or negative:
P(positive, negative) = 2/6*3/6 = 6/36;
P(negative,positive ) = 3/6 * 3/6 = 9/36
P = 6/36 + 9/36
P = 15/36
P = 5/12
Answer: D #### D
QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers?
options: A)4 B)2 C)3 D)5 E)1
SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42
factors of 104 - 1,2,4,8,13,26,52,104
Comparing both, we have two common factors of 40 and 104- 1,2,
Answer(B) #### B
QUESTION:A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings?
options: A)12 B)13 C)46 D)37 E)26
SOLUTION:16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D #### D
QUESTION:Sophika can buy watches at a price of P dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of P and X and Y, what is the percent of the markup from her buy price to her sell price?
options: A)(YP)/100X B)100X/(YP) C)(YP)+100X D)(YP)-100X E)(YP)*100X
SOLUTION:Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/P *100 = 100X/(YP)
Answer : B #### B
QUESTION:An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
options: A)8877 B)3000 C)7787 D)1799 E)1711
SOLUTION:4 --- 2000
5 --- ? => 3000
Answer: B #### B
QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph
SOLUTION:Speed downstream = 55 + 20
= 75 kmph
Speed upstream = 55 - 20
= 35 kmph
Answer: C #### C
QUESTION:If n = 20! + 19, then n is divisible by which of the following?
I. 15
II. 17
III. 19
options: A)I only B)II only C)III only D)I and II E)II and III
SOLUTION:19 divides 20! so 19 also divides 20! + 19.
15 and 17 divide 20! so they do not divide 20! + 19.
The answer is C. #### C
QUESTION:Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
options: A)7/8 B)1/8 C)1/3 D)1/5 E)1/9
SOLUTION:Original share of 1 person =1/6
New share of 1 person =1/5
Increase =1/5 - 1/6 =1/30
Required fraction = (1/30)/(1/6)=1/5
Answer is D. #### D
QUESTION:Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.?
options: A)8 B)12 C)14 D)16 E)18
SOLUTION:Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+30
3x + 6 = x + 30
2x = 24
\inline \therefore x = 12
\inline \therefore Middle number = x + 2 = 12+2 = 14
C #### C
QUESTION:Reeya obtained 40, 60, 70, 80 and 80 out of 100 in different subjects, What will be the average
options: A)66 B)75 C)80 D)85 E)90
SOLUTION:Explanation:
(40+60+70+80+80 / 5)=66
Option A #### A
QUESTION:If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area?
options: A)26% B)21% C)15% D)18% E)12%
SOLUTION:a =1/2 x b x h or 1/2 x 2a x a(for simplification)
New h = 220a / 100 = 22a / 10
New b =(110a x 100) ==11a/10
New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100)
increased area== (121a²/100) - a²
Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21%
answer :B #### B
QUESTION:A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
options: A)130 B)360 C)500 D)540 E)580
SOLUTION:L = 800 m
S = 78kmph = 65/3 mps
Time to pass tunnel = 1min = 60 sec
t.f (800+X)/(60) = (65/3)
=500
ANSWER:C #### C
QUESTION:A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
options: A)2880. B)4860. C)5780 D)4320 E)6380.
SOLUTION:Normal Day = 600 kw/h
Stormy Day = 600*1.2=720 kw/h
3 windmills for 2 hours on stormy day
720*3*2=4320
Answer: D #### D
QUESTION:A and B can do a work in 8 days, B and C can do the same work in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days?
options: A)7 B)6 C)5 D)8 E)9
SOLUTION:Let the total units of work be 48.
Units of work completed by A and B in one day = 6.
Units of work completed by B and C in one day = 4
Units of work completed by A, B, and C in one day = 8.
From the above information we get the work completed by A and C in one day is 6 units.
Therefore, the number of days taken by A and C to complete the whole work = 48/6 = 8 days.
ANSWER:D #### D
QUESTION:A corporation ten times its annual bonus to 25 of its employees. What percent of the employees’ new bonus is the increase?
options: A)25% B)44% C)38% D)9% E)90%
SOLUTION:Let the annual bonus be X.
A corporation triples its annual bonus.
So new bonus = 10X.
Increase = 10X-X =9X
The increase is what percent of the employees’ new bonus
= (9X/10X)*100
= 90%
Hence E. #### E
QUESTION:How many digits are required to number a book containing 260 pages?
options: A)784 B)672 C)492 D)372 E)300
SOLUTION:9 pages from 1 to 9 will require 9 digits.
90 pages from 10 to 99 will require 90*2=180 digits.
260-(90+9)=161 pages will require 161*3=483 digits.
The total number of digits is 9+180+483=672.
The answer is B. #### B
QUESTION:A man buys 1kg of sandalwood and 1kg of teakwood. He sells one for 10% profit and other for 10% loss. What is total profit/loss percentage?
options: A)1% loss B)2% loss C)3% loss D)4% loss E)5% loss
SOLUTION:if x is both the profit and loss % then it must be loss of x^2/100;
so 10*10/100=1;
1% loss
ANSWER:A #### A
QUESTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
options: A) Two B) Three C) Four D) Six E) Eight
SOLUTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 8p have.
p = 3 --> 8p = 24--> 24 has 6 even divisors: 2, 4, 6, 8, 12, 24.
Answer: D. #### D
QUESTION:Sixty percent of a number is 21 less than four fifth of that number. What is the number ?
options: A)240 B)140 C)230 D)130 E)105
SOLUTION:Let the number be x.
Then, 4*x/5 –(60% of x) = 21
4x/5 – 60x/100 = 21
x = 105.
Answer E. #### E
QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
options: A)256 B)512 C)4096 D)1024 E)1536
SOLUTION:0.4*2^10=0.4*1024=409.6
The answer is C. #### C
QUESTION:If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number S of integers that can be negative?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:Minimuum should be 1
Maximum should be 4:
1 out of a or b to make the multiplication negative
3 out of c, d, e or f to make the multiplication negative.
Negative+Negative<0
Answer:C
maximum will be 5..
you dont require both the multiplicatin to be negative for entire equation to be negative...
any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers...
actually by writing minimum required as 1 out of 6,you are actually meaning S= 5 out of 6 also possible as you will see 5 or 1 will give you same equation..
ans D #### D
QUESTION:Five carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if four of the carpenters work together at their respective rates ?
options: A)11/15 B)3/5 C)11/30 D)47/75 E)5/9
SOLUTION:Farmer A, B, C, and D
A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour
By intuition we know that the three fastest farmers are A B and C.
As such
(1/3 + 1/4 + 1/5)*(4/5) = ?
47/75 or (D) #### D
QUESTION:A train 310 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
options: A)4 B)6 C)5 D)17 E)13
SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [310 * 3/55] sec = 17 sec
ANSWER:D #### D
QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E?
options: A)60 B)80 C)40 D)120 E)160
SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30
(9/8)x - (3/4)x = 30
x = 80=E
Answer: B #### B
QUESTION:The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
options: A)6535 B)6532 C)6725 D)6874 E)6972
SOLUTION:C
6725
CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725 #### C
QUESTION:If f(x)=x^2 and x is a positive integer, which of the following will not be the value of f(f(x))?
options: A)1 B)16 C)81 D)256 E)144
SOLUTION:f(x)=x^2
f(f(x)) = (x^2)^2
=x^4
A. 1 , x=1
B. 16 , x=2
C. 81 , x=3
E. 144
f(x)=12
Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) .
D. 256 , x=4
Answer E #### E
QUESTION:A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
options: A)a) 5 inches B)b) 6 inches C)c) 7 inches D)d) 8 inches E)e) 10 inches
SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
25=5*5
35=5*7
GCF = 5
P.S you can make squares with side of 5
Answer : A #### A
QUESTION:A shopping mall give 40% sale on T-shirts and increase 25% price of pants. The cost price of pants and T-shirts are 1500 and 400 respectively. Overall they makes a?
options: A)200 B)250 C)300 D)215 E)180
SOLUTION:Let the SP of the pants and T-shirts be Rs. p and Rs. t respectively.
p = 1500(1 + 25/100) = 1500 + 375
t = 400(1 - 40/100) = 400 - 160
Total SP - Total CP = p + t - (1500 + 400) = 375 - 160 = Rs. 215
As this is positive, an overall profit of Rs. 500 was made.
Answer: D #### D
QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
options: A)8:9 B)8:7 C)8:1 D)8:2 E)8:8
SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
Answer:B #### B
QUESTION:A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m?
options: A)29798 B)27908 C)24000 D)25000 E)27991
SOLUTION:24 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
24 = 1/100 * x => x
= 24000
Answer: C #### C
QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
options: A)20% B)30% C)32% D)73% E)84%
SOLUTION:SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 ---20 => 20%
Answer:A #### A
QUESTION:Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 27 seconds. What is the length of each train (in meters)?
options: A)50.5 B)88.5 C)37.5 D)55.5 E)23.5
SOLUTION:The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 27 seconds, the relative difference in distance traveled is 27 * 25/9 = 75 meters
This distance is twice the length of each train.
The length of each train is 75/2 = 37.5 meters
The answer is C. #### C
QUESTION:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth?
options: A)39 B)24 C)28 D)26 E)30
SOLUTION:x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
x+32
x+36
10x+180=340
10x=160
x=16
3rd question = x+8 = 16+8 = 24
Answer B #### B
QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
options: A)20% B)26% C)42% D)27% E)22%
SOLUTION:SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A #### A
QUESTION:How many numbers are there between 200 and 800 which are divisible by both 5 and 7?
options: A)35 B)16 C)17 D)can’t be determined E)None of these
SOLUTION:Answer C
Solution
In the given range, the last number which is divisible by both 5 and 7. i.e., 35 is 210 and the highest number is 770. So the total number of numbers between 200 and 800 which are divisible by both 5 and 7 is
(770-210/35)+ 1 = 17
Hence option C #### C
QUESTION:Marie has 248 $ in her account of the bank. She has to buy presents for her 7 children and wants to distribute the money fairly. How much he will once have the money shared fairly?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:(248$ / 7children) = 35.42
Took the lowest number = 35 * 7 children = $245
$248 - $245 = staying $3
Correct option: C) 3$ #### C
QUESTION:Subtracting 10% from X is the same as multiplying X by what number?
options: A)80% B)90% C)10% D)50% E)60%
SOLUTION:Explanation:
X - (10/100) X = X * ?
? = 90%
ANSWER IS B #### B
<<<Examples ends
QUESTION:Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
options: A)30 B)90 C)120 D)168 E)188
SOLUTION:I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168
Using your analysis:
We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168 = 232
So, in the image we know that the number of students in the zone with the black boundary = 232
Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)
And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w
Since the total number of students = 400, we can write:
232 +b+w= 400
Or,b+w= 400 - 232 = 168
That is,b= 168 -w
So, the maximum value ofbwill happen forw= 0
This is how we get, the maximum value ofb= 168
D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?
options: A)25% B)33 1/3% C)50% D)66 2/3% E)75%
SOLUTION:General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the time between maintenance checks increased by 25−20/20∗100=25
Answer: A. #### A
QUESTION:The remainder when 1!+2!+3!...+50! divided by 8! will be
options: A)21 B)5193 C)77 D)9275 E)19
SOLUTION:The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!.
So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!.
So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320)
So remainder is 5193.
Answer:B #### B
QUESTION:A ball is bought for Rs.400 and sold at a gain of 20% find its selling price?
options: A)Rs.480/- B)Rs.490/- C)Rs.500/- D)Rs.520/- E)Rs.540/-
SOLUTION:100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
A #### A
QUESTION:Evaluate combination
100C100
options: A)10000 B)1000 C)10 D)1 E)0
SOLUTION:Explanation:
nCn=1
100C100=1
Option D #### D
QUESTION:Set A contains all the even numbers between 8 and 50 inclusive. Set B contains all the even numbers between 108 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
options: A)2200 B)2550 C)5050 D)6275 E)11325
SOLUTION:Set A contains 8, 10, 12... 50
Set B contains 108 , 110 , 112 ... 150
Number of terms in each set = 22
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*22 = 2200
Answer A #### A
QUESTION:A scuba diver descends at a rate of 32 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 6400feet below the sea level..how long will he take to reach the ship?
options: A)200 minutes B)240 minutes C)220 minutes D)210 minutes E)77 minutes
SOLUTION:Time taken to reach = 6400/32= 200 minutes
ANSWER:A #### A
QUESTION:A company spends an average of $500 for its 20 employees's salaries and an average of $100 for its 5 drivers' salaries. What is the average expenditure of the company?
options: A)$360 B)$290 C)$420 D)$600 E)$240
SOLUTION:Number of employees is 20
Their average salary is $500
Number of drivers is 5
Their average salary is $100
Total salary of the employees is 20*500=$10,000
Total salary of the drivers is 5*100=$500
Total expenditure for company is 10,000+500=$10,500
Average expenditure is 10,500/20+5=$420
Answer is C #### C
QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40
SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35
P(at least one graduate) = 1- 1/35 = 34/35
The answer is D. #### D
QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ?
options: A)-1 B)-5 C)-2 D)-3 E)-4
SOLUTION:Use answer options to solve this problem -
x is negative integer (-1,-2,-3......)
put x=-1
7x+3y=14
7(-1)+3y=14
-7+3y=14
3y=14+7
3y=21
y=7
Answer will be (A) #### A
QUESTION:Find a sum for first 12 prime no's from number series?
options: A)190 B)178 C)197 D)189 E)100
SOLUTION:Required sum = (2+ 3+ 5+ 7+11+ 13+17+ 19+23+ 29+31+37) = 197
Note: 1 is not a prime number
Option C #### C
QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13
SOLUTION:Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 650 = 13
Answer: E #### E
QUESTION:If A = B/C, -1 < C < 0 and 4 < B, which of the following is correct?
options: A)A > 4. B)0 < A <4. C)-4 < A < 0. D)A < -4. E)A < -20.
SOLUTION:B is +veC is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take B=4.1A=-0.9
A=4.1/-0.9
A<-4
Ans D #### D
QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence?
I. w-6,x-6,y-6,z-6
II. 5w,2x,3y,5z
III. 5w,5x,5y,5z
options: A)II and III B)III only C)I and III D)I and II E)II only
SOLUTION:lets look at the three choices...
I. w-6,x-6,y-6,z-6
since the difference is constant, it is an arithmetic sequence...
II. 5w,2x,3y,5z
since the difference is not constant, it is not an arithmetic sequence
III. 5w,5x,5y,5z
since the difference is constant it is an arithmetic sequence...
Answer is A) #### A
QUESTION:Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3.
options: A)131 B)197 C)207 D)219 E)227
SOLUTION:Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3.
Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1) = 131.
ANSWER:A #### A
QUESTION:In what time will a train 125 m long cross an electric pole, it its speed be 130 km/hr?
options: A)3.5 B)2.7 C)2.9 D)2.3 E)2.1
SOLUTION:Speed = 130 * 5/18 = 36 m/sec
Time taken = 125/36
= 3.5 sec.
Answer: A #### A
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent?
options: A)28% B)25% C)11.11% D)28% E)55%
SOLUTION:900 --- 100
100 --- ? => 11.11%
Answer: C #### C
QUESTION:The true discount on a bill of Rs.4320 is Rs.720.The banker's discount is
options: A)862 B)864 C)866 D)868 E)None of these
SOLUTION:Solution
P.W = Rs.(4320 - 720)
= Rs. 3600
S.I on Rs. 4320 =Rs.(720/3600 x 4320)
= Rs. 864.
Answer B #### B
QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
options: A)20% B)40% C)50% D)60% E)70%
SOLUTION:70 + 55 + 35 = 160%
The number is 60% above 100% because 60% of the counties were counted twice.
The answer is D. #### D
QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.
options: A)13 B)14 C)15 D)16 E)17
SOLUTION:Length of longest pole = Length of the diagonal of the room
= sqrt(12^2+8^2+9^2= sqrt(289)= 17 m.
Answer is E. #### E
QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5
options: A)45 B)20 C)25 D)27 E)22
SOLUTION:Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5 = 20.
Answer:B #### B
QUESTION:The average of first four prime numbers greater than 30 is?
options: A)38 B)20 C)30 D)40 E)50
SOLUTION:31 + 37 + 41 + 43 = 152/4 = 38
ANSWER:A #### A
QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers?
options: A)28 B)56 C)76 D)84 E)85
SOLUTION:Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 48
=> 12x = 48
=> x = 48/12 = 4
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 4 = 28
Answer: Option A #### A
QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B?
options: A)7 B)9 C)8 D)11 E)10
SOLUTION:Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 22
⇒ 5x = 20
⇒ x = 4.
Hence, B's age = 2x = 8 years.
Answer: C #### C
QUESTION:In expressing a length of 25.461 km as nearly as possible with the three significant digits, find the percentage error
options: A)0.353% B)0.153% C)0.035% D)0.015% E)None of these
SOLUTION:Explanation:
Error = (25.5 - 25.461) = 0.039
Required percentage =
0.039/ 25.461×100=0.153
Option B #### B
QUESTION:The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
options: A)47.55 kg B)48 kg C)48.55 kg D)49.25 kg E)59.25 kg
SOLUTION:16*50.25+8*45.15/24=48.55
ANSWER:C #### C
QUESTION:In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive?
options: A)48400 B)48000 C)48100 D)48500 E)48600
SOLUTION:Assume that investment of C =x
Then, investment of A =2x
Investment of B =4x/3
A:B:C =2x:(4x)/3:x
=2:4/3:1=6:4:3
B's share =157300×4/(6+4+3)
=157300×4/13=12100×4=48400
Answer is A. #### A
QUESTION:If 18 is 15 percent of 25 percent of a certain number, what is the number?
options: A)9 B)36 C)480 D)81 E)400
SOLUTION:Let the certain number be x.
=> (15/100)*(25/100)*x = 18;
=> x=480;
Ans is (C). #### C
QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is?
options: A)1 B)4 C)5 D)6 E)7
SOLUTION:4.5 4.5
45% 55%
45% ----- 4.5
55% ------? => 5.5 - 4.5 = 1 ml
ANSWER:A #### A
QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h?
options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4
SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E #### E
QUESTION:Find the compound interest on $1000 in 2years at 4% per annum, the interest being compounded half-yearly?
options: A)$645.56 B)$82.43 C)$954.26 D)$745.69 E)$1020.45
SOLUTION:Principle = $10000
Rate = 2% half yearly = 4 half years
Amount = 1000*(1 + 2/100)^4 = 1000 * 51/50 * 51/50 * 51/50 * 51/50
= $1082.43
C.I. = 1082.43-1000 = $82.43
Answer is B #### B
QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
options: A)26 B)39 C)42 D)65 E)156
SOLUTION:Here 156 has three two's
two three's
and one 13
rest of them must be in w
so w= 13*3*4 = 156
Answer: E #### E
QUESTION:Machine A can put caps on a set of bottles in 8 hours at a constant rate. If Machine A does the job for 6 hours and Machine B does the rest of the job, which works at 1/4 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?
options: A)4hrs B)6hrs C)8hrs D)10hrs E)16hrs
SOLUTION:machine A will do 6/8 in 6 hrs, so A does 3/4 of the work ..
Therefore, B will do the remaining 1/4 th work alone..
As the speed of B is 1/4 rate of A, B will do the 1/4th work in same time that A takes to complete full job...
ans 8
C #### C
QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet?
options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am
SOLUTION:meet x hrs after 8 a.m.
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
==>60x+75(x-1) = 330
x=3.
So,they meet at (8+3). i.e 11a.m.
ANSWER A #### A
QUESTION:Some of the 68% solution of acid was removed and this was replaced with an equal amount of 11% solution of acid. As a result, a 35% solution of acid was obtained. What fraction of the original solution was replaced?
options: A)7/11 B)7/17 C)8/17 D)8/19 E)11/19
SOLUTION:Let x be the fraction of the original solution that was replaced.
0.68*(1-x)+0.11(x)=0.35
0.57x=0.33
x=33/57=11/19
The answer is E. #### E
QUESTION:A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
options: A)40 B)50 C)62 D)45 E)56
SOLUTION:Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+100 = 11x
x = 100-50 = 50
Answer is B #### B
QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:For: (2^(3x+3)+3)/3
Let n = 3x + 3
2^n
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, ....
Rule: x^(m+n) = (x^m)(x^n)
(2^(3x))(2^3)
Rule: x^(mn) = (x^m)^n
((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1.
Answer: B #### B
QUESTION:The cost of an item was reduced from its usual selling price of $23.99 to $16.99. Which of the following is closest to the percent decrease in the price of the item?
options: A)17% B)21% C)24% D)29% E)42%
SOLUTION:The price decreased by 23.99 - 16.99 = $7.
$7 is a bit more than 29% of original price of $24.
Answer: D. #### D
QUESTION:The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
options: A)21:22 B)7:8 C)2:1 D)21:24 E)14:16
SOLUTION:Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
= (120/100) 7x and (110/100) 8x
= 42x/5 and 44x/5
Therefore, The required ratio = (42x/5):(44x/5)
= 21 : 22. Answer is A. #### A
QUESTION:If the area of a square with sides of length 5 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
options: A)4 B)8 C)12 D)7 E)18
SOLUTION:Let length of rectangle = L
5^2 = L*4
=> L = 25/4 = 7
Answer D #### D
QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29
options: A)12 B)9 C)1 D)3 E)29
SOLUTION:12 is an even number. All other given numbers are odd
Answer is A #### A
QUESTION:Find the odd man out. 12, 24, 36, 48, 61, 72, 84
options: A)15 B)25 C)61 D)90 E)115
SOLUTION:Explanation :
All except 61 are multiples of 7
Answer : Option C #### C
QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840
SOLUTION:11+6=17%, therefore 17/100*6000= 1020, now add 1020 + 580= 1600. (B) #### B
QUESTION:If the set S is composed of the following numbers {99, 100, 100, 105, 106, 115, 124}, which of the following is largest?
options: A)The average (arithmetic mean) of set S B)The median of set S C)The mode of set S D)The range of set S E)The standard deviation of set S
SOLUTION:A) 99, 100, 100, 105, 106, 115, 124 = 749 and its mean is 749/7 = 107.
B) The list is of 7 numbers and median is 105.
C) Mode is number of repetition of a number in the list , here it is 100.
D) Range = Max value - min value = 124 -99 = 25.
E) SD = square root of (sum of ( mean of series - number)^2 ) / n => < 100
IMO option A is correct answer.. #### A
QUESTION:Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year?
options: A)142% B)150% C)165% D)176% E)188%
SOLUTION:Let last year's salary be x.
Last year, Sandy save 0.1x
This year, Sandy saved 0.15*1.1x = 0.165x
0.165x / 0.1x = 1.65 = 165%
The answer is C. #### C
QUESTION:Due to 10% decrease in the price of sugar and John can buy 4kg more sugar in Rs100 , then find the CP of sugar?
options: A)s. 1(2/9) B)s. 2(7/9) C)s. 2(1/9) D)s. 3(2/7) E)s. 4(2/9)
SOLUTION:Here r = 10 % ,x = 100 and A = 4 kg
Actual price of sugar = 10*100/((100-10 )*4) = Rs. 2(7/9)
B #### B
QUESTION:If the cost price is 96% of the selling price, then what is the profit percent?
options: A)4.17% B)5% C)6.12% D)3.25% E)5.75%
SOLUTION:Let S.P. = $100
C.P. = $96
Profit = $4
Profit% = 4/96 * 100 = 25/6 = 4.17%
Answer is A #### A
QUESTION:The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?
options: A)5 kmph B)67 kmph C)22 kmph D)88 kmph E)12 kmph
SOLUTION:Speed of the boat in still water
= (60+70)/2
= 65 kmph. Speed of the stream
= (70-60)/2
= 5 kmph.
Answer:A #### A
QUESTION:Which of the following describes all values of x for which 4–x^2 >= 0?
options: A) x >= 1 B) x <= –1 C) 0 <= x <= 1 D) x <= –1 or x >= 1 E) –2 <= x <= 2
SOLUTION:4 - x^2 >=0
means x^2 - 4 <=0
=> (x-2)(x+2) <= 0
=> -2 <= x <= 2
Answer - E #### E
QUESTION:Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side?
options: A)20,25 B)21,25 C)27,23 D)28,25 E)30,25
SOLUTION:Let the two parallel sides of the trapezium be a cm and b cm.
Then, a-b = 4 ------ (1)
And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2)
Solving 1 and 2, we get: a=27,b=23
So, the two parallel sides are 27 cm and 23 cm.
C #### C
QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
options: A)1687 B)1478 C)1480 D)14000 E)1500
SOLUTION:25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D #### D
QUESTION:If two-third of a bucket is filled in one minute then the time taken to fill the bucket completely will be .
options: A)90 seconds B)70 seconds C)60 seconds D)100 seconds E)120 seconds
SOLUTION:2/3 filled in 1 mint
1/3 filled in 1/2 mint
thn 2/3+1/3=1 in mint 60 sec+30 sec=90 sec
ANSWER:A #### A
QUESTION:A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
options: A)270 B)360 C)480 D)600 E)400
SOLUTION:as given 3 out of every 4 bruised apple is not fit to sell
or, 75% of the bruised apples are not fit to sell.
as per the question 12 are not fit to sell
or,
0.75x=12
x=1200/75=16
thus total number of bruised apples =16
total number of apples =25*16=400
Answer: E #### E
QUESTION:In store A there are 10 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores B earned to the total amount store A earned?
options: A)3:1 B)2:3. C)1:3. D)3:4. E)2:5.
SOLUTION:1st statement : ratio of pants
Store A : Store B
10x : 40x
X:4X
Price :
4y:3y
Total revenue
4xy : 12xy
3:1
Answer : A #### A
QUESTION:A car covers a distance of 424 km in 6 ½ hours. Find its speed?
options: A)65.9 kmph B)75.2 kmph C)65.2 kmph D)66.2 kmph E)55.2 kmph
SOLUTION:424/(13/2) = 424*2/13
=65.2 kmph
ANSWER:C #### C
QUESTION:1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus?
options: A)98 B)99 C)97 D)96 E)95
SOLUTION:Let x be the no of initial passenger
no of passengr left in 1st stop (2x/3)+30
no of passenger in the 2nd stop 3/4((2x/3)+30) + 12
which is equal to 84 (passngr on last stop)
so final eqn....3/4((2x/3)+30) + 12 = 84
Ans x = 99
ANSWER:B #### B
QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
options: A)4:5 B)3:5 C)6:8 D)3:5 E)5:4
SOLUTION:third number be x.
first no = 120% of x = 6x/5
second no = 150% of x = 3x/2
ratio in first two nos = (6x/5:3x/2)=> 4:5
ANSWER A #### A
QUESTION:A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
options: A)days B)days C)days D)1/2 days E)days
SOLUTION:Explanation:
10/40 + 10/30 + 10/x = 1
x = 24 days
Answer: A #### A
QUESTION:The lowest number which should be added to 8247 so that the sum is exactly divisible by 5, 6, 7, 8 and 9 is:
options: A)1833 B)1853 C)1733 D)1233 E)1832
SOLUTION:L.C.M. of 5, 6, 7, 8 and 9 = 2520.
On dividing 8247 by 2520, the remainder is 687.
Number to be added = (2520 - 687) = 1833. Answer: Option 'A' #### A
QUESTION:The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds?
options: A)4 B)9 C)39 D)48 E)63
SOLUTION:Given: z=s^2+2s for 0≤s≤7
z(4) = 4^2 + 2*4 = 24
z(7) = 7^2 + 2*7 = 63
Therefore z(7) - z(3) = 63 - 24 = 39 km/hr
Option C #### C
QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
options: A)72 6/7% B)82 6/7% C)22 6/7% D)42 6/7% E)82 2/7%
SOLUTION:Explanation:
SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D #### D
QUESTION:In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively?
options: A)10,16 B)8,14 C)16,22 D)14,20 E)12, 18
SOLUTION:Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 4) + (x + 10) = 30
=> 2x + 14 = 30 => x = 8
The third number = x + 4 = 8 + 4 = 12.
The sixth number = x + 10 = 8 + 10 = 18.
Answer: E #### E
QUESTION:A bag contains 6 green jacks and 24 white jacks. One jack is drawn at random. What is the probability that the jack is white?
options: A)3/4 B)4/5 C)7/8 D)1 E)None of these
SOLUTION:Explanation:
Total cases = 6 + 24 = 30
Favourable cases = 24
So probability = 24/30 = 4/5
Answer: A #### A
QUESTION:A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
options: A)10 B)12 C)15 D)20 E)30
SOLUTION:Two students can be selected from 6 in 6C2 =15 ways.
Therefore, the teacher goes to the zoo 15 times.
Option C is answer #### C
QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total?
options: A)16 B)12 C)18 D)22 E)08
SOLUTION:2*6=12.Answer is B. #### B
<<<Examples ends
QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 10 years?
options: A)30 B)35 C)40 D)50 E)60
SOLUTION:Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 10 years = (20 + 10) years =30 years.
Answer : A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
options: A)5 B)9 C)4 D)1 E)3
SOLUTION:US = 25
DS = 35
M = (35 - 25)/2
= 5
Answer: A #### A
QUESTION:A starts a business with a capital of Rs. 9,000. B joins in the business with Rs.18,000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
options: A)2 months B)6 months C)7 months D)8 months E)None of these
SOLUTION:Explanation :
Let B joins for x months. Then
A:B = 9000*12 : x* 18000 = 3 : 1
=> 9*12 : 18x= 3 : 1
=> 9*12/ 18x = 3/1 = 3
=> 9*4 /18x = 1
=> 2/x = 1
=> x = 2. Answer : Option A #### A
QUESTION:Which of the following lines has x-intercept and y-intercept that are integers T?
options: A)y=3x+1 B)y=√x+1 C)y=-2/x D)y=x^2-1 E)xy=1
SOLUTION:Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers T and the correct answer is D. #### D
QUESTION:If n is a positive integer, what is the remainder when (6^(4n+3))(6^n) is divided by 10?
options: A)7 B)2 C)4 D)6 E)8
SOLUTION:This one took me bout 3 1/2 min. Just testin numbers and what not.
First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.
1-7 stands for ^1 thru 6
1: 7*1=7
2: 7*7=9
3: 7*9=3
4: 7*3=1
5: 7*1=7
6: 7*7=9
7: 7*9=3
Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.
so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8
Now from here if id double check just to make sure.
7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit).
Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern)
so again 3*6=18/10 ---> R =7.
A or J in this problem. #### A
QUESTION:A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
options: A)6 ½ days B)1 ½ days C)8 ½ days D)5 ½ days E)2 ½ days
SOLUTION:Explanation:
3/20 * 2 + (2 + x)/5 = 1
x = 1 ½ days
Answer:B #### B
QUESTION:How many quarters are equal to 7 dollars?
options: A)1 B)28 C)12 D)9 E)7
SOLUTION:7 * 4 = 28 quarters
Answer : B #### B
QUESTION:400 students took a mock exam in Delhi, 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination?
options: A)50 B)100 C)120 D)140 E)180
SOLUTION:60%*x+80%*(400-x)=65%*400
Ans=100
ANSWER:B #### B
QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed?
options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr
SOLUTION:Let the speed be x km/hr
50x-50* 9/10 *x = 450
50x - 45x = 450
x = 90km/hr
Answer is E #### E
QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)?
options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5
SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57)
4.5/(4.5 - 2) = 9/5 (1.8)
3.5/(3.5 - 2) = 7/3 (~2.33)
2.5/(2.5-2) = 5
1.5/(1.5 - 2) = -3
Thus, the answer is D. #### D
QUESTION:An investment compounds annually at an interest rate of 33.34% What is the smallest investment period by which time the investment will more than triple in value?
options: A)1 B)2 C)3 D)5 E)4
SOLUTION:Assume initial amount is x
Annual Interest is 34.1% so after 1 year the amount will become x * (100+33.34)/100 => x*4/3
now we need to find n for x * (4/3)^n = 3x
or in other words n = 4
E #### E
QUESTION:There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
options: A)A)3/7 B)B)5/8 C)C)6 D)D)6/7 E)E)5/12
SOLUTION:Let the two numbers be x and y.
60/100 * x + y = 5/4y
=> 3/5 x = 1/4 y => x/y = 5/12
E) #### E
QUESTION:24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M?
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D #### D
QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11
SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10
Answer: D #### D
QUESTION:Which of the following is greatest?
options: A)1/2 B)1/4 C)1/3 D)1/6 E)1/7
SOLUTION:simply we know that 1/2 is greater than all others.
So, Answer : A #### A
QUESTION:A certain kind of necklace is made from 9 gold, 6 blue, and 3 white beads. What is the maximum number of these necklaces that can be made from 36 beads of each color ?
options: A)8 B)4 C)6 D)5 E)4
SOLUTION:Atleast 9 gold breads are needed to make a necklace, so irrespective of the combinations of blue and white beads, the number of necklaces that can be formed will be
36/9 =4
Answer:- E #### E
QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make?
options: A)30% B)75% C)40% D)70% E)None of these
SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150
Profit(%) = (31150 - 17800)/17800* 100 = 75%
ANSWER:B #### B
QUESTION:simplify : 3x - 5 + 23x - 9
options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7)
SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9
= 26x - 14, = 2(13x - 7). correct answer : (B) #### B
QUESTION:If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?
I. LCM : 24; HCF : 6
II. LCM : 18; HCF : 8
III. LCM : 16; HCF : 9
options: A)I only B)II and III only C)I and II only D)I and III only E)I, II and III
SOLUTION:We need to keep two things in mind here:
1. Product of two numbers = LCM*HCF
2. LCM should be a multiple of HCF
Only Statement I follows these two rules.
Correct Option A #### A
QUESTION:The average of 35 students in a class is 18 years. The average age of 25 students is 20. What is the average age of remaining 10 students?
options: A)17 years B)16 years C)15 years D)14 years E)13 years
SOLUTION:Sum of the ages of 14 students
= (18 * 35) - (20 * 25) = 630 - 500 = 130
Required average = (130/10) = 13 years.
Answer:E #### E
QUESTION:there are 15 cars and 16 trucks? which is greater15 or 16?
options: A)15 B)14 C)12 D)17 E)16
SOLUTION:E #### E
QUESTION:Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
options: A)23 B)21 C)25 D)26 E)24
SOLUTION:Solution
Given Data
3 positive integers
Average of a, b, and c = 20.
So, a+b+c3a+b+c3 = 20 or a + b + c = 60
a ≤ b ≤ c
Median = (a + 11)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 11
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11)
Or 3a = 38 or a = 12.66
So, b = c = 12.66 + 11 = 23.66
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 11) + (a + 12) = 60
Or 3a = 37. The value of the numbers is not an integer in this scenario as well.
Let us increment c again by 1. i.e., c = b + 2
Now, a + (a + 11) + (a + 13) = 60
Or 3a = 36 or a = 12.
If a = 12, b = 23 and c = 25.
The least value for c that satisfies all these conditions is 25.
Correct answer is choice C. #### C
QUESTION:Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
options: A)$1 B)$1.84 C)$1.92 D)$2.13 E)$2.15
SOLUTION:Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B #### B
QUESTION:The least number which when increased by 4 each divisible by each one of 22, 32, 36 and 54 is :
options: A)427 B)859 C)860 D)4320 E)None of these
SOLUTION:Solution
Required number = (L.C.M. of 24, 32, 36, 54) - 4 = 864 - 4 = 860. Answer C #### C
QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg?
options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these
SOLUTION:Solution
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg
Answer D #### D
QUESTION:Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
options: A)2777 B)2888 C)8400 D)2882 E)2781
SOLUTION:Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23 = Rs. 8400.
Answer: C #### C
QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c − a?
options: A)25 B)70 C)90 D)140 E)It cannot be determined from the information given
SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=160 --2
subtracting 1 from 2 we have
c-a=70;
ANSWER:B #### B
QUESTION:If A(k)=(k+1)^k, and k=1, what is the value of A(A(A(k-1)))?
options: A)0 B)2 C)1 D)6 E)9
SOLUTION:A(A(A(0)))=A(A(0))=A(0)=1.
Thus, the answer is C. #### C
QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit?
options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these
SOLUTION:Ratio of quantities sold at 8% profit and 18% profit
=>4:6 = 2:3
Therefore,the quantity sold at 18% profit
=>50/(2 + 3) x 3
=>30 kg
ANSWER:A #### A
QUESTION:Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is:
options: A)0.20887 B)0.3887 C)0.33487 D)0.20833 E)0.38222
SOLUTION:Explanation:
Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
Answer: D #### D
QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers
options: A)2 B)4 C)8 D)12 E)14
SOLUTION:Explanation:
Let the ten digit be x, unit digit is y.
Then (10x + y) - (10y + x) = 36
=> 9x - 9y = 36
=> x - y = 4.
Option B #### B
QUESTION:Find out the next word in the series below...
FAG, GAF, HAI, IAH, ...?
options: A)GAK B)JAK C)HGF D)JAH E)KHG
SOLUTION:In first FAG it was reodering the first and last letters and these are the continuous alphabets
ANSWER:B #### B
QUESTION:A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?
options: A)30 days B)20 days C)25 days D)35 days E)45 days
SOLUTION:Work done by A in 10 days = 10/80 = 1/8
Remaining work = (1 - (1/8)) = 7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42 x 8/7) = 48 days
Therefore, A’s one day’s work = 1/80
B’s one day’s work = 1/48
(A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30
Hence, both will finish the work in 30 days.
ANSWER:A #### A
QUESTION:x and y are positive integers of h. If 1/x + 1/y < 2, which of the following must be true?
options: A) x + y > 4 B) xy>1 C) x/y + y/x < 1 D) (x - y)^2 > 0 E) None of the above
SOLUTION:Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B #### B
QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent?
options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3%
SOLUTION:750 ---- 50
50 ---- ? => 6 2/3%
Answer: E #### E
QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
options: A)50 B)75 C)69 D)79 E)82
SOLUTION:number of pens = 100
number of pencils = 50
Required number of students = H.C.F. of 100 and 50 = 50
Answer is A #### A
QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
options: A)2528 B)2526 C)2522 D)2722 E)2426
SOLUTION:A = 1600(21/20)3 = 2522
Answer: C #### C
QUESTION:The greatest number of four digits which is divisible by 7, 10, 40 and 60 is:
options: A)9200 B)9300 C)9400 D)8400 E)7400
SOLUTION:Greatest number of 4-digits is 9999.
L.C.M. of 7, 10, 40 and 60 is 4200.
On dividing 9999 by 4200, the remainder is 1599.
Required number (9999 - 1599) = 8400.
ANSWER :D #### D
QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
options: A)Rs.400 B)Rs.450 C)Rs.550 D)Rs.500 E)Rs.650
SOLUTION:Explanation:
P - 340 = (P*4*8)/100
P = 500
ANSWER IS D #### D
QUESTION:3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is:
options: A)2/9 B)1/9 C)8/9 D)7/9 E)1/4
SOLUTION:let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house
there will be 1 case when x,y,z will buy house a
another when they buy house b
and another when they buy house c
so the prob that they buy same house is 3*1/27=1/9
ANSWER:B #### B
QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score?
options: A)662 B)678 C)652 D)642 E)721
SOLUTION:8 * 86 = 688 – 10 = 678
ANSWER:B #### B
QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
options: A)1350 B)8837 C)2377 D)3772 E)3881
SOLUTION:Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350 Answer: A #### A
QUESTION:How many three letter words are formed using the letters of the word TIME?
options: A)28 B)21 C)26 D)24 E)29
SOLUTION:The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃
= 4 * 3 * 2 = 24.
Answer: D #### D
QUESTION:A train 130 m long crosses a platform with a speed of 70 kmph in 20 sec; find the length of the platform?
options: A)150 B)145 C)165 D)162 E)152
SOLUTION:D = 130 + x
T = 20
S = 130+x/15 * 18/5 = 70 kmph.
=> (130+x) * 18 = 5250
=> 130 + x = 292 => x= 162 m
Answer: D #### D
QUESTION:A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain?
options: A)12.5% B)16.7% C)22.5% D)27.5% E)33.3%
SOLUTION:Let x be the original number of each color so there are a total of 5x candies.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = 1.2x
red + yellow = 0.45x
red = 0.225x, since red = yellow.
The answer is C. #### C
QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-4)(x+9)(2X+5) = 0?
options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2
SOLUTION:x = -2.5
Prob =1/12
Answer - A #### A
QUESTION:The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
options: A)7 years B)9 years C)6 years D)4 years E)5 years
SOLUTION:28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer: D #### D
QUESTION:A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1
SOLUTION:(4*6 + 8*6): (4*12)
72:48 =>
3:2
Answer:C #### C
QUESTION:A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?
options: A)10.21 days B)10.23 days C)18.25 days D)10.25 days E)40.25 days
SOLUTION:Explanation:
A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work.
=> In one day A came complete 1/9th of the task(x/9)
=> In one day B can complete 1/12th of the job.(x/12)
First day x/9th work will be done next day x/12th and so on:
Together A and B can do x/9 + x/12 work.
=>(x/9) + (x/12) = 7/36th work done
In 10 days 35/36th of the work will be done.
On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work.
So, 1/36th work will be done in 1/4 days.
=>10.25 days
ANSWER: D #### D
QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
options: A)$5 B)$15 C)$50 D)$100 E)$105
SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
1,000(1.10)^2 = 1,000(1.21) = 1,210
and Lana would have
2,000(1.05)^2 = 2,000(1.1025) = 2,205
Thus, Tim earned 210 dollars, while Lana earned 205 dollars
The difference is $5 and the answer is A. #### A
QUESTION:Each factor of 230 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?
options: A)1/16 B)5/42 C)1/8 D)3/16 E)1/4
SOLUTION:210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=3/16.
Answer: D #### D
QUESTION:The sale price sarees listed for Rs.150 after successive discount is 20% and 10% is?
options: A)187 B)120 C)108 D)178 E)175
SOLUTION:150*(80/100)*(90/100)
= 108
Answer:C #### C
QUESTION:A shop owner has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 years. How much sale must she have in the 6th year so that she gets an average sale of Rs. 6500?
options: A)5000 B)5500 C)4991 D)5600 E)5700
SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991
C #### C
QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years. The age of the 15th student is
options: A)9 years B)11 years C)17 years D)21 years E)25 years
SOLUTION:Solution
Age of the 15th student =[15x15-(14x8+16x6)]
= (225 - 208)
= 17 years.
Answer C #### C
QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 2years ago?
options: A)152460 B)214560 C)160000 D)210000 E)200000
SOLUTION:population 2 years ago = 176400/(1 + 5/100)^2
= 176400* 20/21 * 20/21
=160000
Answer is C #### C
QUESTION:If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?
options: A)1/2 B)1 C)-1/2 D)-1 E)0
SOLUTION:When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero.
Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p
=> x = (p + q - r + p - q + r + q + r - p) / (r + q + p)
=> x = (r + q + p) / (r + q + p) = 1
p + q + r is non-zero.
ANSWER:B #### B
QUESTION:A committee of three people is to be chosen from 6 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
options: A)16 B)24 C)26 D)30 E)160
SOLUTION:One of the approaches:
Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 6 to send only onerepresentativesto the committee: 6C3=20.
But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.
Total # of ways: 6C3*2^3=160.
Answer: E. #### E
QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
options: A)1/2 B)17/36 C)190/827 D)11/36 E)25/216
SOLUTION:Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 10 in any attempt =3/36=1/12
Probability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12
Probability of losing game =(11/12)*(11/12)*(11/12)=637/827
I.e. Probability of wining game = 1-(637/827) = 190/827
Answer : Option C #### C
QUESTION:|16 - 5| - |5 - 12| = ?
options: A)3 B)2 C)1 D)0 E)4
SOLUTION:|16 - 5| - |5 - 12| = | 11 | - | -7 | =11 - 7 = 4
correct answer E #### E
QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
options: A)2,145 B)6,435 C)326,040 D)12,870 E)25,740
SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All four
2. One symmetry and other three non
3. Two symmetry and other two non
4. Three symmetry and one non
4. All the three letters can be arranged in 24 ways
( 11c4 + 11c1 * 15c3 + 11c2 * 15c2 + 11c3 *15c1 ) * 6
(330 +5005 + 5775+2475 ) * 24
326,040
IMO option C is the correct answer..
OA please...will correct if I missed anything.. C #### C
QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
options: A)29 B)30 C)30.5 D)31 E)32
SOLUTION:to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30
hence B #### B
QUESTION:In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females?
options: A)16% B)25% C)32% D)40% E)52%
SOLUTION:We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 38 are employed males,hence 26% are employed females.
(employed females)/(total employed people)=26/64=40%
Answer: D. #### D
QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9?
options: A)0 B)1 C)3 D)4 E)6
SOLUTION:Lets take the number as y
when y is divided by 9 the remainder is 5 hence y can be written as
y=9k +5
Multiplying by 3 will give
3y = 27k + 15
we can also write
3y = 27k + 9 + 6
Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E
QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None
SOLUTION:Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1250 x 2/5) = Sterling 500.
Answer: Option C #### C
QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265
options: A)800 B)700 C)750 D)850 E)900
SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265
253/160p=1265==> p =800
ANSWER A #### A
<<<Examples ends
QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
options: A)2:3:9 B)24:25:36 C)7:6:10 D)12 : 15 : 16 E)None of these
SOLUTION:Explanation:
Aman : Rakhi : Sagar =(70000×36)=(70000×36) :(105000×30):(105000×30) :(140000×24):(140000×24)
=12:15:16=12:15:16.
ANSWER IS D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A club wants to mix 15 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
options: A)20 B)30 C)40 D)50 E)60
SOLUTION:Let number of pounds of 5$ candy to be used be w
6 = (15*8 + 5*w)/(15 +w)
=>90 + 6w = 120 + 5w
=> w = 30
Answer B #### B
QUESTION:The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z?
options: A)35 B)33 C)28 D)21 E)15
SOLUTION:The smallest possible product is 33 which is 3*11.
All other products are too big.
The answer is B. #### B
QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?
options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2
SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts
B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts
C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts
D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts
E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest.
Answer (E) #### E
QUESTION:Which of the following number will completely divide (49^15)-1?
options: A)8 is the number B)6 C)22 D)12 E)14
SOLUTION:x^n - 1 will be divisible by x+1 only when n is even.
49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8
Answer is A #### A
QUESTION:Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
options: A)66 B)74 C)78 D)80 E)None of these
SOLUTION:Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 74
Therefore total marks in 6 subjects = 74 * 6 = 444
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 444 – 370 = 74
ANSWER B #### B
QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
options: A)72 min B)25.11628 min C)70 min D)74.11682 min E)76 min
SOLUTION:x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
185x+15*2x=180
x=180/215
x=0.837209
time taken for type A problem=15*2*0.837209=25.11628min
ANSWER:B #### B
QUESTION:At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
options: A)5% B)3 1/2% C)4% D)5 1/2 % E)6%
SOLUTION:150 = (750*5*R)/100
R = 4%
Answer :C #### C
QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours?
options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44)
SOLUTION:Explanation:
Here clock-wise and anti-clockwise arrangements are same.
Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}}
Answer: C) 18!(6 x 24) #### C
QUESTION:How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
options: A)24 sec B)30 sec C)27 sec D)28 sec E)29 sec
SOLUTION:Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 400 * 3/50
= 24 sec.
Answer:A #### A
QUESTION:If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
options: A)-f(x) B)f(x) C)2*f(x) D)1/f(x) E)2/f(x)
SOLUTION:If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x)
answer A #### A
QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded?
options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these
SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :-
letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..)
Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get
IDAATRE
ANSWER:D #### D
QUESTION:A and B invests Rs.4000 and Rs.6000 in a business. After 4 months, A withdraws three-fourth of his capital and 4 months later, B withdraws half of his capital. In what ratio should they share the profits at the end of the year?
options: A)2:5 B)3:5 C)4:5 D)3:7 E)5:7
SOLUTION:A : B
(4000*4)+(1000*8) : (6000*8)+(3000*4)
24000 : 60000
2 : 5
Answer: A #### A
QUESTION:There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
options: A)1/9 B)2/9 C)5/9 D)4/9 E)2/3
SOLUTION:total 9 from take one.
9c1=9
red 5 from one
5c1=5
5/9
ANSWER:C #### C
QUESTION:Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
options: A)28 B)10 C)28 D)27 E)13
SOLUTION:4/12 + x/15 = 1
x = 10
Answer:B #### B
QUESTION:Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 30 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
options: A)20 miles B)30 miles C)40 miles D)50 miles E)60 miles
SOLUTION:Every hour, Nil gets ahead of Ethan 30 - 20 =
10 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 30 × 1 = 30 miles.
correct answer B #### B
QUESTION:How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 3 can be used only once?
options: A)20 B)150 C)225 D)250 E)316
SOLUTION:4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 6): 4*5*4*4=320
Numbers with three 3-s, 3X3X3 4*1*1*1=4
Thus there are 320-4=316 such numbers.
Answer: E. #### E
QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed?
options: A)104 B)190 C)109 D)278 E)211
SOLUTION:Explanation:
624/6 = 104 kmph
Answer:C #### C
QUESTION:In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden. What is the length of the garden?
options: A)22 B)24 C)26 D)28 E)30
SOLUTION:Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length
Also, 3 meter is left from all sides of the boundary of the garden.
Hence, length of the garden = (11 × 2) + 3 + 3 = 28 meter
Answer is D. #### D
QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds
SOLUTION:Let the total number of shots be x. Then,
Shots fired by A =(5/8)x
Shots fired by B =(3/8)x
Killing shots by A =(1/3)of (5/8)x=(5/24)x
Shots missed by B =(1/2) of (3/8)x =(3/16)x
3x/16= 27 or x =(27 x 16)/3= 144.
Birds killed by A =(5x/24) =(5/24*144)= 30.
Answer is C. #### C
QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture?
options: A)294 B)235 C)350 D)288 E)580
SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A
QUESTION:n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
options: A)3 B)2 C)1 D)0 E)None of these
SOLUTION:Let n=4q+3.
2n=8q+6=4(2q+1)+2
Thus, when 2n is divided by 4, the remainder is 2.
Correct Option: B #### B
QUESTION:In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 8 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
options: A) 400 B) 625 C) 1,250 D) 2,500 E) 312
SOLUTION:total fish = x
percentage of second catch = (8/50)*100 = 16%
so, x * 16% = 50
x = 312 ans.E #### E
QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least?
options: A)John B)Susan C)Sam D)Mark E)Lynn
SOLUTION:Let J – John’s weight
S – Susan’s weight
M – Mark’s weight
A – Sam’s weight
L – Lynn’s weight
J = 2S
S = 0.6A
M = 0.5L
L = 1.9J
Let us convert these weights to one variable
S = J/2
A = S/0.6 = J/1.2 = 5J/6
L = 1.9J
M = 0.5 * 1.9J = 0.95J
So Susan has the least weight.
Answer - B #### B
QUESTION:Of the science books in a certain supply room, 50 are on botany, 60 are on zoology, 90 are on physics. 40 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
options: A)81 B)159 C)309 D)285 E)324
SOLUTION:First, you can take all 50 Botany books, all 60 zoology books and all 40 geology books because you're sure to never pick 80 of them.
There are still 90 on physics and 110 on chemistry
The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry.
Minimum number of books picked to reach 80 in the same science should be : 50 + 60 + 40 + 79 +79 + 1 = 309
C #### C
QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
options: A)2:35:16 B)2:15:16 C)2:15:77 D)2:15:98 E)2:15:23
SOLUTION:Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer: B #### B
QUESTION:In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ?
options: A)27 B)26 C)25 D)24 E)20
SOLUTION:Explanation:
n(A)=(60/100∗96)=288/5
n(B)=(30/100∗96)=144/5
n(A∩B)=(15100∗96)=72/5
People who have either or both lunch n(A∪B)=288/5+144/5−72/5
=360/5=72
So People who do no have either lunch were = 96 -72
= 24
ANSWER IS D #### D
QUESTION:One-third of 600 is what percent of 120 ?
options: A)313.2 B)30.1 C)12.24 D)None of these E)166.6
SOLUTION:Answer
Let one-third of 600 is N% of 120.
∵ 600/3 = (N x 120)/100
∴ N = (200x 100) / 120 = 166.6
Correct Option: E #### E
QUESTION:What proximate value should come in place of the question mark (?) in the following question?
6.795 × 1084 + 2568.34 – 1708.34 = ?
options: A)6,000 B)12,000 C)10,340 D)8,204 E)9,000
SOLUTION:? ≈ 6.8 × 1080 + 2560 – 1700 ≈ 7344 + 860 ≈ 8204
Answer D #### D
QUESTION:The ratio, by volume, of bleach to detergent to water in a certain solution is 4 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain?
options: A)80 B)70 C)60 D)40 E)50
SOLUTION:B:D:W = 4:40:100
Bnew / Dnew = (1/3)*(4/40) = (1/30)
Dnew / Wnew = (1/2)*(40/100) = (1/5)
Wnew = 300
Dnew = Wnew/5 = 300/5 = 60
So, answer will be
C #### C
QUESTION:If x+1/x=5 then find out the value of x^5+1/x^5=?
options: A)2515 B)2525 C)2535 D)2545 E)2555
SOLUTION:given,(x+ 1/x) = 5
x^2 + 1/x^2 = (x+ 1/x)^2 - 2*x*1/x = 5^2 - 2 = 23 -------(1)
x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2)
multiplying (1)& (2), we get
=>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110
=> x^5 + 1/x + x + 1/x^5 = 2530
=> x^5 + 1/x^5 + (x+ 1/x)= 2530
=> x^5 + 1/x^5 + 5 = 2530
=> (x^5+ 1/x^5)= 2525
ANSWER:B #### B
QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced?
options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None
SOLUTION:Explanation :
Time = 80*4 / 60 = 5 hours 33 mins
Answer – B #### B
QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?
options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5
SOLUTION:Explanation:
Let the capacity of 1 bucket = x.
Then, capacity of tank = 25x.
New capacity of bucket = 2/5 x.
Required no of buckets = 25x / (2x /5) = 62.5
ANSWER IS B #### B
QUESTION:A man buys an article and sells it at a profit of 5%. If he had bought it at 5% less and sold it for Rs.25 less, he could have gained 5%. What is the cost price?
options: A)197 B)476 C)279 D)278 E)268
SOLUTION:CP1 = 100 SP1 = 105
CP2 = 95 SP2 = 95 * (105/100) = 99.75
5.25 ----- 100
25 ----- ? => 476
Answer:B #### B
QUESTION:Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point?
options: A)20sec B)15sec C)30sec D)24sec E)1min
SOLUTION:They meet every 360/7+8 = 24sec
Answer is D #### D
QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
options: A)1350 B)2997 C)2087 D)2697 E)9824
SOLUTION:Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5
=> 675
675 * 2
= Rs.1350
Answer:A #### A
QUESTION:A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to
options: A)the same as one 45 percent discount B)the same as one 38 percent discount C)the same as one 36 percent discount D)the same as one 30 percent discount E)the same as one 28 percent discount
SOLUTION:0.9*0.8*x=0.72x from initial value, meaning 0.28 or 36% discount
E #### E
QUESTION:23,8,34,81,33,...
options: A)24 B)25 C)26 D)27 E)28
SOLUTION:23 : 2^3=8
34 : 3^4=81
33 : 3^3=27
ANSWER:D #### D
QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
options: A)3002 B)3000 C)3018 D)3019 E)3012
SOLUTION:60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer: B #### B
QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
options: A)220 B)250 C)320 D)420 E)560
SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7.
We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers.
Hence , answer is D. #### D
QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
options: A)12 B)14 C)15 D)19 E)10
SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15. Answer:C #### C
QUESTION:What is the difference between the greatest and the smallest five digit numbers formed using the digits 7, 0, 3, 4 and 2 without repeating the digits?
options: A)53978 B)53916 C)53961 D)56781 E)None of these
SOLUTION:Explanation:
The greatest 5 digit number that can be formed using the given digits = 74320
The smallest 5 digit number that can be formed using the given digits = 20342
.: The required difference = 74320 - 20342 = 53978
Answer: Option A #### A
QUESTION:2 identical circles intersect so that their centre and point at which they intersect form a square of 1 cm.the area of portion that is common two circles is
4
options: A)π2-1 B)4 C)√2-1 D)√5 E)π/2-1
SOLUTION:the area of the sector is pi*r^2*90/360 (as it is a square, so the angle is 90)
=pi*r^2/4
=pi/4 (as the area of the square is 1cm^2, so the sides are 1 cm each. the sides of the square are the radii of the circle)
now, the area of the triangle formed by two radii and a line which joins the point of intersection of the two circles = 0.5*1*1=0.5
So, half of the portion of our desired area= (pi/4 - 0.5)
therefore, the area of our desired portion is 2* (pi/4 - 0.5)
= pi/2 - 1
ANSWER:E #### E
QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides?
options: A)3 B)6 C)5 D)9 E)1
SOLUTION:S = (1 + 2 + 7)/2
= 5 Answer:C #### C
QUESTION:Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x?
options: A)4 B)5 C)3 D)9 E)6
SOLUTION:9 x + x = 13 + 27
10 x = 40 => x = 4
Answer:A #### A
QUESTION:In the xy-coordinate system, line k passes through points (-8m, 0) and (0, 2m). Which of the following is a possible equation of line k?
options: A)y = -4x + 2m B)y = 1/4*x - 8m C)y = 4x + 2m D)y = 1/4*x + 2m E)y = -1/4*x - 8m
SOLUTION:The slope of the line is 2m/8m=1/4.
The y-intercept is 2m.
the equation of the line is: y = 1/4*x +2m
The answer is D. #### D
QUESTION:12,?,68,129,220,347,516
options: A)129 B)220 C)347 D)31 E)520
SOLUTION:2*2*2 + 4 = 12
4*4*4 + 4 = 68
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
3*3*3 +4 = 31
ANSWER : D #### D
QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
options: A)1/2 B)17/36 C)190/827 D)11/36 E)25/216
SOLUTION:Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 10 in any attempt =3/36=1/12
Probability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12
Probability of losing game =(11/12)*(11/12)*(11/12)=637/827
I.e. Probability of wining game = 1-(637/827) = 190/827
Answer : Option C #### C
QUESTION:A, B and C invested Rs.6600, Rs.4400 and Rs.11000 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
options: A)Rs.3300 B)Rs.3100 C)Rs.3500 D)Rs.4200 E)Rs.3400
SOLUTION:6600:4400:11000
3:2:5
3/10 * 11000
= Rs.3300
AnswerA #### A
QUESTION:After decreasing 56% in the price of an article costs Rs.4400. Find the actual cost of an article?
options: A)12000 B)15000 C)1200 D)1000 E)10000
SOLUTION:CP* (44/100) =4400
CP= 100 * 100 => CP
= 10000
Answer:E #### E
QUESTION:J is 25% less than P and 20% less than T. T is r% less than P. What is the value of r?
options: A)93.5 B)90 C)6.75 D)6.25 E)2
SOLUTION:Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables.
Let, P = 400
then J = (75/100)*400 = 300
also J = (80/100)*T
i.e. T = 300*100/80 = 375
and T = [1-(r/100)]*P
i.e. 100-r = 100*T/P = 100*375/400 = 93.75
i.e. r = 6.25
Answer: Option D #### D
QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
options: A) 15 B) 17 C) 10 D) 25 E) 30
SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
50 will be in team A
50 will be in team B
The larger diff is
70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10.
Answer choice C #### C
QUESTION:John bought 2 shares and sold them for $98 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
options: A) a profit of $10 B) a profit of $8 C) a loss of $4 D) a loss of $10 E) neither a profit nor a loss
SOLUTION:$ Profit of the share sold at 20% profit =
120-98
20-?
$18 profit on the sale of 1 share.
$ Loss of the share sold at 20% loss=
80-98
20-?
$22 loss on the sale of 1 share.
18-22=Loss of $4
Answer: C #### C
QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
options: A)8 B)12 C)18 D)24 E)48
SOLUTION:In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6
Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E
QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good.
options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980
SOLUTION:Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6400
1 = 6400/68.4
100 = (6400*100)/68.4 = Rs. 9357.
Answer: Option D #### D
QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ?
options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1
SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer:C #### C
QUESTION:What percent of 180 is 45?
options: A)0.25% B)4% C)25% D)40% E)250%
SOLUTION:Here's an algebraic approach.
Let p = the required percent.
This means p/100 = the percent as a fraction.
So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45
Or: (p/100)(180) = 45
Divide both sides by 180 to get: p/100 = 45/180
Simplify right side: p/100 = 1/4
Multiply both sides by 100 to get: p = 25
ANSWER:C #### C
QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank?
options: A)50% B)40% C)33.5% D)37.5% E)None of these
SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8
∴ required% = 3A⁄ (8 × A) × 100 = 37.50%
Answer D #### D
QUESTION:The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
options: A)17 litres B)21.3 litres C)11 litres D)07 litres E)38 litres
SOLUTION:262.85(32)+3,104.35x = 1,399.45(32 + x)
Solve the equation.
262.85(32)+3,104.35x = 1,399.45(32 + x)
8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x
8,411.2 + 1,704.9x = 44,782.4
1,704.9x = 36,371.2
x ≈ 21.3
Answer is B. #### B
QUESTION:Consider two statements
Statement 1 => If R is an integer and R=2p+1 where p is not an integer.
Statement 2 => If S is an integer and S=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of R and S respectively
options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined
SOLUTION:answer will be E
R = integer
R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even R would odd
if n odd R would be even
ANSWER IS E #### E
QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2!
SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 boys are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 boys do not sit together would be: 7!-3!5!.
Answer: D). #### D
QUESTION:A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is?
options: A)5 B)6 C)10 D)8 E)9
SOLUTION:US = 15
DS = 35
M = (35 - 15)/2 = 10
Answer: C #### C
QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
options: A)9.30 a.m B)10 a.m C)10.40 a.m D)11 a.m E)11.40 am
SOLUTION:Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
answer B #### B
QUESTION:Rs.8000 become Rs.11256 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
options: A)6 YEARS B)7 C)5 D)3 E)4
SOLUTION:Explanation:
11256 = 8000(21/20)N
(21/20)7 = (21/20)N => N = 7
Answer: Option B #### B
QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1232?
options: A)1000 B)2217 C)1100 D)2777 E)2991
SOLUTION:1232 = P [1 + (5*12/5)/100]
P= 1100
Answer: C #### C
<<<Examples ends
QUESTION:The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches?
options: A)31.23 B)25.12 C)36.25 D)23.17 E)27.66
SOLUTION:Total score of the batsman in 22 matches = 616.
Total score of the batsman in the next 13 matches = 195.
Total score of the batsman in the 35 matches = 811.
Average score of the batsman = 811/35 = 23.17.
Answer: D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A car moves at 80 km/hr. What is the speed of the car in meters per second ?
options: A)20 2/9m sec B)22 2/9m sec C)24 2/9m sec D)26 2/9m sec E)28 2/9m sec
SOLUTION:Explanation:
Speed=(80∗5/18)m/sec
=200/9m/sec
=22 2/9msec
Option B #### B
QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats?
options: A)12 B)302 C)1 D)250 E)286
SOLUTION:Total number of hats = 13
Possible number of formations = 13C3 = 286
Correct answer is E #### E
QUESTION:Given that 268x74= 19632, find the value of 2.68x.74.
options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None
SOLUTION:Solution
Sum of decimals places =(2+2)
= 4.
Therefore, = 2.68×.74
= 1.9632
Answer A #### A
QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform?
options: A)240 B)188 C)177 D)260 E)320
SOLUTION:Speed = 72 * 5/18 = 20 m/sec.
Length of the train = 20 * 20 = 400 m.
Let the length of the platform be x m . Then,
(x + 400)/36 = 20 => x = 320.
Answer: E #### E
QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11
SOLUTION:Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12.Answer:B #### B
QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference W between the greatest and least of the five integers?
options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4
SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference W= 10k - 3 - (10k - 7)
= 4
Answer - D #### D
QUESTION:A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together?
options: A)120 B)110 C)105 D)140 E)135
SOLUTION:we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together
so 8C6 + (8C5 * 2C1)
this is 28 + 112=140
Answer : D #### D
QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
options: A)4 B)8 C)9 D)2 E)9
SOLUTION:Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer:A #### A
QUESTION:What is the HCF of 2/3, 4/15 and 6/5
options: A)7/45 B)2/45 C)4/15 D)8/45 E)2/15
SOLUTION:Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 15, 5) = 2/15
Answer: Option E #### E
QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?
options: A)1500 B)2000 C)3000 D)3500 E)2500
SOLUTION:Profit as x
since 5% and 95% of x will be divided b/w A and B ration 3:2
=>profit 95x/100 * 3/5
given that A's share is Rs 855 =>
95x/100 * 3/5 = 855
hence x = 1500
ANSWER A #### A
QUESTION:10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
options: A)2267 B)287 C)268 D)228 E)225
SOLUTION:1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/6
15 women's 1 day work = (1/6 - 10/100) = 1/15
1 woman's 1 day work = 1/225
1 woman alone can complete the work in 225 days.
Answer: E #### E
QUESTION:For which of the following values of n is (500+n)/n NOT an integer?
options: A) 1 B) 2 C) 3 D) 4 E) 5
SOLUTION:Solution:
This problem is easiest solved by plugging in each answer choice.
A) (500 + 1)/1 = 501/1 = 501
Answer choice A yields an integer.
B) (500 + 2)/2 = 502/2 = 251
Answer choice B yields an integer.
C) (500 + 3)/3 = 503/3 = 167, remainder 2
Answer choice C DOES NOT yield an integer.
Although we believe answer choice C is correct, we should still test the other answer choices.
D) (500 + 4)/4 = 504/4 = 126
Answer choice D yields an integer.
E) (500 + 5)/5 = 505/5 = 101
Answer choice E yields an integer.
Thus, the correct answer is answer choice C. #### C
QUESTION:A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
options: A)229 B)108 C)278 D)72 E)112
SOLUTION:S = 120/6 * 18/5 = 72 kmph
Answer: D #### D
QUESTION:What is the smallest number which when diminished by 20, is divisible 15, 30, 45 and 60?
options: A)200 B)220 C)240 D)322 E)342
SOLUTION:Required Number
= (LCM of 15, 30, 45 and 60) + 20
= 180 + 20 = 200
Option A #### A
QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
options: A)28880 B)31200 C)28770 D)29990 E)12770
SOLUTION:Let A be the amount received at the end of the three years.
A = 48000[1 + 10/100][1 + 20/100][1 + 25/100]
A = (48000 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.79200
So the interest = 79200 - 48000 = Rs.31200
Answer: B #### B
QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr
SOLUTION:Work done by the tank in 1 hour
= (1/2 - 1/3)
= 1/14 Leak will empty the tank in 14 hrs.
Answer:D #### D
QUESTION:A tiger is chasing its prey at a constant speed. It entire body passes a blade of grass in 1 second. It then runs above a fallen tree trunk that is 20 meters long in 5 seconds. What is the length of the tiger?
options: A)6 m B)5 m C)4 m D)3 m E)None of the above
SOLUTION:Sol.
Let the length of the tiger be x metres and its speed be y m/sec. Then, x / y = 1 ⇒ y = x
∴ (x + 20) / 5 = x ⇔ x = 5 m. Answer B #### B
QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?
options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 %
SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6
S.P. of 1 kg = Rs. 6.50
Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C
QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680?
options: A)1500 B)2777 C)2889 D)27670 E)2771
SOLUTION:1680 = P [1 + (5*12/5)/100]
P= 1500.Answer:A #### A
QUESTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
options: A) Two B) Three C) Four D) Six E) Eight
SOLUTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 8p have.
p = 3 --> 8p = 24--> 24 has 6 even divisors: 2, 4, 6, 8, 12, 24.
Answer: D. #### D
QUESTION:A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain?
options: A)12.5% B)16.7% C)22.5% D)27.5% E)33.3%
SOLUTION:Let x be the original number of each color so there are a total of 5x candies.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = 1.2x
red + yellow = 0.45x
red = 0.225x, since red = yellow.
The answer is C. #### C
QUESTION:The first three terms of a proportion are 3, 9 and 12. The fourth term is?
options: A)22 B)28 C)27 D)36 E)88
SOLUTION:(9*12)/3 = 36
Answer:D #### D
QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA
options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these
SOLUTION:Explanation:
Let A = 2x, B = 3x, C = 4x, then,
AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24
Answer: D #### D
QUESTION:In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
options: A)32 B)16 C)64 D)80 E)16 or 48
SOLUTION:Let total number be x
No in the interior = (x/8)^2
No outside = 16
So : x - (x/8)^2=16
x^2-64x+16*64=0
(x-32)^2=0
x=32
A #### A
QUESTION:How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2.
options: A)4:3 B)4:7 C)4:9 D)4:2 E)4:1
SOLUTION:Explanation:
No explanation is available for this question!
ANSWER: A #### A
QUESTION:The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?
options: A)33 1/3% B)33 1/8% C)33 6/3% D)33 8/3% E)31 1/3%
SOLUTION:100
75
-------
75 ------- 25
100 ------ ? => 33 1/3%
Answer: A #### A
QUESTION:A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half?
options: A)14 B)15 C)18 D)22 E)33
SOLUTION:The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.
The time T2 to run the second half must be twice the time T1 to run the first half.
T2 = 2*T1 = T1+11
T1 = 11 and so T2 = 22.
The answer is D. #### D
QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %?
options: A)18 B)16 C)26 D)17 E)11
SOLUTION:Explanation:
1500 ---- 390
100 ---- ? => 26%
Answer:C #### C
QUESTION:Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 0.5. What value is exactly 2 standard deviations less than the mean?
options: A) 10.5 B) 11 C) 11.5 D) 12 E) 12.5
SOLUTION:The value which is exactly two SD below the mean is: mean-2*SD=13.5-2*0.5=12.5.
Answer: E. #### E
QUESTION:Find the average of first 4 multiples of 11?
options: A)10 B)12.6 C)27.5 D)31.3 E)40.8
SOLUTION:average = (11+22+33+44)/4 = 27.5
Answer is C #### C
QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6?
options: A)5 B)4 C)3 D)2 E)1
SOLUTION:Let's test out some values of p and q that satisfy the given information.
p leaves are remainder of 2 when divided by 6
So, p COULD equal 8
q leaves are remainder of 3 when divided by 6
So, q COULD equal 3
What is the remainder when p – q is divided by 6?
So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5
Answer: A #### A
QUESTION:The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
options: A)39 B)41 C)42 D)43 E)44
SOLUTION:Total age of mother and 6 children = avg x n = 9 x (6+1)= 63
If mother is excluded new average is (9 - 5) = 4
so for 6 children = 6 x 4 =24
so mother's age is 63 - 24 =39
Answer: Option A #### A
QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ?
options: A)10 B)20 C)60 D)120 E)600
SOLUTION:Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
245_ --> 4
246_ --> 3
247_ --> 2
248_ --> 1
256_ --> 3
257_ --> 2
258_ --> 1
267_ --> 2
268_ --> 1
Number of integers =20
B #### B
QUESTION:In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden. What is the length of the garden?
options: A)22 B)24 C)26 D)28 E)30
SOLUTION:Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length
Also, 3 meter is left from all sides of the boundary of the garden.
Hence, length of the garden = (11 × 2) + 3 + 3 = 28 meter
Answer is D. #### D
QUESTION:The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 60 percent of b, what is the value of m/x?
options: A)2/5 B)3/4 C)4/5 D)5/4 E)2/7
SOLUTION:a/b = 4/5
m/x = (2/5)*5 / (7/4)*4 = 2/7
The answer is E. #### E
QUESTION:If n = 20! + 19, then n is divisible by which of the following?
I. 15
II. 17
III. 19
options: A)I only B)II only C)III only D)I and II E)II and III
SOLUTION:19 divides 20! so 19 also divides 20! + 19.
15 and 17 divide 20! so they do not divide 20! + 19.
The answer is C. #### C
QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was
options: A)960 B)980 C)900 D)970 E)1000
SOLUTION:Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 1000
Answer: E) Rs 1000 #### E
QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
options: A) 15 B) 17 C) 10 D) 25 E) 30
SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
50 will be in team A
50 will be in team B
The larger diff is
70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10.
Answer choice C #### C
QUESTION:A student got twice as many sums wrong as he got right. If he attempted 27 sums in all, how many did he solve correctly ?
options: A)12 B)16 C)18 D)9 E)12
SOLUTION:Explanation:
Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 27 3x = 27 x = 9.
Answer:D #### D
QUESTION:What are the next two letters in the following series and why?
W A T N T L I T F S _ _
*Hint : Look into the title of the Riddle
options: A)A and W B)A and E C)B and W D)A and C E)S and W
SOLUTION:A
A and W.
The letters are the first letters of the words in the question. Thus, the next two letters are A and W. #### A
QUESTION:Two whole numbers whose sum is 72 cannot be in the ratio
options: A)3 : 4 B)3 : 5 C)4 : 5 D)5 : 7 E)None
SOLUTION:Sol.
The sum of the ratio terms must divide 72. So, the ratio
cannot be 3 : 4.
Answer A #### A
QUESTION:Two representatives must be selected from each of two groups of students. One group consists of two men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?
options: A)1/6 B)1/4 C)5/9 D)1/3 E)1/2
SOLUTION:Group 1: 2 Men and 1 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 2C2*2C2 = 1 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 2*1*1*2 = 4 ways
Total Favorable cases = 1+4 = 5
Total Possible ways of selecting students 2 from each group = 3C2*3C2 = 3*3 = 9
Probability = 5/9
Answer : Option C #### C
QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55
SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;
A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents.
Answer: C. #### C
QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?
options: A)3 days B)5 days C)7 days D)11 days E)12 days
SOLUTION:That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
A) #### A
QUESTION:Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
options: A)4! B)8! C)9! D)10! E)12!
SOLUTION:Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways #### B
QUESTION:On day one, a store sold 125 bags. On each of the next d days, the company sold 83 bags. If the average daily sales of bags over this time period (including day one) is 90 bags, what is the value of d?
options: A)4 B)5 C)6 D)7 E)8
SOLUTION:125 + 83d = 90(d+1).
7d = 35.
d = 5.
The answer is B. #### B
QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr.
SOLUTION:Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=24 or x=12.
Rate upstream=12 km/hr,rate downstream=36 km/hr.
Hence,rate of stream=1/2(36-12)km/hr=12 km/hr.
Answer is B. #### B
QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?
options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2
SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts
B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts
C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts
D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts
E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest.
Answer (E) #### E
QUESTION:From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 13 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?
options: A)38 B)39 C)40 D)41 E)42
SOLUTION:Soln:-
13x=45 --> 87/77*x=45 --> x=45*77/87=677/17=~40.
Answer: C. #### C
QUESTION:What should come in place of the question mark (‘?) in the following equation?
18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16
options: A)2764.44 B)2864.34 C)1864.44 D)2684.44 E)None of these
SOLUTION:? = 8697.32 – 3058.16 – 92⁄5 × 150.8
= 5639.16 – 2774.72 = 2864.44
Answer E #### E
QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n?
options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years
SOLUTION:Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $700.
Therefore, the Simple Interest earned = 700 - 100 = $600.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 600 = (100 * n * 8) / 100
Or 8n = 600
Or n = 75 years.
correct choice is (E) #### E
QUESTION:The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
options: A)A)17 B)B)18 C)C)19 D)D)22 E)E)24
SOLUTION:Explanation:
10 * 16 + 36 – 26=170 => 170/10 = 17
A) #### A
QUESTION:Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes?
options: A) 911 B) 100 C) 101 D) 160 E) 785
SOLUTION:Let's take the approach that uses the answer choices to eliminate wasted time.
32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt.
Looking at the answers it is clear...we can only choose (D)
THE CORRECT ANSWER IS D. #### D
QUESTION:In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday?
options: A)Thursday B)Friday C)Saturday D)Sunday E)Monday
SOLUTION:Day of week after 64 days after Arman's birthday = 7*9 + 1
Saturday as the period will have 9 weeks and 1 days .
The 1 days in the end will be Friday .
Answer B #### B
QUESTION:A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his
average after 17th match
options: A)36 B)37 C)38 D)39 E)40
SOLUTION:Explanation:
Let the average after 17th match is x
then the average before 17th match is x-3
so 16(x-3) + 87 = 17x
=> x = 87 - 48 = 39
Answer: Option D #### D
QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2
SOLUTION:RT = W
Given:
R = 1/3 + 1/3 = 2/3
T = ?
W = 1
T = 1 / (2/3) = 3/2 = 1 1/2
Answer: E #### E
QUESTION:If mn > 0, which of the following must be negative?
options: A)mn B)mn^2 C)m/-n D)m/n E)m+n
SOLUTION:Given mn> 0 So both will be the positive integers. If both are positive, then A,B,D,E also positive.
Answer :C #### C
QUESTION:If 2994 ÷ 14.5 = 179, then 29.94 ÷ 1.45 = ?
options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.9
SOLUTION:29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 179 in the place of 2994/14.5 ]
= 179/10
= 17.9
Answer is E. #### E
QUESTION:If 1^3 + 2^3 + 3^3 +......+ 10^3 = 516 then the value of 2^3 + 4^3 + 63 + ..... + 203 is
options: A)1032 B)1030 C)1034 D)1035 E)1036
SOLUTION:2(13 + 23 + 33 + ---------- + 103)
2 × 516 = 1032
A #### A
QUESTION:For what value of x, is |x – 3| + |x + 1| + |x| = 8?
options: A) 0 B) 3 C) -3 D) 4 E) -2
SOLUTION:For what value of x, is |x – 3| + |x + 1| + |x| = 8?
It's easiest just to plug in answer choices:
(E): -2
|x – 3| + |x + 1| + |x| = 8?
|-2 - 3| + |-2 + 1| + |-2| = 8?
|1| + |5| + |4| = 8
(E) #### E
QUESTION:In how many a committee of 5 members can be selected from 6men
5 ladies consisting of 3 men and 2 ladies
options: A)200 B)300 C)400 D)500 E)600
SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
ANSWER A #### A
QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is
options: A)35 B)37 C)38 D)41 E)42
SOLUTION:Explanation:
Let B's age = x years.
Then, As age = (x+ 8) years.
(x+8+10)=2(x—10)
hence x=38.
Present age of B = 38 years
Answer: Option C #### C
QUESTION:864.942 - ? + 45.76 = 547.905
options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these
SOLUTION:Explanation:
362.797
Answer: Option D #### D
QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount?
options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00
SOLUTION:sale price = (original price - 10% decrease) - 10% decrease
price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10
The answer is C. #### C
<<<Examples ends
QUESTION:If x^2 + y^2 = 13 and xy = 3, then (x − y)^2 =
options: A)7 B)11 C)14 D)17 E)20
SOLUTION:but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 13-2*3=7..
Answer A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Which of the following CANNOT be a value of 8/(x–8)?
options: A)-1 B)-1/2 C)0 D)2 E)8
SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation.
If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0.
The answer is C. #### C
QUESTION:What is the leastvalue of x. So that 23x57 is divisible by 3?
options: A)3 B)4 C)1 D)5 E)6
SOLUTION:The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
C #### C
QUESTION:On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4*[sqrt(t-9)] for t>9, where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?
options: A)17 B)21.25 C)12.25 D)14.05 E)18
SOLUTION:radius=7mm.
So dia= 14mm.
putting D=14 in equation we can easily calculate
t=21.25
ANSWER:B #### B
QUESTION:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar?
options: A) 9 B) 12 C) 15 D) 18 E) 21
SOLUTION:(Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)
í.ẹ. Red*White = Blue*Total Coins
Let, Red = 3a
White = 3b
Blue = 3c
Total Coins = 3(a+b+c)
í.ẹ. 3a * 3b = 3c*3(a+b+c)
í.ẹ. a*b = c*(a+b+c)
For smallest values of a, b and c
2*3 = 1*(1+2+3)
í.ẹ. Minimum Total Coins = 3*(1+2+3) = 15
Answer: Option C #### C
QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced?
options: A)70% B)15% C)20% D)25% E)30%
SOLUTION:price of a coat in a certain store = $500
the price of the coat is to be reduced by $350
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (350)*100 / 500 = 70%
Answer: Option A #### A
QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is
options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12
SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
= 4/13
Answer:D #### D
QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
options: A)11 B)15 C)6 D)8 E)76
SOLUTION:Explanation:
Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years.
Answer: A) 11 #### A
QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it?
options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days
SOLUTION:Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/13 work in 1 day
B alone can do (1/6 -1/13) =7/78 work in 1 day
=> complete work can be done in 78/7 days by B
Answer: Option C #### C
QUESTION:A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is:
options: A)90 cm B)6 dm C)1 m D)1.1 cm E)None of these
SOLUTION:Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (160 - x)] = 8000 × 1000
=> 320 × 250 × (160 - x) = 8000 × 1000
=> (160 - x) = 8000×1000/320=
100
=> x = 60 cm = 6 dm.
Answer: B #### B
QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
options: A)5 B)6 C)7 D)82 E)43
SOLUTION:US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A #### A
QUESTION:If x^2 + y^2 = 13 and xy = 3, then (x − y)^2 =
options: A)7 B)11 C)14 D)17 E)20
SOLUTION:but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 13-2*3=7..
Answer A #### A
QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
options: A)4 B)8 C)16 D)17 E)None of these
SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B #### B
QUESTION:Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I?
options: A)111 B)145 C)110 D)119 E)120
SOLUTION:There are five letters in the given word.
Consider 7 blanks ....
The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways.
The number of words = 5! = 120.
Answer:E #### E
QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA
options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these
SOLUTION:Explanation:
Let A = 2x, B = 3x, C = 4x, then,
AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24
Answer: D #### D
QUESTION:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth?
options: A)39 B)24 C)28 D)26 E)30
SOLUTION:x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
x+32
x+36
10x+180=340
10x=160
x=16
3rd question = x+8 = 16+8 = 24
Answer B #### B
QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE.
If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE?
options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards
SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question.
1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle.
2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus.
3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle.
4) From (1), we know that x = 202+y2−−−−−−−√202+y2.
5) From (3), we know x = 25 - y.
6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y
7) Solving for y, we get 4.5.
8) 25 - 4.5 = 20.5 = x
9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82.
The answer is B, 82 #### B
QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 4x+ 4y > 4z
III. yz > xz
IV. xy > y + z
options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only
SOLUTION:we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 4x+ 4y > 4z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B #### B
QUESTION:A man and his wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is (1/7) and the probability of wife’s selection is (1/5). What is the probability that only one of them is selected?
options: A)1/7 B)2/7 C)3/7 D)4/7 E)5/7
SOLUTION:P(A)=1/7
P(B)=1/5
P(A’)=6/7
P(B’)4/5
Required probability= P((A and B’) or ( B and A’))
=(1/7x4/5)+(1/5x6/7)
=2/7
ANSWER B 2/7 #### B
QUESTION:If both 5^2 and 3^3 are factors of n x (2^5) x (12^2) x (7^3) x (10), what is the smallest possible positive value of n?
options: A)15 B)45 C)75 D)125 E)150
SOLUTION:(2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and one appearance of 5 (in the 10).
Thus n must include at least 3 * 5 = 15
The answer is A. #### A
QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B?
options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above
SOLUTION:et ratio of A and B be 6x & 7x
so net loss = 6x+7x= 7800
x=600
A=6x=6(600)=3600
B= 7x=7(600)=4200
so, B= 4200
ANSWER:A #### A
QUESTION:When n is divided by 48, the remainder is 6. What is the remainder when 4n is divided by 8?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 48)
4n = 4(6) =24, which leaves a remainder of 0 when divided by 8.
Answer A #### A
QUESTION:A group of people,dogs, and birds has seventy legs, thirty heads, and twenty
tails. How many cats are among this group? (Assume all birds have two legs and a tail.)
options: A)0 B)5 C)13 D)15 E)20
SOLUTION:Write P, C, and B for the number of people, dogs, and birds respectively, so that
we have
2P + 4C + 2B = 70, P + C + B = 30,C + B = 20:
Comparing the last two equations we obtain P = 10, and the first equation simplifies to
4C + 2B = 50, or 2C + B = 25. Therefore,
C = (2C + B) -(C + B) = 25- 5 = 5
correct answer B #### B
QUESTION:A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)
options: A)$15,360 B)$17,360 C)$25,560 D)$21,360 E)$27,360
SOLUTION:For every $3 earn above $9360, the recipient loses $1 of benefit.
OR
For every $1 loss in the benefit, the recipient earns $3 above $9360
If earning is; 9360+3x
Benefit = 12000-x
Or the vice versa
If benefit is 12000-x, the earning becomes 9360+3x
He lost 50% of the benefit;
Benefit Received= 12000-0.55*12000 = 12000-6600
x=5400
Earning becomes 9360+3x=9360+3*5400=25560
Ans:C #### C
QUESTION:In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1200 employees, then the no. of female employees who are computer literate ?
options: A)504 B)674 C)672 D)960 E)None
SOLUTION:Solution: Total employees,
= 1200
Female employees, 60% of 1200.
= (60 *1200) /100 = 720.
Then male employees,
= 480
50 % of male are computer literate,
= 240 male computer literate.
62 % of total employees are computer literate,
= (62 *1200) /100 = 744 computer literate.
Thus, Female computer literate = 744 - 240
= 504.
Answer: Option A #### A
QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold?
options: A)6 B)4 C)8 D)10 E)12
SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies;
14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22
# of paperback copies sold is 30-22=8
Answer: C #### C
QUESTION:At a game of billiards,A can give B 15 points in 60 and A can give C 20 points in 60.How many points can B give C in a game of 90 ?
options: A)30 points B)20 points C)10 points D)12 points E)None of these
SOLUTION:Solution
A : B = 60 : 45 and A : C = 60 : 40.
∴ B/C =( B/A x A/C) = (45/60 x 60/40) = 45/40 =90/80= 90 : 80
∴ B can give C 10 points in a game of 90.
Answer C #### C
QUESTION:In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals.
options: A) 10 B) 12 C) 17 D) 22 E) 30
SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach:
100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to
W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)267 B)240 C)166 D)111 E)121
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300
= 540 ==> x
= 240 m.
Answer: B #### B
QUESTION:If x is less than y by 25% then y exceed x by:
options: A)33.33% B)25% C)75% D)66.66% E)None of these
SOLUTION:Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 25(100-25)*100
=33.33%
ANSWER:A #### A
QUESTION:A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
options: A)37 sec B)89 sec C)36 sec D)87 sec E)45 sec
SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 250 + 120 = 370 m.
Time taken = 370/10
=37 sec.
Answer: A #### A
QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream?
options: A)30/18 hours B)37/13 hours C)80/13 hours D)20/9 hours E)30/43 hours
SOLUTION:Speed downstream = 20 + 7 = 27 kmph.
Time required to cover 60 km downstream
= d/s = 60/27
= 20/9 hours.
Answer: D #### D
QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
options: A)288 B)165 C)881 D)1277 E)121
SOLUTION:Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 25 = 375 m.
Let the length of the platform be x m . Then,
(x + 375)/36 = 15 => x = 165 m.
Answer: B #### B
QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he
can cover?
options: A)20km B)40km C)60km D)80km E)160km
SOLUTION:t=d/s, so
36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)
36=x(18/80)
x=160km
ANSWER:E #### E
QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
options: A)29 B)30 C)30.5 D)31 E)32
SOLUTION:to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30
hence B #### B
QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
options: A)2 B)8 C)9 D)11 E)15
SOLUTION:220 + 43 = 263/17 = 8 (Remainder)
B #### B
QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls?
options: A)12 B)32 C)5 D)28 E)30
SOLUTION:number of kids playing with white color balls = 26
total number of kids in the play school = 35
number of kids playing with both white and yellow color balls = 19
we have to find,
number of kids playing with yellow color balls
35 = 26 + n(B) - 19
35 + 19 - 26 = 28
Hence, Answer is 28 kids play with yellow color
balls. ANSWER D #### D
QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
options: A)1.7 B)1.4 C)1.1 D)1.5 E)1.2
SOLUTION:M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D #### D
QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by
options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these
SOLUTION:P = Q×r×t/100 and Q = R×r×t/100
⇒ P/Q=Q/R=r×t/100
∴ Q2 = PR.
Answer B #### B
QUESTION:A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train?
options: A)230 m B)250m C)643m D)832m E)270m
SOLUTION:Speed = (72 x 5/18)m/sec = 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then, x + 270/26 = 20
x + 270 = 520
x = 250.
Answer:B #### B
QUESTION:John bought 2 shares and sold them for $98 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
options: A) a profit of $10 B) a profit of $8 C) a loss of $4 D) a loss of $10 E) neither a profit nor a loss
SOLUTION:$ Profit of the share sold at 20% profit =
120-98
20-?
$18 profit on the sale of 1 share.
$ Loss of the share sold at 20% loss=
80-98
20-?
$22 loss on the sale of 1 share.
18-22=Loss of $4
Answer: C #### C
QUESTION:If 15% of a class averages 100% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 63% on the test, what is the overall class average? (Round final answer to the nearest percent).
options: A)76% B)77% C)78% D)79% E)80%
SOLUTION:This question is a Weighted Average question with a series of dependent variables.
The remaining portion of the class represents 100% - 15% - 50% = 35% of the class
Converting the portions of the class population to decimal weights, we find:
Class Average = 0.15x100 + 0.50x78 + 0.35x63 = 76.05
The class average (rounded) is 76%
Final Answer
A) 76% #### A
QUESTION:A coin is tossed live times. What is the probability that there is at the least one tail?
options: A)1/15 B)31/32 C)1/10 D)30/32 E)25/27
SOLUTION:Probability of getting least one tail at the coin tossed five times.
= There is not even a single tail.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
ANSWER B #### B
QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
options: A)5 B)10 C)24 D)32 E)120
SOLUTION:If it were a line/column combination/permutation problem, the solution would be : 5! = 120.
However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24.
ANS:C #### C
QUESTION:There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen?
options: A)2 B)3 C)14 D)16 E)20
SOLUTION:60% of 30 = 18.
So, there are 18 red socks and there are 12 blue socks.
Check out this possible cases once we have selected TWO socks:
case a: 2 red socks, in which case we have a pair of matching socks. DONE!
case b: 2 blue socks, in which case we have a pair of matching socks. DONE!
case c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet.
Since the first 2 cases result in a pair of matching socks, let's focus on case 3 and what happens when we select a 3rd sock.
If we have 1 red sock and 1 blue sock, then the next sock we select will EITHER match the red sock OR match the blue sock.
In both cases, we are guaranteed to have a pair of matching socks.
So, selecting 3 socks guarantees that we have a pair of matching socks.
ANSWER:B #### B
QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
options: A)8% B)7% C)10% D)6% E)9%
SOLUTION:Explanation:
Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol,
such that Benson buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Benson spends additional 15% on petrol,
amount spent by Benson = 100× (100+15)/100 = Rs.115
Hence Quantity of petrol that he can purchase = 115/125 Litre
Quantity of petrol reduced = (1−115/125) Litre
Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8%
Answer: Option A #### A
QUESTION:From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn
options: A)4/13 B)1/52 C)1/4 D)1/5 E)None of above
SOLUTION:Explanation:
Total number of cases = 52
Total face cards = 16 [favourable cases]
So probability = 16/52 = 4/13
Answer: A #### A
QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually.
options: A)812 B)712 C)412 D)512 E)612
SOLUTION:Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112.
therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612.
Answer is E. #### E
QUESTION:M and N invested in a shop. The profits were divided in the ratio of 4 : 5 respectively. If M invested Rs. 40,000, the amount invested by N is:
options: A)35000 B)40000 C)50000 D)60000 E)None
SOLUTION:Suppose N invested Rs. x. Then, 40000/x = 4/5 or y = [40000 x 5/ 4] = 50000.
Answer C #### C
QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km
SOLUTION:Explanation:
Speed in still water = 6 kmph
Speed of the current = 1 kmph
Speed downstream = (6+1) = 7 kmph
Speed upstream = (6-1) = 5 kmph
Let the required distance be x km
Total time taken = 1 hour
⇒ x/7+x/5=1
⇒5x+7x=35
⇒12x=35
⇒x=2.9 km
Answer: Option C #### C
QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by:
I. 12 II. 24 III. 48
options: A)I B)I & III C)II D)II & III E)III
SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24.
So answer is III
Answer : E #### E
QUESTION:We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Let x be the number of canoes.
Then 2x/3 is the number of kayaks.
12x+(2x/3)*18=504
12x+12x=504
24x=504
x=21 (canoes)
2x/3=14 (kayaks)
There were 21-14 = 7 more canoes rented out.
The answer is C. #### C
QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers?
options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2!
SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 8 is 8!.
2. # of arrangements when 3 boys are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!6!.
# of arrangements when 3 boys do not sit together would be: 8!-3!6!.
Answer: B). #### B
QUESTION:When asked what the time is,a person answered that the amount of time left is 1/5 of the time already completed.what is the time.
options: A)2 B)9 C)3 D)8 E)6
SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)
24−x=15x⇒x=2024−x=15x⇒x=20
Time is 8 PM
Answer:D #### D
QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point?
options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west
SOLUTION:she is currently at 5km north east from the starting point
ANSWER:A #### A
QUESTION:In a bag containing only blue, red and green marbles, all but 15 are blue, all but
13 are red and all but 12 are green. How many are red?
options: A)13 B)7 C)25 D)20 E)10
SOLUTION:All but blue means number of marbles except blue..hence, let x be the red marble,y
be the green marble,z be the blue marble...
x+y=15
y+z=13
x+z=12
solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7
ANSWER:B #### B
QUESTION:Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?
options: A)ab/(a+b) B)(a-b)/(a+b) C)b/(b+a) D)a/(a+b) E)b/(a-b)
SOLUTION:Randy can do the job in a hrs, Alvin can do the job in b hrs.
When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.
Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)
So Randy does a/(a+b) of the work and Alvin does b/(a+b) of the work.
Answer (C). #### C
QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
options: A)29 B)29 C)60 D)19 E)12
SOLUTION:Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5
= 60 km/hr.
Answer:C #### C
QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
options: A)17% B)19% C)18% D)14% E)16%
SOLUTION:Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer: C #### C
QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class?
options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm
SOLUTION:The total height was 45 cm too much.
The average height should be reduced by 45 cm/30 = 1.5 cm
The answer is B. #### B
QUESTION:Two cars start at the same time from opposite ends of a highway that is 333 miles long. One car is riding at 54 mph and the second car is riding at 57 mph. How long after they begin will they meet?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:As cars are moving in opposite directions their speeds will be added. So their relative speeds: 57+54 = 111 mph
Total distance to be covered = 333 miles.
Time taken would be: 333 miles/111 mph = 3 hours
C is the answer. #### C
QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity?
options: A)7/18 B)9/18 C)2 D)18/7 E)18/5
SOLUTION:Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D
QUESTION:A train 120 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
options: A)11 s B)10 s C)8 s D)12 s E)None of these
SOLUTION:We know from the formula Time = Distance/ Speed
Thus, Time = 120/ 54 x 5/18
or, Time = 8 sec.
ANSWER:C #### C
QUESTION:A numberais squared and then multiplied by negative 3. The result of this operation Q is equal to three times the sum of three timesaand two. What is one possible value ofa?
options: A)-3 B)-2 C)1 D)2 E)3
SOLUTION:Q=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B #### B
QUESTION:For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 60, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.
options: A)K+35 B)2K+35 C)(60+K)/2 D)(70-K)/2 E)2(70-K)
SOLUTION:Say Sue was hired when she was already 60 years old (k=60), then she could retire right away, at the age of 60. Now, plug k=60 in the answer choices and see which yields 60. Only C fits.
Answer: C. #### C
<<<Examples ends
QUESTION:There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly then what is the probability that neither blue nor green?
options: A)2/21 B)3/31 C)4/17 D)3/19 E)probability=8/21
SOLUTION:Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21. #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition
options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980
SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum.
i,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) }
so,here by putting the values as,
(0+1+2+3+4){(5-1)!*(11111)-(5-2)!*1111}
= 10{(4!*11111)-(3!*1111)}
= 10{266664-6666}
= 2599980
ANSWER:A #### A
QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125
options: A)123 B)143 C)166 D)190 E)210
SOLUTION:28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C #### C
QUESTION:A bag contains 8 red and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
options: A)4/7 B)2/3 C)8/11 D)1/4 E)5/7
SOLUTION:Total number of balls = 8+3 = 11
number of white balls = 8
Probability = 8/11 = 8/11
Answer is C #### C
QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
options: A)7500 B)3600 C)8900 D)9000 E)5000
SOLUTION:35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
ANSWER A #### A
QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 140 sandwiches were made, how many bologna sandwiches
were made?
options: A)15 B)30 C)38 D)42 E)49
SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
140 / 20 = 7 sandwiches in one part
For bologna we have 7 parts so:
7 * 7 = 49
Answer is E #### E
QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
options: A)20% B)30% C)32% D)73% E)84%
SOLUTION:SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 ---20 => 20%
Answer:A #### A
QUESTION:A train 350 m long passed a pole in 35 sec. How long will it take to pass a platform 650 m long?
options: A)100 sec B)89 sec C)85 sec D)16 sec E)15 sec
SOLUTION:Speed = 350/35 = 10 m/sec.
Required time = (350 + 650)/10
= 100 sec.
Answer: A #### A
QUESTION:In how many ways the word "KIT" can be arranged?
options: A)6 B)8 C)18 D)21 E)24
SOLUTION:Explanation :
The required number of ways = 3!
= 6
Answer : A #### A
QUESTION:The price of a T.V. set worth Rs. 30000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
options: A)22678 B)26699 C)29000 D)19000 E)26711
SOLUTION:Money paid in cash = Rs. 1000
Balance payment = (30000 - 1000) = Rs. 29000
Answer: C #### C
QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
options: A)5:4 B)4:5 C)2:5 D)5:2 E)None of them
SOLUTION:Let the third number be x.
Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2
Therefore, Ratio of first two numbers = (6x/5 : 3x/2)
= 12x : 15x = 4 : 5.
Answer is B. #### B
QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day?
options: A)10 B)41 C)31 D)21 E)22
SOLUTION:Explanation:
1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12
1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16
1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48
Let ‘x’ be the No. of boys required.
Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1
= (4 + 3 + x)/48 = 1
i.e. 7 + x= 48 and x = 41.
Answer: Option B #### B
QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3%
SOLUTION:675 ---- 225
100 ---- ? => 33 1/3%
Answer:C #### C
QUESTION:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 123, what is the least possible value of n?
options: A)37 B)123 C)41 D)52 E)87
SOLUTION:123 is 3 * 41, so n needs to be at least 41, so the answer is C. #### C
QUESTION:There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
options: A)435 B)367 C)361 D)297 E)261
SOLUTION:Explanation:
Total number of persons = n = 30
Shakehands involve only 2 persons = r = 2
Number of shakehands = nCr = 30C2
30C2 = (30 * 29) /(2 * 1) = 435
nCr = (n!) / r! (n – r)!
= 30! / 2! 28!
= 435
ANSWER:A #### A
QUESTION:Walking at 8KMPH From Point E to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point E to Railway station?
options: A)A)9KM B)B)6.66KM C)C)7.25KM D)D)12.40KM E)E)13KM
SOLUTION:Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point E and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point E and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B #### B
QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
options: A)160 B)175 C)180 D)195 E)205
SOLUTION:Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 * 8 * 4) = 160.
Therefore, 160 * 2.40 + x * 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER:B #### B
QUESTION:A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers Q are possible?
options: A)2 B)4 C)6 D)3 E)Not possible
SOLUTION:Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total of Q= 6 possibilities.
C. #### C
QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 8 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
options: A) 5 B) 9 C) 10 D) 12 E) 15
SOLUTION:This is an inverse proportional problem......
5 pipes in 8 days; So for 4 days, it will be = 8 x 5 / 4 = 10
So, 10-5 = 5
Answer A #### A
QUESTION:The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides?
options: A)2 B)7 C)5 D)3 E)4
SOLUTION:S = (1 + 1 + 2)/2
= 2
Answer: A #### A
QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution?
options: A)45 B)33 1/3 C)27 D)16 2/3 E)15
SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution?
3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x:
1.5/x = 1/20
x = 30
Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution.
Answer is A. #### A
QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is:
options: A)27% B)87% C)15% D)66% E)88%
SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900.
Face value = Rs. (50 x 20) = Rs. 1000.
Dividend = Rs. 27 x 1000 = Rs. 135.
2 100
Interest obtained = 135 x 100 % = 15%
900
View Answer Discuss in Forum
Answer: C #### C
QUESTION:A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is:
options: A)260 B)262 C)270 D)272 E)None of these
SOLUTION:Explanation:
Volume will be length * breadth * height, but in this case two heights are given so we will take average,
Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3
Option C #### C
QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
options: A)4 B)8 C)16 D)17 E)None of these
SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B #### B
QUESTION:What is the smallest positive integer x, such that 6000x is a perfect cube?
options: A)4 B)6 C)36 D)12 E)18
SOLUTION:Take out the factors of 6000 that will come 2*3*10^3. for perfect cube you need every no. raise to the power 3. for 6000x to be a perfect cube, need two 2 and 2 3 that means 36 or 6^2
C is the answer. #### C
QUESTION:A grocer buys apples for 63¢ per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price?
options: A)66¢ B)70¢ C)75¢ D)77¢ E)84¢
SOLUTION:for making calculation simple let us consider he buys 10 pounds @ 63/pound=630¢ in total .
10% apples lost...means 9 pounds left.
further he wants 20% profit on 630 ¢
means he wants to earn 756¢
sales price should be 756/9==¢ 84
ANSWER:E #### E
QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
options: A)37 B)85 C)48 D)43 E)84
SOLUTION:Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer: Option C #### C
QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
options: A)228 B)200 C)279 D)480 E)221
SOLUTION:SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480.Answer:D #### D
QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these
SOLUTION:Explanation:
Let the cost of one pen is ‘5x’ and pencil is ‘x’
3 X 5x + 5x = Rs.150
15x + 5x = Rs.150
X = 150/20 = 7.50
:. Cost of 1 pen = 5x = 5 x 7.50 = 37.50
:. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450
Answer: Option D #### D
QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
options: A)12 B)14 C)15 D)19 E)10
SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15. Answer:C #### C
QUESTION:9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere?
options: A)4 cm B)6 cm C)8 cm D)10 cm E)12 cm
SOLUTION:Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
9*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 12 = 64 cm^3
R = 4 cm
D = 8 cm
The answer is C. #### C
QUESTION:A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
options: A)14 years B)18 years C)20 years D)22 years E)16 years
SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 20) + 2 = 2(x + 2)
x + 22 = 2x + 4
x = 18.
answer :B #### B
QUESTION:If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?
options: A)10 B)15 C)20 D)25 E)None of them
SOLUTION:Let the required number of days be x.
More men, Less days (indirect proportion)
Less hours per day, More days (indirect proportion)
Men 18 : 15
Hours per day 8: 9 } : :16 : x
(18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15
Hence, required number of days = 15.
Answer is B. #### B
QUESTION:The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ?
options: A)20 years B)21 years C)22 years D)34 years E)24 years
SOLUTION:The average age of the 5 members is 20 years
=> The sum of the ages of the 5 members is 20*5 = 100 years
Once the new member joins, the average age becomes 24 years.
Let the age of the new member be x.
Then (110+x)/6 = 24
=> x = 34 years
Answer D #### D
QUESTION:In the city of San Durango, 60 people own cats, dogs, or rabbits. If 36 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
options: A)2 B)4 C)7 D)12 E)32
SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR
60 = 36 + 40 + 10 - (12) - 2x
x = 7
So, answer will be C #### C
QUESTION:In a certain lottery, the probability that a number between 1 and 15, inclusive, is drawn is 1/3 . If the probability that a number 1 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 15 is drawn?
options: A)2/3 B)1/3 C)1/4 D)1/6 E)2/5
SOLUTION:You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 1 or larger
Set 2: Number 15 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or less OR both)
2/3 + P(Set 2) - 1/3 = 1
P(Set 2) = 2/3
Answer A #### A
QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ?
options: A)6 B)2 C)-1 D)-3 E)-4
SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even
now subtract X + (X+2) - (X+4)
doing this leaves us with X -2
what even number can we substitute in X to yield an answer choice
B works 2 (plug in 4 for X) #### B
QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute?
options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min
SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
68 kilometers per hour = 68 km/hr
= (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute
correct answer is B)1133.33m/min #### B
QUESTION:The area of a triangle is with base 4m and height 5m?
options: A)20 m2 B)10 m2 C)82 m2 D)54 m2 E)28 m2
SOLUTION:1/2 * 4 * 5
= 10 m2
Answer:B #### B
QUESTION:How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest?
options: A)2.35 years B)4.25 years C)7 years D)1.25 years E)2 years
SOLUTION:Explanation:
Time = (100 x 60)/(400 x 12) years
= 1.25 years.
Answer: D #### D
QUESTION:Find the odd man out
864, 420, 200, 93, 40, 16, 6
options: A)420 B)200 C)16 D)93 E)6
SOLUTION:6x2+4=16
16x2+8=40
40x2+12=92
92x2+16=200.. and so on. 93
ANSWER:D #### D
QUESTION:What number has a 3:4 ratio to the number 400?
options: A)130 B)100 C)200 D)300 E)120
SOLUTION:3:4 = x: 200
4x = 3*400
x=300
ANSWER:D #### D
QUESTION:At what rate percent on simple interest will a sum of money double itself in 20 years?
options: A)2% B)6% C)3% D)4% E)5%
SOLUTION:P = (P*20*R)/100
R = 5%
ANSWER:E #### E
QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
options: A)7 B)6 C)5 D)4 E)3
SOLUTION:Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:7
Webs 7:1
1 x 7 x x = 7 x 1 x 7
=> x= 7
Answer is 7 #### A
QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is:
options: A)3000 B)3200 C)3450 D)4000 E)3570
SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5
= 105 : 40 : 36.
Let the initial investments be 105x, 40x and 36x.
=> A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12)
= 1680x : 480x : 432x
= 35 : 10 : 9.
Hence, A2's share = Rs. 21600 x 10/54
= Rs. 4000. Answer : D #### D
QUESTION:The ratio of two quantities is 2 to 3. If each of the quantities is increased by 4, what is the ratio of these two new quantities?
options: A)5/5 B)It cannot be determined from the information given. C)11/5 D)12/5 E)13/5
SOLUTION:let the actual ratio be 2k/3k, increase numerator and denominator by 4=> 2k+4/3k+4
Until the value of k is unknown we can not determine the actual ratio.
OR
let the actual be 3/4. After increasing 4 => 7/8
let the actual be 6/8. After increasing 4 => 10/12
Therefore without actual quantities we cannot determine the actual ratio.
Answer : B #### B
QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
options: A)565 B)444 C)676 D)420 E)663
SOLUTION:1h ----- 3
? ------ 60
12 h
RS = 16 + 19 = 35
T = 12
D = 35 * 12 =420
Answer: D #### D
QUESTION:If 18!/3^x is an integer, what is the greatest possible value of x?
options: A)3 B)4 C)5 D)6 E)8
SOLUTION:18 - 3*3*2
15 - 5*3
12 - 4*3
9 - 3*3
6 - 2*3
3 - 1*3
Hence max of 3^8 is allowed. IMO E. #### E
QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?
options: A)120cc B)360cc C)450cc D)589C E)478cc
SOLUTION:Explanation:
r1 = x r2 = 3x
Π * x2 * h = 40
Π9 x2h = 40 * 9 = 360cc
Answer: B #### B
QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam?
options: A)52% B)64% C)72% D)76% E)80%
SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A
QUESTION:If p and q are two different prime numbers, which of the following cannot be true?
options: A)pq is odd. B)p + q is even. C)p + q is odd. D)pq is even. E)p/q is an integer
SOLUTION:A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (p/q=integer means that p is a multiple of q).
Answer: E.
All other options are possible:
A. pq is odd --> p=3 and q=5;
B. p + q is even --> p=3 and q=5;
C. p + q is odd --> p=2 and q=3;
D. pq is even --> p=2 and q=3;
E #### E
QUESTION:When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y?
options: A)560 B)616 C)672 D)728 E)784
SOLUTION:ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
W=8(2+3+4....+12)=616 #### B
QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a spade and the second card is a jack is?
options: A)1/50 B)1/13 C)1/26 D)1/52 E)1/4
SOLUTION:Probability of a spade = 13/52 = 1/4
Probability of a jack = 4/52 = 1/13
Probability of both = P1*P2 = 1/(4*13) = 1/52
Answer is D. #### D
QUESTION:Three clocks were set to true time and starts to run together, makes a beep sound at intervals of 8,10 and 12 minutes respectively. In 2 days, how many times do they will make the sound together ?
options: A)12 B)15 C)25 D)30 E)35
SOLUTION:Explanation :
The clocks make sound at intervals of 8, 10 and 12 minutes respectively.
The LCM of 8,10 and 12 is 120.
So, the clocks will make sound together after every 120 minutes. i.e., after every 2 hours.
In 2 days(48 hours), they will make the sound together (48/2) = 24 times.
At the end of 2nd day, they will make one more beep together.
Therefore, totally (24+1) 25 times beep sound is made together.
Hence the answer is 25 times.
Answer : C #### C
QUESTION:$500 will become $1000 in 6 years find the rate of interest?
options: A)A)16.67% B)B)20% C)C)25% D)D)30% E)E)50%
SOLUTION:SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*6 =16.67%
Answer is A #### A
QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is?
options: A)1994 B)1494 C)1349 D)1496 E)1500
SOLUTION:LCM = 1400
1400 - 6 = 1394
ANSWER:C #### C
QUESTION:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
options: A)17% B)24% C)30% D)32% E)79%
SOLUTION:take it as original output =100.
to meet demand increase by 10%, then output=110.
to meet holiday demand , new output increase by 10% then output equals 121
To restore new holidy demand output to original 100.
final -initial/final*100
=21/121*100=8/33*100=17% approxiamately.
option A is correct. #### A
QUESTION:12, 24, 16, 32, 24, 48, ?
options: A)31 B)32 C)36 D)37 E)40
SOLUTION:E
40
This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E
QUESTION:Two consecutive traffic signals each show either red or green. How many different arrangements of the two signals are possible? (Note: “Red-green” is different from “green-red.”)
options: A)10 B)9 C)8 D)7 E)4
SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 2 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 2 signals are possible.
Total Options: 4
Final Answer:
E #### E
QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
options: A)38 B)41 C)30 D)31 E)29
SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: C #### C
QUESTION:A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 45 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
options: A)40 B)45 C)50 D)55 E)60
SOLUTION:A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 45 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
45 = 180/4t
t = 60
B-C = 60 mph
Answer E #### E
QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y?
options: A)3/2 B)2 C)4/3 D)4 E)9/2
SOLUTION:Its simple
equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.
Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4.
Thus, correct ans is E #### E
QUESTION:8^100 is divisible by 17. Find the remainder?
options: A)8 B)12 C)16 D)18 E)20
SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 = (816)6×8417
Now this problem simply boils down to (1)6×8417 = 8417
84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.
C #### C
QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3
SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D #### D
QUESTION:10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
options: A)2267 B)287 C)268 D)228 E)225
SOLUTION:1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/6
15 women's 1 day work = (1/6 - 10/100) = 1/15
1 woman's 1 day work = 1/225
1 woman alone can complete the work in 225 days.
Answer: E #### E
<<<Examples ends
QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ?
options: A)118 B)290 C)119 D)139 E)132
SOLUTION:Number of words which can be formed
= 5! - 1 = 120 - 1
= 119.
Answer:C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 70% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
options: A)a) 50% B)b) 53% C)c) 54% D)d) 55% E)e) 57%
SOLUTION:Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=55%
D #### D
QUESTION:S1 = 5 S2 = 8 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?
options: A)15 B)14 C)13 D)12 E)16
SOLUTION:term 16 = 3*16+4 = 52
Answer : E #### E
QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes
options: A)18kms B)16kms C)50kms D)30kms E)40kms
SOLUTION:total eastward distance= 25kmph*1/4hr=6.25 km
total westward distance= 40kmph*1/4hr=10 km
total distn betn them= 6.25+10=16.25km
ans 16km
ANSWER:B #### B
QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make an orange juice. How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice.
options: A)25 B)34 C)50 D)67 E)100
SOLUTION:A =25
1 oz concentrate + 3 oz ofwater = 4 oz jucie
300 oz concentrate +900 oz of waer = 1200 oz juice
no of cans==300/12=25
Ratio of juice to water ===> 1:3
total 200*6 ounces
12 ounce juice cans ==> 1200/12 == 100*1/4 (ratio of jiuce to total) == 25 #### A
QUESTION:hat should come in place of question mark (?) in the following equation ?
197 × ? + 16(2) = 2620
options: A)22 B)12 C)14 D)16 E)None of these
SOLUTION:? = 2620−256 /197=12
Answer B #### B
QUESTION:A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?
options: A) 75 and 80 B) 80 and 85 C) 74 and 74 D) 75 and 75 E) 70 and 80
SOLUTION:Ans: C
Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value.
C #### C
QUESTION:Three numbers are in the ratio 1:2:3 and their H.C.F is 62. The numbers are:
options: A)62, 124, 186 B)60, 124, 186 C)10, 20, 30 D)62, 24, 186 E)12, 24, 186
SOLUTION:Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 62.
The numbers are 62, 124, 186.
ANSWER:A #### A
QUESTION:In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ?
options: A)30 B)45 C)42 D)72 E)75
SOLUTION:Let the number of benches in the class be x.
Then, 6(x + 1) = 7x - 5
x = 11.
Hence, number of students in the class = 6 ( x + 1)
= 6 x 12
= 72.
ANSWER:D #### D
QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.
options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these
SOLUTION:Explanation:
=[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06
Answer: D #### D
QUESTION:Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
options: A)22 B)30 C)48 D)99 E)12
SOLUTION:Relative speed = 90 + 30 = 120 km/hr.
120 * 5/18 = 100/3 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 3/100 = 30 sec.
Answer: B #### B
QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900?
options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391
SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009.
Reqd.sale=Rs.[(6900*6)-34009]
= Rs.(41400-34009)
= Rs.7391.
ANSWER:E #### E
QUESTION:Harish can paint a wall in just 3 hours. However it takes 6 hours for Ganpat to complete the same job of painting the wall.
How long would it take for both of them to paint the wall , if both work together ?
options: A)3 Hours B)1 Hours C)3.20 Hours D)2 Hours E)1.35 Hours
SOLUTION:D
Two hours.
Harish who could paint the wall in 3 hours could paint 2/3 of the wall in just two hours. Ganpat who paint the wall in 6 hours could paint 1/3 of the wall in two hours.
2/3 + 1/3 = 1. #### D
QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
options: A)10years B)12 years C)5 years D)3 years E)24 years
SOLUTION:Explanation:
9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3 years
Answer:D #### D
QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items?
options: A)15% B)12.16% C)13.4% D)20.2% E)None of these
SOLUTION:Explanation :
Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively.
And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively.
Overall loss percentage of the 1st two items = 14.33%
=>(0.21p+0.11q)/(p+q)=0.1433
=>p/q=1/2.
Overall loss percentage of the 2nd and 3rd item =10.4%
=>(0.11q+0.1r)/(q+r)=0.104.
=>q/r=2/3.
Therefore, the overall loss percentage is :
=>(0.21p+0.11q+0.1r)x100/(p+q+r).
=>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3).
=>0.1216×100.
=>12.16%.
Answer : B #### B
QUESTION:A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
options: A)2400 B)2880 C)2787 D)3087 E)0728
SOLUTION:1200 * 12: x * 9 = 2:3
x = 2400
Answer: A #### A
QUESTION:How many four letter words are formed using the letters of the word POLICE?
options: A)280 B)321 C)330 D)360 E)370
SOLUTION:The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 6P4
= 6 * 5 * 4 * 3 = 360.
Answer: D #### D
QUESTION:The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
options: A)76 B)29 C)26 D)19 E)11
SOLUTION:Explanation:
Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 - 320 = 76
Answer: A #### A
QUESTION:In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13. If the shop carries 352 dogs and bunnies total in stock, how many dogs are there?
options: A)42 B)66 C)98 D)112 E)154
SOLUTION:Let us assume the number of dogs, cats and bunnies to be 3x, 7x and 13x
Total dogs and bunnies = 16x.
And we are given that 16x = 352.
Hence x = 22.
Dogs = 3x = 3*22 = 66 (Option B) #### B
QUESTION:A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
options: A)5/6 km/hr B)25 km/hr C)79.2 km/hr D)15 km/hr E)38 km/hr
SOLUTION:Explanation:
Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr
Answer:C #### C
QUESTION:Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
options: A)326 B)372 C)375 D)381 E)312
SOLUTION:A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C #### C
QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ?
options: A)-1 B)-5 C)-2 D)-3 E)-4
SOLUTION:Use answer options to solve this problem -
x is negative integer (-1,-2,-3......)
put x=-1
7x+3y=14
7(-1)+3y=14
-7+3y=14
3y=14+7
3y=21
y=7
Answer will be (A) #### A
QUESTION:A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
options: A)37 sec B)89 sec C)36 sec D)87 sec E)45 sec
SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 250 + 120 = 370 m.
Time taken = 370/10
=37 sec.
Answer: A #### A
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was:
options: A)14 B)16 C)19 D)22 E)24
SOLUTION:Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21.
Son's age 5 years back (21 - 5) = 16 years.
answer :B #### B
QUESTION:A cylinder of height h is 7/8 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
options: A)25% B)50% C)69% D)80% E)100%
SOLUTION:Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 7/8
New cylinder 3/5
So 3/5/7/8 = 3/5*8/7 = 0.69 or 69%.
Answer C #### C
QUESTION:3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last?
options: A)6 B)9 C)12 D)15 E)18
SOLUTION:2 oxen = 3 buffaloes = 4 cows
Also: 15 buffaloes + 8 oxen + 24 cows
= 10 oxen + 8 oxen + 12 oxen = 30 oxen
There is enough fodder for 1 oxen for 30*24 days.
60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen
The new total is equal to 80 oxen instead of 30 oxen.
30*24 / 80 oxen = 9 days
The answer is B. #### B
QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place.
options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours
SOLUTION:1/5+2/8 + 3/x = 1
x =20 hours. ANSWER =D #### D
QUESTION:In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x?
options: A)-2 B)-1 C)0 D)1 E)2
SOLUTION:The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3
4/3 = 22-2 / 13-x
52-4x = 66-6
x = -2
The answer is A. #### A
QUESTION:if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
options: A)11x/y B)10x/y C)x/11y D)11/xy E)xy/11
SOLUTION:Answer is B.
The rate of running hards: 10 minutes per y hards.
Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y #### B
QUESTION:Submarine M and Submarine N are equipped with sonar devices that can operate within a 4,000 yard range. Submarine M remains in place while Submarine N moves 3,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West
options: A)I,II only B)II,III only C)II only D)I and III only E)III only
SOLUTION:It's evident if we make a diagram for the Movement of N respect to M.
From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.
Thus it can only move north or west or anything in that curve.
Answer : D #### D
QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8840 and in 3 years to Rs.9261?
options: A)8054 B)8877 C)2877 D)2678 E)1011
SOLUTION:8840 ---- 421
100 ---- ? => 4.76%
x *104.76/100 * 104.76/100 = 8840
x*1.0975=8840
x=8840/1.0975 => 8054.54
Answer: A #### A
QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet?
options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec
SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (36 + 36)*5/18 = 4*5 = 20 mps.
The time required = d/s = 100/20 = 5 sec.
Answer : C #### C
QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
options: A)37 B)85 C)48 D)43 E)84
SOLUTION:Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer: Option C #### C
QUESTION:The area of the maximum size of the circle described from the 10 inch square?
options: A)75.5 sq inch B)76.5 sq inch C)77.5 sq inch D)78.5 sq inch E)79.5 sq inch
SOLUTION:10 inch square means sides of sq are 10inch
then circle is within square so diameter would be 10 inch maximum and radius is 5inch
so area of the circle is = pi*r*r=3.14*5*5=78.5 sq inch
ANSWER:D #### D
QUESTION:If the integer w is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when w is rounded to the nearest ten. which of the following is a possible value of w?
options: A)64 B)67 C)99 D)133 E)147
SOLUTION:We have to check options 1 by 1.
64 rounded to nearest hundred = 100
64 rounded to nearest ten = 60
now difference = 40
the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.
therefore 40/60)*100 = 66 2/3 ==>this is the answer.
99 rounded to nearest ten = 100
133 rounded to nearest ten = 130
133 rounded to nearest hundred w= 100=A #### A
QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
options: A)90 B)2,700 C)3,300 D)5,400 E)324,000
SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 110*30=3,300 copies.
Answer: C. #### C
QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
options: A)11 B)10 C)8 D)12 E)15
SOLUTION:Suppose they meet x hours after 8 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 11 a.m.
Answer: A #### A
QUESTION:A reduction of 15% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
options: A)s.24 B)s.46 C)s.40 D)s.41 E)s.34
SOLUTION:800*(15/100) = 120 ---- 5
? ---- 1 => Rs.24
Answer: A #### A
QUESTION:The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes?
options: A)5! B)10!/(5!5!) C)10!/5! D)10! E)10!*5!
SOLUTION:Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations R of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B #### B
QUESTION:How many possible integer values are there for x if |4x - 3| < 6 ?
options: A)One B)Two C)Three D)Four E)Five
SOLUTION:Solution: |4x-3| < 6
let 4x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =4x ==> -3<4x<9
dividing all values by +4 we have -0.75 <x < 2.24
Now question says Integer values (not rational ) therefore we have 0,1,2
ANSWER:C #### C
QUESTION:What is the sum of the numbers between 1 and 20, inclusive?
options: A)310 B)200 C)215 D)285 E)210
SOLUTION:Sol. 1+2+3...17+18+19+20
answer. E #### E
QUESTION:How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
options: A)482 B)226 C)276 D)266 E)181
SOLUTION:Explanation:
20000(11/10)4 - 20000(6/5)2
= 482
Answer: A #### A
QUESTION:The wages earned by Robin is 40% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
options: A)14% B)23% C)30% D)50% E)100%
SOLUTION:Let wage of Erica = 10
Wage of Robin = 1.4*10 = 14
Wage of Charles = 1.6 *10 = 16
Percentage by which wage earned by Charles is more than that earned by Robin = (16-14)/14 * 100%
= 2/14 * 100%
=14%
Answer A #### A
QUESTION:The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number?
options: A)3 B)6 C)9 D)12 E)15
SOLUTION:Sol.
Let the numbers be x, x + 2 and x + 4.
Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7.
∴ Middle number = x + 2 = 9.
Answer C #### C
QUESTION:In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
options: A)L(L-N) /L-M B)L(N-M) / L-M C)L-N D)M-N E)M+
SOLUTION:the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:
L = 200
M = 10
N =20.
So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect, A.
Out of which, i choose A. #### A
QUESTION:There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
options: A)410 B)490 C)493 D)455 E)445
SOLUTION:Answer: A. #### A
QUESTION:The ratio of cats to dogs to birds to fish is 3:4:5:6. There are no other types of animals in the pet store. which of the following cannot be the total number of animals in the store?
options: A)36 B)54 C)72 D)90 E)101
SOLUTION:The parts add up to 3 + 4 + 5 + 6 = 18, so we know that any possible number of total answers must be a multiple of 18. All five answer choices are multiples of 18:
(A) 36 = 18*2
(B) 54 = 18*3
(C) 72 = 18*4
(D) 90 = 18*5
(E) 101 = not a multiple of 18
ans is E #### E
QUESTION:A person was fined for exceeding the speed limit by 10 km/hr.Another person was also fined for exceeding the same speed limit by twice the same.If the second person was traveling at a speed of 35 km/hr,find the speed limit.
options: A)487 B)15 C)76 D)29 E)12
SOLUTION:If x is speed limit,
Speed of first person = x + 10
Speed of 2nd person = x + 20
But speed of 2nd person = 35 kmph
x + 20 = 35
x = 15 kmph.
so speed limit is 15 kmph option D
Answer: B #### B
QUESTION:What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
options: A)3: 5 B)3: 9 C)3: 4 D)3: 1 E)3: 2
SOLUTION:d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3: 1
Answer: D #### D
QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule?
options: A)205 B)207 C)220 D)225 E)250
SOLUTION:24600/12=2050
2050*5=10250
10250-10000=250
Answer E #### E
QUESTION:If cost of sugar increases by 50%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
options: A)33% B)50% C)20% D)90% E)60%
SOLUTION:100
150
-----
150 ----- 50
100 ------ ? => 33%
Answer: A #### A
QUESTION:3 Years ago, the average age of a family of 5 members was 16 years. A baby having been born, the average age of the family is the same today. The present age of the baby is
options: A)1 year. B)1.5 Years. C)2 Years. D)3 Years. E)4 Years.
SOLUTION:We're told that 3 YEARS AGO, the average age of a family of 5 members was 16 years.
This means that the SUM of their ages was (5)(16) = 80 years.
A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.
This means that the sum of the ages is (6)(16) = 96 years.
We're asked for the PRESENT age of the baby.
Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...
80 + (5)(3) = 95.
A #### A
QUESTION:In a 8 x 8 chess board what is the total number of squares.
options: A)238 B)204 C)678 D)169 E)161
SOLUTION:Ans: The total number of squares in a n x n chess board is equal to "the sum of first n natural number squares"
i.e., n(n+1)(2n+1)6n(n+1)(2n+1)6
So Substituting 8 in the above formula we get 204
Answer:B #### B
QUESTION:By the how much is two-fifth of 300 greater than three -fifths of 125?
options: A)15 B)3 C)5 D)45 E)None of these
SOLUTION:Reqd no. = 2â„5 × 300 - 3â„5 × 125
= 120 - 75 = 45
Answer D #### D
QUESTION:A man can row upstream at 15 kmph and down strem 30 kmph. He takes 9 hours to row from lower point A to upper point B and back to A. What is the total distance traveled by him in 9 hours? He must return back to base point A in remaining time.
options: A)80 B)120 C)140 D)180 E)200
SOLUTION:Upward distance traveled per hour - 15 km,
distance traveled after 6 hours = 90 km.
He remained with 3 hours travel downward, i.e. distance traveled in remaining 3 hours downward = 90 km
so total distance traveled from A to B and Back to point A = 90 km upward + 90 km downhill = 180 km
(Answer : D) #### D
QUESTION:What is the perimeter of a square with area 9p^2/25 ?
options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3
SOLUTION:Area of square, (side)^2 = (3p/5)^2
Therefore side of the square = 3p/5
Perimeter of square = 4*side = 4* (3p/5) = 12p/5
Answer is C. #### C
QUESTION:The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?
options: A)50 B)55 C)60 D)65 E)70
SOLUTION:6C1*5C2 = 6*10 = 60
The answer is C. #### C
QUESTION:Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
options: A)15hrs B)20hrs C)25hrs D)30hrs E)32hrs
SOLUTION:Part filled by A in 1 hour = 1/50
part filled by B in 1 hour = 1/75
Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30
Both the pipes will together will fill the tank in 30 hours.
Answer is D #### D
QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres
options: A)1200 B)2400 C)1400 D)2500 E)None of these
SOLUTION:Explanation:
It means that 0.08% of x = 2
=>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500
Option D #### D
QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
options: A)5 B)8 C)9 D)10 E)11
SOLUTION:Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5
Option A #### A
QUESTION:E = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set E and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
options: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33
SOLUTION:The total number of pairs E,B possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.
Answer: B. #### B
QUESTION:A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
options: A)288 m B)256 m C)400 m D)278 m E)287 m
SOLUTION:Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60
= 65/3
x = 400 m.
Answer:C #### C
QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream?
options: A)60/18 B)30/29 C)60/12 D)60/13 E)30/82
SOLUTION:Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 120/26
= 60/13 hours.
Answer:D #### D
QUESTION:What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300?
options: A) 100 B) 150 C) 140 D) 200 E) 250
SOLUTION:{100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200.
Answer: D. #### D
QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.
options: A)13 B)14 C)15 D)16 E)17
SOLUTION:Length of longest pole = Length of the diagonal of the room
= sqrt(12^2+8^2+9^2= sqrt(289)= 17 m.
Answer is E. #### E
<<<Examples ends
QUESTION:An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
options: A)2200 kmph B)1800 kmph C)1900 kmph D)2100 kmph E)none
SOLUTION:Explanation: Distance = (1500 x 2) = 3000 km.
Speed = Distance/Time
Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = 3000 x 3/5 km/hr = 1800 km/hr.
Answer: Option B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
options: A)2007 B)2008 C)2002 D)2000 E)2001
SOLUTION:(10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: D #### D
QUESTION:Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift?
options: A)1/27 B)1/54 C)1/81 D)1/6 E)1/216
SOLUTION:Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2
Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)
Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6
Answer: option D #### D
QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
options: A)4 B)16 C)25 D)36 E)100
SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number.
The answer is C. #### C
QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
options: A)11 B)15 C)6 D)8 E)76
SOLUTION:Explanation:
Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years.
Answer: A) 11 #### A
QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double?
options: A)1/3 B)1/6 C)1/12 D)1/24 E)1/36
SOLUTION:ways you can get double - 6...as each dice showing any number from 1 to 6...
total ways = 6∗6=36.6∗6=36..
P=6/36=1/6
ANSWER: B #### B
QUESTION:If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is
options: A)Rs.1820 B)Rs.1040 C)Rs.1120 D)Rs.1680 E)None of these
SOLUTION:Explanation:
Let the sum of money be x
then
(x × 4 × 8)/100 = (560 × 12 × 8)/100
x × 4 × 8 = 560 × 12 × 8
x × 4 = 560 × 12x = 560 × 3 = 1680
Answer: Option D #### D
QUESTION:A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
options: A)8p B)pq C)pq + 27 D)-p E)(p - q)^6
SOLUTION:A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject.
B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject.
C. Hold.
D. since p is a perfect cube, -p will also be a perfect cube. reject.
E. (p-q)^6, is a perfect cube, so reject.
By elimination C is the answer.
Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube.
ANSWER:C #### C
QUESTION:in base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 1*72+3*7+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7?
options: A)11101 B)11110 C)10111 D)11011 E)11010
SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0)
3+4 + 1 carry from above step= 1 and 1 carry to next digit
2+5 + 1 carry to next digit= 1 and 1 carry
1+6= 11
so ans=11110
ANSWER:B #### B
QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
options: A)14355 B)15432 C)17576 D)18543 E)16878
SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C #### C
QUESTION:Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam?
options: A) 1/4 B) 12/47 C) 1/3 D) 5/12 E) 20/47
SOLUTION:Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.
adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work
R>( 60/47 *12)/60 =12/47
Answer B #### B
QUESTION:In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year?
options: A)74 B)75 C)76 D)77 E)78
SOLUTION:let the age is 'x' so after 1st yr 2x=40 and x=20
after 2nd year (now age become 21)
2*21+ 20=62 grades
after 3rd year(now age becomes 22)
2*22+31=75
ANSWER:B #### B
QUESTION:If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ?
options: A)x-2 B)x-4 C)x+4 D)x-3 E)x-1
SOLUTION:Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 36 more than 10x+y
10x+y+36=10y+x
10x-x+36=10y-y
9x+36=9y
x+4=y
OR
y=x+4
Answer : C #### C
QUESTION:If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?
options: A)9 B)10 C)11 D)12 E)13
SOLUTION:0.003^5= (3*10^-3)^5 = 243*10^-15 = 0.243*10^-12 which would have 12 zeros to the right of the decimal point. The answer is D. #### D
QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15
SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B
QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible?
options: A)90 B)79 C)64 D)57 E)36
SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible.
Total Options: 64
Final Answer:
C #### C
QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund?
options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000
SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5
1/5 of fund = 841---
Fund = 5 * 841---
Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it.
Answer (E). #### E
QUESTION:If d is the mean of x, y, and z, what is the mean of x + 5, y + 5, z + 5 ?
options: A)d B)3d C)15d D)d + 5 E)d + 15
SOLUTION:If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case mean will increase by 5 as we are adding 5 to each term in a set --> Mean =d + 5.
Answer: D. #### D
QUESTION:When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these
SOLUTION:Let the first and the second numbers be x and y respect then
y + 30% of x = 140% of y
or, y + 0.3x = 1.4y
or, 0.3x = 0.4y
∴ x : y = 0.4 : 0.3 = 4 : 3
Answer B #### B
QUESTION:The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?
options: A)AOTDSP B)AOTPDS C)AOTDPS D)AOSTPD E)None of these
SOLUTION:Explanation :
In alphabetical order : A D O P S T
A _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A.
A D _ _ _ _ : empty places can be filled in 4!=24
A O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24
this total crosses 42. So We should not consider all the words starting with AO.
A O D _ _ _ : 3!= 6
A O P _ _ _ : 3!=6
Till this 36 words are obtained, we need the 42nd word.
AOS _ _ _ : 3!= 6
Exactly we are getting the sum 42. So last 3 letters in the descending order are TPD.
So given word is AOSTPD
Answer : D #### D
QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?
options: A)7:6 B)7:3 C)7:4 D)7:2 E)7:1
SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40 => x = 20.
Required ratio = (3x + 10):(x + 10)
= 70:30
= 7:3
Answer: B #### B
QUESTION:At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock
options: A)47 B)76 C)28 D)66 E)99
SOLUTION:Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 45/5 = 9 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 9 = 99 secs.
Answer: E #### E
QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
options: A)1350 B)2997 C)2087 D)2697 E)9824
SOLUTION:Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5
=> 675
675 * 2
= Rs.1350
Answer:A #### A
QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10
SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 5*4*1=20.
P(dispensing one of each color)=20/120=1/6.
The answer is D. #### D
QUESTION:The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?
options: A)106.75 B)213.5 C)427 D)729 E)1,156
SOLUTION:Diagonal of a square =√2*side of square
=> side =Diagonal/(√2)
Area of square =s*s
=(diagonal^2)/2
Difference of both tv's =(34^2-27^2)/2
=427
ANSWER:C #### C
QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B the present age of B is
options: A)37 B)38 C)39 D)40 E)41
SOLUTION:let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+9
=>2b-b-9 = 30
b=39
so the present age of b is 39 years
ANSWER:C #### C
QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
options: A)18% B)19% C)28% D)68% E)48%
SOLUTION:1500 ---- 270
100 ---- ? => 18%
Answer: A #### A
QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 7 robots altogether, if the robots build only one robot at a time?
options: A)70 1/7 min B)94 1/7 min C)110 1/7 min D)112 1/7 min E)131 1/7 min
SOLUTION:First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
Now the 4 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 = 5/2
so they complete one robot in 2/5th of an hour - (3)
Now the 5 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2+1/2 = 3
so they complete one robot in 1/3th of an hour - (4)
Now the 6 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2
so they complete one robot in 2/5th of an hour - (5)
And now we have 7 robots
So Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes
Answer - E #### E
QUESTION:Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get?
options: A)57% B)57.3% C)65% D)90% E)80%
SOLUTION:total votes are 20280 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*11620/20280 = 57.3%
ANSWER:B #### B
QUESTION:If the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers?
options: A)4:9 B)4:3 C)3:7 D)2:5 E)1:6
SOLUTION:The ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9.
The ratio of apples to bananas to cucumbers is 4 to 3 to 9.
The answer is A. #### A
QUESTION:Mohan has 8 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 16 shoes, what is the probability that she will select 2 shoes of the same color?
options: A)2/5 B)1/15 C)1/9 D)1/10 E)1/25
SOLUTION:Can be tackled in this way as well: Probability of selecting any 1 out of 16 shoes = 16/16 = 1
Probability of selecting the next shoe (out of 16 available) having the same color = 1/16 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/15=1/15.
B is the correct answer. #### B
QUESTION:How many factors does 35^2 have?
options: A)2 B)8 C)24 D)25 E)26
SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 6*4 = 24
Answer C. #### C
QUESTION:Which of the statements can be dispensed with while answering the above question?
options: A)A only B)B only C)A or C only D)B or C only E)C or D only
SOLUTION:Explanation:
Justification:
We can find the code for 'home' from the second and third statements.
For finding the code for 'they', we need the code for 'go' which cannot be determined from the given data.
Clearly, statement A is not necessary.
Answer: A #### A
QUESTION:If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars?
options: A)3⁄20 B)11⁄60 C)9⁄40 D)1⁄5 E)2⁄15
SOLUTION:Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 60.
It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total.
Answer E #### E
QUESTION:xy=1 then what is (6^(x+y)^2) / (6^(x-y)^2)
options: A)1296 B)4 C)8 D)16 E)32
SOLUTION:(x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
6^4 = 1296
Answer A #### A
QUESTION:Louie takes out a three-month loan of $2000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
options: A)A)333 B)B)383 C)C)402 D)D)433 E)E)804
SOLUTION:Here's the calculation for that case, assume monthly payment is X.
After 1st month: (2000)(1.1)-X = 2200-X
After 2nd month: (2200-X)(1.1)-X = 2420-2.21X
After 3rd month: (2420-2.21X)(1.1)-X = 2662-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
2662-3.31X = 0
X = 2662/3.31 = 804
Answer E #### E
QUESTION:A man swims downstream 40 km and upstream 56 km taking 8 hours each time, what is the speed of the man in still water?
options: A)6 B)24 C)8 D)12 E)44
SOLUTION:40 --- 8 DS = 5
? ---- 1
56 ---- 8 US = 7
? ---- 1 M = ?
M = (5 + 7)/2 = 6
Answer: A #### A
QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00
SOLUTION:Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer: Option D #### D
QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet?
options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m
SOLUTION:D = 50 * 1 ½ = 75 km
RS = 75 – 50 = 25
T = 75/25 = 3 h
3.30 + 3 h = 6.30 p.m.
Answer: C #### C
QUESTION:For 1rs 6p interest
wat will be for 1000rs?
options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs
SOLUTION:For 1rs , 4p interest
for 1000rs, x
x= 1000/1 * 6p ==> 6000 paise
To express in rs, 6000/100 = 60rs
ANSWER:E #### E
QUESTION:What is the difference between the greatest and the smallest five digit numbers formed using the digits 7, 0, 3, 4 and 2 without repeating the digits?
options: A)53978 B)53916 C)53961 D)56781 E)None of these
SOLUTION:Explanation:
The greatest 5 digit number that can be formed using the given digits = 74320
The smallest 5 digit number that can be formed using the given digits = 20342
.: The required difference = 74320 - 20342 = 53978
Answer: Option A #### A
QUESTION:The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches?
options: A)66 B)83.5 C)84 D)95 E)76
SOLUTION:sum of last 4 matches = (10 × 66) – (6 × 54)= 336
Average =
336/4
= 84
ANSWER:C #### C
QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article?
options: A)2777 B)2987 C)1200 D)1240 E)1671
SOLUTION:CP* (50/100) = 620
CP= 12.4 * 100 => CP = 1240
Answer: D #### D
QUESTION:Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 6 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
options: A)1/2 B)1/3 C)1/4 D)2/3 E)2/5
SOLUTION:Tom paints 1/6 of the room in the first hour.
Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.
The three people then paint the remaining 2/6 in a time of (2/6) / (4/6) = 1/2 hours
Peter worked for 3/2 hours so he painted 3/2 * 1/3 = 1/2 of the room.
The answer is A. #### A
QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels?
options: A)480 B)540 C)600 D)720 E)900
SOLUTION:4C2 x 3C3 x 5! = 720
The answer is D. #### D
QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b?
options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given.
SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2.
Answer: A. #### A
QUESTION:John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip?
options: A) 24 B) 30 C) 48 D) 54 E) 75
SOLUTION:Speed = Distance/Time
Distance for John = Speed * Time = 40 * 1/2 = 20 miles
Distance for Beth = Distance for John +5 = 20+5 = 25 miles
Time taken by Beth = Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour
Hence, B is the answer. #### B
QUESTION:A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B?
options: A)9/30 B)14/30 C)4/9 D)3/5 E)6/25
SOLUTION:I guess it's mean that square B is placed within rectangle A entirely.
Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16;
Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30.
Answer: B. #### B
QUESTION:If f(x) = -2x2 + 8x - 4, which of the follwoing is true?
options: A)The maximum value of f(x) is -4. B)The graph of f opens upward. C)The graph of f has no x-intercept D)f is not a one to one function. E)The maximum value of f(x) is 4.
SOLUTION:f(x) is a quadratic function and its graph is a parabola that may be intercepted by horizontal lines at two points and therefore is not a one to one function. The answer is D
correct answer D #### D
QUESTION:A certain galaxy is known to comprise approximately 5 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
options: A)800 B)1,250 C)8,000 D)12,000 E)10,000
SOLUTION:Total no. of stars on galaxy = 5 * 10^11
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 5 * 10^11 / 50 * 10^6
=50 * 10^3 /5
= 10000
therefore answer is E #### E
QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum E of even integers from 102 to 200 inclusive?
options: A)5100 B)7550 C)10100 D)15500 E)20100
SOLUTION:My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
E=2550+(100*50)=7550.B #### B
QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
options: A)2.3 B)2.5 C)3.5 D)3.6 E)4.6
SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E #### E
QUESTION:Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving.
options: A)180% B)124% C)160% D)154% E)140%
SOLUTION:Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24%
correct answer - B #### B
QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 3 days at a time. If A starts they finish the task in exactly 9 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?
options: A)8 B)6 C)4 D)5 E)9/2
SOLUTION:Work done by AB in a day = xy respectively.
When A starts:
No. of days when A works = 6No. of days when B works = 3 → 6x + 3y = 1
When B starts:
No. of days when A works = 4 No. of days when A works = 5 → 5x + 4y = 1
Solving the above two equations for xy
x = 1/9 y = 1/9
→ Total work done by AB in a day = 1/9 + 1/9 = 2/9
→ No. of days to complete the work when both work together = 9/2;
Answer: E #### E
QUESTION:The lowest number which should be added to 8247 so that the sum is exactly divisible by 5, 6, 7, 8 and 9 is:
options: A)1833 B)1853 C)1733 D)1233 E)1832
SOLUTION:L.C.M. of 5, 6, 7, 8 and 9 = 2520.
On dividing 8247 by 2520, the remainder is 687.
Number to be added = (2520 - 687) = 1833. Answer: Option 'A' #### A
QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent?
options: A)10% B)20% C)30% D)40% E)50%
SOLUTION:5*SP = 7*CP
SP = 1.4*CP
The profit percent is 40%.
The answer is D. #### D
QUESTION:If P(A) = 5/7 and P (B) = 2/5, find P (A n B) if A and B are independent events.
options: A)7/25 B)3/25 C)8/25 D)2/7 E)3/17
SOLUTION:P (A n B) = P(A) . P(B)
P (A n B) = 5/7 . 2/5
P (A n B) = 2/7.
D #### D
QUESTION:he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
options: A)0 B)1 C)10 D)19 E)8
SOLUTION:Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a).
Answer: Option D #### D
QUESTION:Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in.
options: A)40 min B)25 min C)54 min D)65 min E)58 min
SOLUTION:Distance = Speed * time
3*20/3= 20km
New Speed = 18 kmph
Therefore time = 20/18 = 10/9= 54min
Answer : C. #### C
QUESTION:A train ,135 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
options: A)270 m B)245 m C)235 m D)220 m E)240 m
SOLUTION:Explanation:
Assume the length of the bridge = x meter
Total distance covered = 135+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (135+x)/30 m/s
=> 45 × (10/36) = (135+x)/30
=> 45 × 10 × 30 /36 = 135+x
=> 45 × 10 × 10 / 12 = 135+x
=> 15 × 10 × 10 / 4 = 135+x
=> 15 × 25 = 135+x = 375
=> x = 375-135 =240
Answer: Option E #### E
QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd?
options: A)45 B)50 C)30 D)60 E)55
SOLUTION:90 numbers between - 10 and 100
Out of which half would be even, half odd.
Number of odd unit digit number = 45.
correct option is A #### A
QUESTION:A trade analyst announced 15% reduction in the unit price of bike. As a result, the sales volume went up by 15%. What was the net effect on the sales revenue?
options: A)no change B)decreases by 6.5% C)increases by 6.5% D)increases by 5.6% E)None of these
SOLUTION:Explanation :
Reduction of price = (100 -15)% = 85% = 0.85
Increase of sale = (100+15)% = 115% = 1.15
Total effect = 0.85 X 1.15 = 93.5%, Decreases by 6.5%
Answer :B #### B
QUESTION:If 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?
options: A)127 B)237 C)360 D)450 E)281
SOLUTION:Explanation:
Let the required no of hectares be x. Then
Men --- Hectares---Days
10---------80---------24
36---------x---------30
More men, More hectares (Direct proportion)
More days, More hectares (Direct proportion)
x=36/10*30/24*80
x= 360
Answer: C #### C
QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5)
SOLUTION:3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5.
Answer: D. #### D
QUESTION:When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?
options: A)32 B)36 C)40 D)45 E)50
SOLUTION:A = 9k+3 = 5j+4
B = 9m+3 = 5n+4
A-B = 9(k-m) = 5(j-n)
Thus A-B is a multiple of 9 and 5, so it is multiple of 45.
The answer is D. #### D
<<<Examples ends
QUESTION:A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n?
options: A)8/7 B)8 C)9/8 D)7 E)5
SOLUTION:Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 9x+xn and we are told that it equals to 9xn:
9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9
n = 9/8
Answer: C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If the Average (mean ) of 9 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
options: A)8x B)4x C)5x/3 D)3x/2 E)3x/5
SOLUTION:Let the 5 numbers be 1,2,3,4,5,..9 (since no restrictions are given). There mean is 4 (x).
Now the sum of greatest three would be 7+8+9=24
so the answer has to be 8x....that is option A #### A
QUESTION:Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is
options: A)4 : 5 B)1 : 2 C)6 : 7 D)5 : 6 E)None
SOLUTION:Solution
Let us name the brothers
as A and B. = (A'S speed) : (B's speed)
=√b : √a
= √25 : √36
= 5 : 6
Answer D #### D
QUESTION:The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?
options: A)21/55 B)28/55 C)34/55 D)5/8 E)139/220
SOLUTION:Prob of selecting one blue and two green is (4*8*7/12*11*10)
one blue and two green can be arranged in 3!/2! ways
hence the prob becomes 3*4*8*7/12*11*10=28/55
Correct answer is B #### B
QUESTION:If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average R (arithmetic mean) annual increase in the index over this period?
options: A) (x + 100)/18 B) x/18 C) (100 − x)/18 D) (x − 100)/18 E) 100x/18
SOLUTION:CPI in end of 1967 = 100
CPI in end of 1985 = x
Number of years = 18
Average annual increase in CPI R= (x-100)/18
Answer D #### D
QUESTION:A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4
options: A)II,III only B)I only C)I,III only D)II only E)III only
SOLUTION:question is asking for must be there elements.
According to the question if t is there t+4 must be there.
if -3 is the starting element the sequence is as follows.
S ={-3,1,5,9....}
if -3 is not the starting element the sequence is as follows
S = {...-7,-3,1,5,9...}
By observing the above two sequences we can say that 9 must be there in set S.
Answer : B #### B
QUESTION:1395 x 1395
options: A)1946025 B)1981709 C)18362619 D)2031719 E)None of these
SOLUTION:1395 x 1395 = (1398)2
= (1400 - 2)2
= (1400)2 + (5)2 - (5 x 1400 x 5)
= 1946025.
Answer: Option A #### A
QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number?
options: A)10 B)60 C)30 D)40 E)50
SOLUTION:Explanation:
6:7
6x + 10 : 7x + 10 = 7 : 8
8[6x + 10] = 7[7x + 10]
48x + 80 = 49x + 70
49x - 48x = 80 - 70
x = 10
Then smallest number is = 6
6x = 60
Answer: Option B #### B
QUESTION:JOHN and ANDREW can finish the work 9 days if they work together. They worked together for 6 days and then ANDREW left. JOHN finished the remaining work in another 6 days. In how many days JOHN alone can finish the work?
options: A)30 days B)60 days C)18 days D)80 days E)90 days
SOLUTION:Amount of work done by JOHN and ANDREW in 1 day = 1/9
Amount of work done by JOHN and ANDREW in 6 days = 6 × (1/9) = 2/3
Remaining work – 1 – 2/3 = 1/3
JOHN completes 1/3 work in 6 days
Amount of work JOHN can do in 1 day = (1/3)/6 = 1/18
=> JOHN can complete the work in 18 days
Answer : C #### C
QUESTION:Thompson had the following scores in an exam (out of 100):
Social Studies: 60
Science: 89
Art: 62
Music: 69
Spanish:84
Biology: 89
What are his average marks ?
options: A)61.5 B)72.5 C)71.5 D)85.5 E)75.5
SOLUTION:Explanation:
Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75.
Answer: E) 75.5 #### E
QUESTION:Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely?
options: A)15 sec B)19 sec C)12 sec D)10 sec E)11 sec
SOLUTION:Explanation:
D = 250 m + 250 m = 500 m
RS = 80 + 40 = 120 * 5/18 = 100/3
T = 500 * 3/100 = 15 sec
Answer: Option A #### A
QUESTION:Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
options: A)2288 B)2677 C)6000 D)2700 E)2881
SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x
10 * 20 * 90 = 15 * 2 * x => x = 6000
Answer: C #### C
QUESTION:The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
options: A)1267 B)1201 C)1200 D)1209 E)1216
SOLUTION:P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer: C #### C
QUESTION:How many positive integers less than 254 are multiple of 4 but NOT multiples of 6?
options: A)20 B)31 C)42 D)43 E)64
SOLUTION:252/4=63
Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0
240/12=20
63-20=43
Answer: D #### D
QUESTION:A rectangular tiled patio is composed of 48 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 48 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
options: A)5 B)6 C)10 D)13 E)28
SOLUTION:Suppose there are c columns and there are r rows
Original Situation
So, Number of tiles = c*r = 48
Also. Reach column has r tiles and each row has c tiles
New Situation
Number of tiles in each column is r-2 and number of tiles in each row is c+4
So, number of rows = r-2 and number of columns is c+4
So, Number of tiles = (r-2)*(c+4) = 48
Comparing both of them we get
c*r = (r-2)*(c+4)
=> 4r -2c = 8
c = 2r - 4
Putting it in c*r=48
(2r-4)*r = 48
2r^2 - 4r - 48=0
r cannot be negative so r = 6
and c = 8
So, Answer will be B #### B
QUESTION:If a + b = y and a - b = z , then 3ab =
can someone explain!
options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2
SOLUTION:plugging numbers is quite fast in this case:
Let
a=1
b=2
Then; y= 1+2=> 3 and z= 1-2=> -1
Question asks 3ab=.........
As our number 3ab= 3*1*2=6
now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need.
Hence: Ans is A. #### A
QUESTION:What is the units digit of (12^3)(15^4)(31^7)?
options: A)0 B)2 C)4 D)6 E)8
SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8.
The units digit of 15^4 is the units digit of 5^4 which is 5.
The units digit of 31^7 is the units digit of 1^7 which is 1.
The units digit of 8*5*1 is 0.
The answer is A. #### A
QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 3600 interest. The principal amount borrowed by him was.
options: A)Rs 10000 B)Rs 15000 C)Rs 16000 D)Rs 17000 E)None of these
SOLUTION:Explanation:
S.I.=P∗R∗T/100
=>P=S.I.∗100/R∗T
=>P=3600∗100/12∗3=Rs10000
Option A #### A
QUESTION:The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 5 hours. If at 06:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
options: A)16:00. B)18:00. C)20:00. D)22:00. E)24:00.
SOLUTION:Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 5 hours
Time taken by both buses to meet again in St. Louis will be LCM of 2 and 5 = 10
If the buses start at 06:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours
Answer A #### A
QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
options: A)1/2 B)1/2 C)8/15 D)9/20 E)9/24
SOLUTION:Explanation :
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20
Answer : D #### D
QUESTION:A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is?
options: A)A)$58 B)B)$42 C)C)$65 D)D)$48 E)E)$62
SOLUTION:avg = sum of observations/number of observations
avg income=(45+50+60+65+90)/5 = 62
Answer is E #### E
QUESTION:1100 boys and 700 girls are examined in a test; 31% of the boys and 23% of the girls pass. The percentage of the total who failed is ?
options: A)A)63.3% B)B)52.4% C)C)81.2% D)D)75.4% E)E)72.11%
SOLUTION:Total number of students = 1100+700 = 1800
Number of students passed = (31% of 1100+23% of 700) = 341+161 = 502
number of failures = 1298*100/1800= 72.11%
Answer is E #### E
QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
options: A)7 kmph B)8 kmph C)9 kmph D)7 kmph E)6 kmph
SOLUTION:Speed in still water = (10 + 4)1/2 kmph = 7 kmph.
answer :A #### A
QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b?
options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given.
SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2.
Answer: A. #### A
QUESTION:A sum of Rs. 12500 amounts to Rs. 16500 in 4 years at the rate of simple interest. What is the rate of interest?
options: A)4% B)5% C)6% D)8% E)14%
SOLUTION:S.I. = (16500 - 12500) = Rs. 4000/-
Rate = (100 * 4000) / (12500 * 4) = 8%
ANSWER:D #### D
QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is
options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm
SOLUTION:Explanation:
Required Length = H.C.F of 700 cm, 385 cm and 1295 c
= 35 cm. Answer: C #### C
QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is:
options: A)4884 B)5340 C)5342 D)5345 E)5356
SOLUTION:Divisor = (5 * 44) = 220
= 10 * Quotient = Divisor
=> Quotient = 220/10 = 22
Dividend = (Divisor * Quotient) + Remainder
Dividend = (220 * 22) + 44 = 4884.
A #### A
QUESTION:If x, y, and z are all factors of 35, which of the following must be true?
options: A)The product xyz > 35 B)Either x = y, y = z, or x = z C)x – y – z = even D)The product xyz is odd E)yz/x is an integer
SOLUTION:All the factors of 35 are odd numbers.
The product of odd numbers is odd.
The answer is D. #### D
QUESTION:8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work?
options: A)5 days B)15 days C)28 days D)4 days E)7 days
SOLUTION:Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
20 women’s 1 day’s work = 1/192 × 20 = 5/48
1 child’s 1 day’s work = 1/240
10 children’s 1 day’s work = 1/24
Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24
=1/4
The required No. of days = 4 days
Answer: Option D #### D
QUESTION:If x percent of 400 is 20 percent of 700, then x =
options: A)200 B)350 C)700 D)400 E)1,400
SOLUTION:x/100(400) = 2/10(700)
x = 400.
Option D. #### D
QUESTION:The instructions state that Cheryl needs 4/19 square yards of one type of material and 2/13 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/26 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
options: A)4/19 B)1/9 C)2/3 D)1 1/9 E)2 1/9
SOLUTION:Total bought = 4/19+2/13
left part 4/26--->2/13
so used part 4/19+2/13-2/13=4/19
ANSWER:A #### A
QUESTION:The average age of a group of 10 students was 24. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
options: A)22 years B)36 years C)32 years D)44 years E)None of these
SOLUTION:The total age of 10 students with average 24 = 240
The total age of 12 students with average 26 = 312
The total age of 2 new students = 72
Their average =36
Correct Option B #### B
QUESTION:John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He
mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit as the
cost price?
options: A)Rs.12 B)Rs.8 C)Rs.16 D)Rs.20 E)None of these
SOLUTION:Explanation :
CP=20×8.5+35×8.75=170+306.25=476.25Profit=40%SP=(100+Profit%)100×CP=(100+40)100×476.25=140
100×476.25=1404×19.05=35×19.05Total quantity = 20 + 35 = 55 KgSP per
Kg=35×19.0555=7×19.0511≈7×1911≈13311≈12
Answer : Option A #### A
QUESTION:Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
options: A)8/3 B)3/8 C)8/5 D)12/5 E)5/3
SOLUTION:Distance traveled by Eddy = 540 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 540/3 = 180 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 180/75 = 12/5
Answer D #### D
QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%?
options: A)20% B)28% C)29% D)40% E)70%
SOLUTION:SP2 = 2/3 SP1
CP = 100
SP2 = 86
2/3 SP1 = 86
SP1 = 129
100 --- 29 => 29%
Answer:C #### C
QUESTION:Calculate the % profit or loss, if the cost price of 9 balls is equal to the selling price of 14 balls.
options: A)35.7% B)25.7% C)15.7% D)55.7% E)45.7%
SOLUTION:Let the cost price of 1 balls be Rs 1
Cost of 14 balls= Rs 14
Selling price of 14 balls = 9
Gain/loss = 14 - 9 = 5
%=5/14∗100= 35.7
Answer: A #### A
QUESTION:What is the sum of all even numbers from 1 to 401?
options: A)122821 B)281228 C)281199 D)122850 E)40200
SOLUTION:Explanation:
400/2 = 200
200 * 201 = 40200
Answer: E #### E
QUESTION:Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
options: A)4328 B)5382 C)6174 D)7690 E)8436
SOLUTION:The number of ways for the ships to go to the ports is 3! = 6.
At Port A, the number of ways to choose two winners is 7C2 = 21.
At Port B, the number of ways to choose one winner is 7.
At Port C, the number of ways to choose one winner is 7.
The total number of ways to give out gift certificates is 6*21*7*7 = 6174
The answer is C. #### C
QUESTION:If points A and B are (8-3) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
options: A)I only B)II only C)III only D)I and II only E)I and III only
SOLUTION:I. The area of a square region with side AB --> side=AB=(8-3) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A. #### A
QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B?
options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these
SOLUTION:Explanation :
Assume that investment of C = x
Then, investment of A =2x
A receive 48000
Then C will receive = 48000/2 = 24000
And B receive = 180000 - (24000+48000) = 108000
Ratio of investment between A and B = 48000 : 108000 = 4 : 9
Answer : Option A #### A
QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160
SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 8*12=96 five-minute intervals, thus total of 96*30 tickets were sold.
Say x student and 3x regular tickets were sold, then x+3x=96*30 --> x=24*30 and 3x=3*(24*30)=24*90.
Therefore, the total revenue from ticket sales that day was 24*30*6+24*90*10=$25,920.
Answer: B. #### B
QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
options: A)49% B)90% C)60% D)40% E)41%
SOLUTION:8 = (1*20*R)/100
R = 40%
Answer:D #### D
QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?
options: A)1/26 B)1/20 C)1/25 D)1/29 E)1/23
SOLUTION:Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26.Answer: A #### A
QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit?
options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these
SOLUTION:Ratio of quantities sold at 8% profit and 18% profit
=>4:6 = 2:3
Therefore,the quantity sold at 18% profit
=>50/(2 + 3) x 3
=>30 kg
ANSWER:A #### A
QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations T could be chosen from this menu?
options: A)10 B)20 C)40 D)80 E)100
SOLUTION:T=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C #### C
QUESTION:A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
options: A)95 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)56 km/hr
SOLUTION:Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr.
ANSWER: A #### A
QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
options: A)1000 B)817 C)278 D)268 E)280
SOLUTION:2 * 22/7 * 1.75 * x
= 11000
x = 1000
Answer: A #### A
QUESTION:A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
options: A)27 B)29 C)40 D)89 E)22
SOLUTION:1/8 - 1/x = 1/10
x = 40
Answer: C #### C
QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 3a = b = 3c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.
options: A)131 B)292 C)394 D)424 E)969
SOLUTION:Ratio of a:b:c= 1:3:1
Two possible greatest single digit values for b are 9 and 6
if b is 9, then x= 393
if b is 6, then x= 262
difference= 393-262= 131
A is the answer #### A
QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed?
options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr
SOLUTION:Let the speed be x km/hr
50x-50* 9/10 *x = 450
50x - 45x = 450
x = 90km/hr
Answer is E #### E
QUESTION:A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
options: A)1:20 B)1:10 C)1:8 D)1:4 E)1:2
SOLUTION:He needs to make a profit of 20%, which means he needs to sell the milk +water combination for 39.6 (20% of 33 +33)
Now, he plans to sell 1 liter of this solution of milk and water for 36. which means he needs to sell 1.1 liters of this solution to earn 39.6. (36 for 1 liter and so 39.6 for 1.1 liters)
Hence the water added would be .1 liter.
Therefore the ratio of water to milk is .1/1 = 1/10
ANSWER:B #### B
QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now?
options: A)14years B)15years C)16years D)17years E)18years
SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years
ANSWER:A #### A
QUESTION:When positive integer N is divided by positive integer P, the quotient is 20, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 2. What is the value of N?
options: A)107 B)331 C)511 D)691 E)871
SOLUTION:N/P=10 7/P= 20P+7
N/(P+2)=15 2/(P+2)=15P+30+2
solving these two equations
we get P=5 N= 107 answer is A. #### A
QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is:
options: A)14 B)7 C)20 D)70 E)35
SOLUTION:Explanation :
Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2.
Number of Apples = 10x = 20.
Answer : C #### C
QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
options: A)4 B)6 C)8 D)9 E)1
SOLUTION:There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B #### B
QUESTION:A guy was asked to specify his age in years. He said, “Take my age 6 years hence, multiply it by six and subtract six of my age 6 years ago and you will know my age.” What was the age of that guy?
options: A)18 B)35 C)53 D)69 E)72
SOLUTION:Current age of the guy = A years.
Then, 6 (A + 6) – 6 (A – 6) = A
(6A + 36) – (6A – 36) = A
A = 72
E #### E
QUESTION:In how many different ways can the letters of the word ‘INDIGO’ be arranged ?
options: A)420 B)520 C)620 D)720 E)820
SOLUTION:D
720
Required number of arrangements = 6! = 720 #### D
QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
options: A)18:11 B)18:18 C)18:22 D)18:39 E)18:39
SOLUTION:Explanation:
A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer:A #### A
QUESTION:The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is:
options: A)30 B)28 C)24 D)20 E)35
SOLUTION:Product of two nos = product of HCF and LCM
Let one number = x
=> 25 * x = 5 * 150
x=5*150/25=30
ANSWER A #### A
QUESTION:A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture?
options: A)12 liters B)10 liters C)4 liters D)2 liters E)3 liters
SOLUTION:70 * (10/100) = 7
Wine Water
87 1/2% 12 1/2%
87 1/2% ------- 63
12 1/2% -------? => 9-7=2
ANSWER:D #### D
QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
options: A)298 m B)888 m C)120 m D)217 m E)166 m
SOLUTION:Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec
= 20 m/sec.
Length of the train
= 20 * 6
= 120 m.
Answer: C #### C
QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase?
options: A) 45% B) 125% C) 145% D) 150% E) 180%
SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80
So the approximate answer is E #### E
QUESTION:A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route?
options: A)12km B)15km C)18km D)24km E)Data Inadequate
SOLUTION:time=distance/speed
so,
let the distance to the level road from home be x km
and the distance to the hillock from the level road be y km
so, (x/4+y/3)+(y/6+x/4)=6
x+y=12 km.
ANSWER:A #### A
QUESTION:What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
options: A)s.2.04 B)s.2.08 C)s.3.67 D)s.2.83 E)s.2.42
SOLUTION:C.I. when interest is compounded yearly
= [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 9000 * 26/25 * 51/50 = Rs. 9547.2
C.I. when interest is compounded half-yearly
= [9000 * (1 + 2/100)2]
= (9000 * 51/50 * 51/50 * 51/50)
= Rs. 9550.87 Difference
= (9550.87 - 9547.2)
= Rs.3.67.
Answer: C #### C
QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture?
options: A)9! B)9×8! C)4x5! D)10!/2! E)10!
SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!*2! ways.
Total - Restriction =
= 6! - 5!*2! =
= 5!(6- 2!) =
= 4*5!.
Answer: C. #### C
<<<Examples ends
QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 9000 interest. The principal amount borrowed by him was.
options: A)Rs 14000 B)Rs 25000 C)Rs 16000 D)Rs 17000 E)None of these
SOLUTION:Explanation:
S.I.=P∗R∗T/100
=>P=S.I.∗100/R∗T
=>P=9000∗100/12∗3=Rs25000
Option B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 6840 km and comes back to the starting point. The total time taken by him is:
options: A)914.2 hours B)900 hours C)915 hours D)868.6 hours E)915 hours
SOLUTION:Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 6840/18 + 6840/14 = 380 + 488.6 = 868.6 hours
Answer: Option D #### D
QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame?
options: A)12 B)20 C)30 D)40 E)50
SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b
Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so
Area of frame = (1/2) * a^2
Area of Frame + Painting = a^2 + (1/2)*a^2 = (3/2)*a^2 which is equal to b^2
Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2
so, b * sqrt2 = 6
so, b = 3 * sqrt2
b^2 = 18
we know that b^2 = (3/2)*a^2
so, a^2 = (2/3)*b^2 = (2/3)*18 = 12
And area of painting = a^2 = 12
So, answer will be A. #### A
QUESTION:By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
options: A)228 B)480 C)267 D)288 E)276
SOLUTION:SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer: B #### B
QUESTION:In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is :
options: A)12 B)11 C)10 D)27 E)22
SOLUTION:Explanation:
Total employees = \inline \frac{(25-10)\times 20}{10}=30
Hence number of educated employees = 30-20 = 10
Answer: C) 10 #### C
QUESTION:62467 × 9998 = ?
options: A)624545037 B)627745452 C)624545077 D)624545066 E)625454211
SOLUTION:D
624545066
62467 × 9998 = 62467 × (10000 - 2)
= 62467 × 10000 - 62467 × 2
= 624670000 - 124934
= 624545066 #### D
QUESTION:By selling an umbrella for Rs. 300, a shop keeper gains 200%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
options: A)50 B)25 C)400 D)200 E)150
SOLUTION:Marked price = Rs. 300
C.P. = 100/300 * 300 = Rs. 100
Sale price = 90% of Rs. 300 = Rs. 270
Required gain % = 200/100 * 100 = 200%.
Answer:D #### D
QUESTION:Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet?
options: A)15 B)18 C)21 D)24 E)27
SOLUTION:Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him Y: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer. #### D
QUESTION:If 3log(4*5^2) = x, find x
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:3(log2^2*5^2)=x
3log(5*2)^2=x
3*2log(5*2)=x
6log10=x
log10 base 10=1
so
6*1=x
x=6
ANSWER:B #### B
QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?
options: A)1:4 B)3:5 C)3:9 D)3:7 E)1:3
SOLUTION:Number of men in the colony = 4/7 (70) = 40
Number of women in the colony = 3/7 (70) = 30
Number of educated women in the colony = 1/5 (30) = 6
Number of uneducated women in the colony = 4/5 (30) = 24
Number of educated persons in the colony = 8/35 (70) = 16
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30
Number of educated men and uneducated men are in the ratio 10:30 => 1:3
Answer:E #### E
QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
options: A)6 months B)8 months C)10 months D)7 months E)12 months
SOLUTION:Explanation:
7 * 8 : 9 * x = 8:9 => x= 7
ANSWER IS D #### D
QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
options: A)8000 B)8077 C)2776 D)2976 E)2971
SOLUTION:8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000.Answer: A #### A
QUESTION:A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 60 paise per sq. metre
options: A)s510 B)s780 C)s880 D)s480 E)s980
SOLUTION:area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*60
= 51000p
in Rs =51000/100=Rs510
ANSWER:A #### A
QUESTION:Find the base K of the number system, if (524)8 = (664)K ?
options: A)4 B)5 C)6 D)7 E)8
SOLUTION:5*8^2 + 2*8^1 + 4*8^0 = 6*K^2 + 6*K^1 + 4*K^0
320 + 16 + 4 = 6(K^2) + 6K + 4
340 = 6(K^2) + 6K + 4
6(K^2) + 6K + 4 - 340 = 0
6(K^2) + 6K - 336 = 0
dividing by 6;
(K^2) + K - 56 = 0
solving this quadratic equation we get, K=7 and K=-8
thus K=7
ANSWER:D #### D
QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days
SOLUTION:B = 1/4 – 1/20 =0.2 days
ANSWER:E #### E
QUESTION:On a ferry, there are 32 cars and 8 trucks. The cars have an average mass of 900 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry?
options: A)1200 B)1240 C)1280 D)1320 E)1360
SOLUTION:The total mass of the vehicles is 32*900+8*3000=52800
The average mass is 52800/40=1320
The answer is D. #### D
QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
options: A)Rs.400 B)Rs.450 C)Rs.550 D)Rs.500 E)Rs.650
SOLUTION:Explanation:
P - 340 = (P*4*8)/100
P = 500
ANSWER IS D #### D
QUESTION:121,112,...?..,97,91,86
options: A)99 B)104 C)102 D)108 E)100
SOLUTION:121. 112. 104. 97. 91. 86
the decreasing difference is reducing by 1 at each step
so,missing no. will be 104
answer B #### B
QUESTION:In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ?
options: A)64 B)1/8 C)1 D)4 E)1/64
SOLUTION:Say r=2 => V1 = 1/16
when r=1; V2 = 1/4
V2 = 4*V1.
Answer : D #### D
QUESTION:A certain computer manufacturing firm last year produced 80 percent of its computers using parts made by its subsidiary company. If the remaining 10,000 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether?
options: A)60000 B)60100 C)60500 D)50000 E)70000
SOLUTION:80% parts used of subsidary company, so 20% parts used of other companies.
Now, 20% parts = 10,000 computers
So, 1% parts = 10,000/20
Or, 100% parts = 50,000 computers.
Hence answer is (D) #### D
QUESTION:Zoey won the lottery and got $7,348,340. she wants to split it among herself and 5 friends evenly. how much money must she add if she wants to split it evenly?
options: A)$3 B)$2 C)$9 D)$1 E)$4
SOLUTION:Zoey and her 5 friends is 6 people in all. $7,348,340 must be divisible by 6 if she wants to split it evenly. The money is divisible by 6 if it's divisible by 2 and 3. 7+3+4+8+3+4+0=29. 2 and 3 cant go into 29. Adding 1 dollar makes it 30. 2 and 3 can go into 30 so 6 can also. The answer is D. #### D
QUESTION:A car covers a distance of 1080 km in10 hrs. What is its speed in mps.
options: A)40 m/s B)25 m/s C)20 m/s D)15 m/s E)30 m/s
SOLUTION:Explanation:
Distance = Speed x Time
Speed = (1080/10) = 108 kmph
Spees in mps = 108 x 5/18 = 6 x 5 = 30 mps.
Answer: Option E #### E
QUESTION:A person purchased a TV set for Rs. 18000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 46000. What percentage of profit did he make?
options: A)100% B)90% C)140% D)115% E)120%
SOLUTION:The total CP = Rs. 18000 + Rs. 5000
= Rs. 2300 and SP
= Rs. 46000
Profit(%)
= (46000 - 23000)/23000 * 100
= 100%
Answer:A #### A
QUESTION:The probability that a man will be alive for 10more yrs is 3/4 & the probability that his wife will alive for 10 more yrs is 1/5. The probability that none of them will be alive for 10 more yrs, is
options: A)1/2 B)1 C)2/3 D)1/5 E)2
SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/5
Ans.(D) #### D
QUESTION:Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter?
options: A)201 B)132 C)772 D)592 E)261
SOLUTION:2 * 22/7 * 16 = 100.5
100.5 * 2 = Rs.201
Answer: A #### A
QUESTION:The income tax in country X is 8% of any income up to $5000. For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income?
options: A)$10,500 B)$11,000 C)$13,000 D)$13,500 E)$14,000
SOLUTION:Given : For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income?
for first 5000 , 8% tax then we get 400$ as tax.
Now Perry paid 950$ tax... we need to check which option is going to yield 550$ on the remaining amount.
A. $10,500 - 5000 = 5500 , then we get 10% tax , we get 550$... ( $10,500 - 5000 - here already for 5000$ we have calculated the tax and we need to tally for the remaining amount)
550+400 = 950$...hence this is the option.
ANSWER :option A. #### A
QUESTION:There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men?
options: A)1932 B)1933 C)1934 D)1935 E)1936
SOLUTION:(5c3*11c3)+(5c4*11c2)+(5c5*11c1)
1936
ANSWER:E #### E
QUESTION:Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
options: A)$40,000 B)$56,000 C)$64,000 D)$66,667 E)$80,000
SOLUTION:Equation is correct, so math must be a problem.
0.12*40,000+0.2*(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000.
Answer: B. #### B
QUESTION:20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours X will it take 12 beavers that work at the same pace, to build the same dam?
options: A)2. B)4. C)X=5. D)X=6. E)8.
SOLUTION:C. 5 hrs
If there were 10 beavers it qould have taken double X = 6hrs.. so closest to that option is 5. #### C
QUESTION:Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 42 minutes. The waste pipe can empty the full cistern in?
options: A)8 min B)7 min C)5 min D)9 min E)4 min
SOLUTION:1/10 + 1/15 - 1/x
= 1/42
x = 7
Answer: B #### B
QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score?
options: A)662 B)672 C)654 D)642 E)721
SOLUTION:8 * 83 = 664 – 10 = 654
ANSWER:C #### C
QUESTION:hree 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
options: A)1/39 B)1/36 C)1/32 D)1/287 E)1/29
SOLUTION:It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer: B #### B
QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is:
options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg
SOLUTION:EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (30 x 3) = 90 …. (i)
A + B = (25 x 2) = 50 …. (ii)
B + C = (28 x 2) = 56 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 106 …. (iv)
Subtracting (i) from (iv), we get : B = 16.
B’s weight = 16 kg.
Answer E #### E
QUESTION:A number x is 4 times another number y. The percentage that y is less than x is
options: A)12.5% B)75% C)80% D)11% E)1%
SOLUTION:Say y=1 and x=4.
Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%.
Answer: B. #### B
QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players?
options: A)45 B)56 C)64 D)78 E)90
SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players.
=> Required number of ways = 13C11
= 78
D #### D
QUESTION:Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability W that the new color will be one of theJaunecolors?
options: A)5/42 B)37/42 C)1/21 D)4/9 E)5/9
SOLUTION:I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune W= (40 + 34)/84 = 37/42 #### B
QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full?
options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m.
SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m.
Answer: B. #### B
QUESTION:Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48.
options: A)240/1587 B)240/1545 C)240/1547 D)240/1542 E)240/1512
SOLUTION:P : 2/13 = 5/34 : 7/48
As the product of the means is equal to the product of the extremes.
P*7/48 = 2/13 * 5/34
P*7/48 = 10/442
P = 480/3094 => P = 240/1547
Answer: C #### C
QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x?
options: A)20 B)60 C)100 D)120 E)150
SOLUTION:y = 0.5*0.5*x = x/4
y%*x = 9
(y/100)*x = 9
(x/400)*x = 9
x^2 = 9*400
x = 60
The answer is B. #### B
QUESTION:A man can row upstream at 29km/hr and down stream at 15km/hr find mans rate of the current ?
options: A)9.8km/hr B)3.6km/hr C)8.9km/hr D)7km/hr E)5.9km/hr
SOLUTION:given upstream(u) =29km/hr
down stream (v)= 15km/hr rate of the current =1/2(u-v) =1/2(29-15)=7km/hr
Answer is (D) #### D
QUESTION:What approximate value should come in place of the question mark (?) in the following equation?
1.542 × 2408.69 + 5134.632 = ?
options: A)4600 B)4800 C)5200 D)6400 E)8800
SOLUTION:Explanation 3700 + 5100 = 8800
Answer E #### E
QUESTION:Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
options: A)6 B)7 C)8 D)10 E)11
SOLUTION:It's a simple geometry problem. Look at the diagram below:
Answer: E. #### E
QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?
options: A)170 B)185 C)190 D)198 E)200
SOLUTION:185
Answer is B #### B
QUESTION:A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 244 passengers. Find the no of passengers in the beginning?
options: A)292 B)180 C)276 D)144 E)168
SOLUTION:Let no of passengers in the beginning be X
After first station no passengers=(X-X/3)+280=2X/3 +280
After second station no passengers =1/2(2X/3+280)+12
1/2(2X/3+280)+12=244
2X/3+280=2*232 = 464 - 280 = 184
2X/3=184
X=276. So the answer is option C) 276. #### C
QUESTION:A shopkeeper sold an article at $100 with 30% profit. Then find its cost price?
options: A)$120 B)$100 C)$91 D)$77 E)$69
SOLUTION:cost price = selling price *100/(100+profit)
C.P. = 100*100/130 = $77(approximately)
Answer is D #### D
QUESTION:Calculate the circumference of a circular field whose radius is 10 centimeters.
options: A)20 π cm B)19 π cm C)28 π cm D)25 π cm E)30 π cm
SOLUTION:Circumference C is given by
C = 2πr = 2π*10 = 20 π cm
Answer: A #### A
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was:
options: A)14 B)16 C)19 D)22 E)24
SOLUTION:Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21.
Son's age 5 years back (21 - 5) = 16 years.
answer :B #### B
QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4?
options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3
SOLUTION:We can have 6 different outcomes on a dice.
Total outcomes on two dices = 6*6
We need only the cases where total sum of the numbers on the dices is 4
They can be {1, 3}, {2, 2}, {3, 1}
A total of 3 outcomes
Probability = favorable outcomes/ total outcomes = 3/36 = 1/12.
Option A #### A
QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder?
options: A)7 B)10 C)8 D)12 E)15
SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C
QUESTION:The ratio 3 : 5 expressed as a percent equals
options: A)60% B)40% C)80% D)125% E)None
SOLUTION:Solution
3 : 5 = 3/ 5
= (3 / 5 x 100)%.
= 60 %.
Answer A #### A
QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 6?
options: A)82,650 B)64,850 C)64,749 D)49,700 E)56,720
SOLUTION:Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 6
Seeing the Options After Dividing an Finding the Reminder of 2
My Answer was A #### A
QUESTION:30 carrots on a scale weigh 5.94 kg. When 3 carrots are removed from the scale, the average weight of the 27 carrots is 200 grams. What is the average weight (in grams) of the 3 carrots which were removed?
options: A)165 B)170 C)175 D)180 E)185
SOLUTION:27*200=5400.
The other 3 carrots weigh a total of 540 grams.
The average weight is 540/3 = 180 grams.
The answer is D. #### D
QUESTION:If a < b < c , which of the following must be true?
(I) a < b^2
(II) b − a < c
(III) a^2 > b^2 > c^2
options: A)None B)I only C)II only D)III only E)II and III
SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=1, b=2, and c=3.
None of the options must be true.
Answer: A. #### A
QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 4
II. 12
III. 24
options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only
SOLUTION:Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three #### A
QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265
options: A)800 B)700 C)750 D)850 E)900
SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265
253/160p=1265==> p =800
ANSWER A #### A
QUESTION:Anne bought doughnuts for a class breakfast party. She bought 12 chocolate doughnuts, 12 coconut doughnuts, and 10 jam-filled doughnuts. How many doughnuts did Anne buy in all?
options: A)25 B)34 C)39 D)21 E)11
SOLUTION:Add the numbers of doughnuts.
12 + 12 + 10 =34.
Answer is B. #### B
QUESTION:If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
15 * 17 * 19 =?
options: A)89 B)49 C)68 D)38 E)338
SOLUTION:E
338
(19 * 17) + 15 = 338 #### E
QUESTION:Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
options: A)17603 B)17608 C)17628 D)17600 E)176023
SOLUTION:Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375
= Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100
= Rs. 17600
Answer: D #### D
QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is
options: A)277 B)668 C)119 D)177 E)121
SOLUTION:Number of words which can be formed
= 5! - 1 = 120 - 1 = 119.
Answer: C #### C
QUESTION:The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 13%?
options: A)31.5% B)35.9% C)37.5% D)39.5% E)30.5%
SOLUTION:Let marked price = $100.
Then, C.P. = $64, S.P. = $87
Gain % = 23/64 * 100 = 35.9%. B #### B
QUESTION:A car travels at a speed of 65 miles per hour. How far will it travel in 8 hours?
options: A)125 miles B)225 miles C)520 miles D)425 miles E)525 miles
SOLUTION:During each hour, the car travels 65 miles. For 8 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 + 65 + 65 = 8 × 65 = 520 miles
correct answer is C) 520 miles #### C
QUESTION:In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race?
options: A)2min 10 sec B)2min 30 sec C)2min 40 sec D)2min 50 sec E)2min 20 sec
SOLUTION:100 m = 15 sec
1 m = 15/100 sec
1000 m = 15/100*1000
=150 sec
=2min 30 sec
ANSWER:B #### B
QUESTION:The 40 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
options: A)4 B)6 C)8 D)9 E)10
SOLUTION:The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=40
solving for x you get 8
Answer C #### C
QUESTION:A rectangular courtyard 3.78 metres long and 2.25 metres wide is to be paved exactly with square title, all of the same size. What is the largest size of the tile which could be used for the purpose ?
options: A)11 cms B)21 cms C)42 cms D)None of these E)46 cms
SOLUTION:Solution
Largest size of the tile = H.C.F. of 378 cm an= 21 cm = 525 cm. Answer B #### B
QUESTION:A can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work?
options: A)2 1/2days B)4 1/2days C)6 1/2days D)7 1/2days E)10 1/2days
SOLUTION:The required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days
Answer is B #### B
<<<Examples ends
QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6
SOLUTION:Explanation:
40*(48/100) = 19.2 --- 64
? --- 12 => Rs.3.6
Answer: D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches?
options: A)24 B)26 C)28 D)30 E)32
SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x
x=30
answer is D #### D
QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
options: A)47/5 B)13 C)17 D)21 E)23
SOLUTION:Let A contains A, B contains B liters
so, (A-4)/(B+4)= 1/3.......(1)
again, (B-5)/(A+5)= 1/2..........(2)
from (1)(2) we find A= 47/5
ans: (A) #### A
QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is
options: A)16 B)24 C)48 D)96 E)78
SOLUTION:Solution
Required number = (2×4×6)
= 48.
Answer C #### C
QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
options: A)36 B)76 C)98 D)27 E)24
SOLUTION:(3x-9):(5x-9)
= 9:17
x = 12 => 3x
= 36
Answer:A #### A
QUESTION:When I was born, my mother was 23 years of age. After 6 years, when my sister was born, my father was 34 years of age. what is the difference between the ages of my parents?
options: A)17 years B)11 years C)6 years D)5 years E)8 years
SOLUTION:When age of Son=0 ,Mother=23
After 6 years, Son=6 ,Mother=23+6=29 ,Father=34
So difference between ages of Mother & Father=34-29=5
ANSWER:D #### D
QUESTION:Two pipes A and B can fill a cistern in 20 and 40 minutes respectively, and a third pipe C can empty it in 80 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
options: A)19 1/7 min B)15 1/7 min C)17 1/7 min D)7 1/7 min E)16 min
SOLUTION:1/20 + 1/40 - 1/80 = 5/80
80/5 = 16
ANSWER:E #### E
QUESTION:At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
options: A)404 B)452 C)444 D)468 E)422
SOLUTION:312 + 222 - 112 (since 112 is counted twice )= 422
E is the answer #### E
QUESTION:If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
options: A)1/4 B)1/2 C)3/4 D)3/5 E)None of these
SOLUTION:The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer : B #### B
QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
options: A)5 B)4 C)6 D)8 E)3
SOLUTION:65*(90/100)*((100-x)/100) = 56.16
x = 4%.Answer:B #### B
QUESTION:A thief is spotted by a policeman from a distance of 300metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?
options: A)A)1km B)B)500m C)C)650m D)D)750m E)E)1200m
SOLUTION:Relative speed of the policeman = 20-16 = 4 km/hr
time taken by policeman to cover 300m = (300/1000)*(1/4) = 3/40 hr
In 3/40 hr the thief covers a distance of 48/40 km = 6/5 km = 1200m
Answer is E #### E
QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is
options: A)0.092 B)0.92 C)9.2 D)92 E)920
SOLUTION:F(69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33
Now,
7 × 2 = 14
7 × 1 = 7
or better:
6.9 × 1 = 6.9
6.9 × 2 = 13.8
hence,
6.9 <6.928 × 1.33 < 13.8
9.2 is the only answer that satisfies this condition.C #### C
QUESTION:Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
options: A)5 B)6 C)9 D)24 E)26
SOLUTION:Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A #### A
QUESTION:Each child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total?
options: A)16 B)12 C)18 D)22 E)08
SOLUTION:2*8=16.Answer is A. #### A
QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
options: A)6 B)9 C)36 D)120 E)144
SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways
Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places
Second Place, Physics Book - in 4 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.
Total no of ways = 4*3*3*2*2*1*1 = 144 ways
E #### E
QUESTION:If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
options: A)None B)I only C)II only D)III only E)I and II
SOLUTION:given 2x/y is prime and greater than 2.
=> 2x/y could be any of the following
3,5,7....
=> 2x/y is odd and prime (as 2 is the only even prime number and its not in this set)
1. x = y , can't be true
if x=y , 2x/y = 2 which is not odd and prime.
2. y=1. can't be true.
if y=1,2x/y = 2x = even which is not odd & prime.
3. x and y are prime integers, need not be true.
lets say 2x/y = 3 and say y=2 prime
=>x = 6/2 = 3 prime
satisfies the given condition here.
but when 2x/y = 3 and y=5 prime
=> x = 15/2 not prime
My Answer is A #### A
QUESTION:A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
options: A)42 B)43 C)46 D)47 E)49
SOLUTION:A
42
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
125 : 150 :: 35 : x 125 x x = 150 x 35
x = (150 x 35)/125
x = 42 #### A
QUESTION:A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
options: A)2 B)4 C)6 D)8 E)12
SOLUTION:To fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible
so we will take the base as 12 feet by 8 feet
Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less.
Therefore the radius of the cylinder will become Diameter 2===>8/2=4 Diameter
ANSWER:D #### D
QUESTION:Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option?
options: A)1/2 B)1/6 C)1/12 D)6/10 E)3/10
SOLUTION:as coin has only two faces then probability must be 1/2
ANSWER:A #### A
QUESTION:A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.
options: A)21:25 B)27:25 C)21:23 D)31:25 E)33:22
SOLUTION:Solution :
Given SI1 = SI 2
P1 : P2 = 1/R1T1 : 1/R2T2
= 1/(10*5) : 1/(9:6)
27:25
B #### B
QUESTION:What is the remainder when 1014*1047*1050*1053 is divided by 33?
options: A)3 B)6 C)30 D)21 E)18
SOLUTION:OA is 'C'.
OE:
take the remainder from each of 1044/33, 1047/33 and so on..
1014/33 gives remainder = 24
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e = 24*24*27*30
break them into pairs 24*24/33 gives remainder 15
and 27*30/33 gives remainder 18
so 15*18/33 gives remainder 6.
B #### B
QUESTION:In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is-
options: A)42 B)32 C)48 D)28 E)38
SOLUTION:X/63 = 24.
X = 24 *63.
So correct answer would be,
(24 *63) /36 = 42.
ANSWER : A #### A
QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
options: A)6 days B)4 days C)8 days D)5 days E)1 days
SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4
=> 4 days
Answer: B #### B
QUESTION:In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted?
options: A)72% B)47% C)42% D)34% E)28%
SOLUTION:Town A is 40%, therefore town B must be 60%
Town A registered voters:0.70∗0.40=0.28
Town B registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent
ANSWER:B #### B
QUESTION:Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is:
options: A)18 B)19 C)20 D)21 E)22
SOLUTION:Explanation:
Let first number be x.
So,2nd no. = 4x & 3rd no.=8x.
So,x+4x+8x=78 × 3 = 234.
13x = 234
x = 234/13
Hence,smallest Number x=18.
Answer: A #### A
QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4?
options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3
SOLUTION:We can have 6 different outcomes on a dice.
Total outcomes on two dices = 6*6
We need only the cases where total sum of the numbers on the dices is 4
They can be {1, 3}, {2, 2}, {3, 1}
A total of 3 outcomes
Probability = favorable outcomes/ total outcomes = 3/36 = 1/12.
Option A #### A
QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water
options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr
SOLUTION:still in water=1/2(98+10)km/hr
=54km/hr
correct option is :B #### B
QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
options: A)33 B)50 C)99 D)87 E)71
SOLUTION:L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100 = 50%
Answer: B #### B
QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
options: A)2388 B)2380 C)2888 D)2663 E)2922
SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer: B #### B
QUESTION:The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
options: A)22 seconds B)65 seconds C)78 seconds D)12 seconds E)21 seconds
SOLUTION:Speed of the boat downstream
= 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 60/5 = 12 seconds.
Answer:D #### D
QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
options: A)68 km/hr. B)32 km/hr. C)34 km/hr. D)35 km/hr. E)72 km/hr.
SOLUTION:Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240 )/12
2x = 40
x = 20.
Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr.
answer :E #### E
QUESTION:How much 60% of 50 is greater than 40% of 30?
options: A)18 B)28 C)26 D)27 E)23
SOLUTION:(60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer:A #### A
QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
options: A)18 cm B)20 cm C)22 cm D)24 cm E)26 cm
SOLUTION:2(l + b) = 5
b 1
2l + 2b = 5b
3b = 2l
b = 2 l
3
Then, Area = 216 cm2
l x b = 216
l x 2 l = 216
3
l2 = 324
l = 18 cm.
A) #### A
QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show?
options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30
SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour.
The two clocks show 2:00 at 2 0'clock
At 3:00 -
Clock B is at 3:00
Clock A is at 3:20 (1 hour + gains 20 minutes)
AT 4:00 -
Clock B is at 4:00
Clock A is at 4:40 (2 hours + gains 40 minutes)
In 4 hours the clock A gains 4*20=80 minutes or 1 hour 20 minutes
If clock A is at 7:20 the clock B is at 6:00
Answer is B #### B
QUESTION:A family pays $700 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?
options: A)$1,000 B)$1,200 C)$1,500 D)$1,800 E)$2,200
SOLUTION:Assuming the medical expenses are $1000 or more, the family pays $700 + $400 = $1100.
The total amount paid by insurance plan for the first $1000 of expenses is $600.
The insurance will pay another $500 when the medical expenses are $1500.
The answer is C. #### C
QUESTION:The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number?
options: A)12 B)20 C)45 D)60 E)52
SOLUTION:Given ratios
5 : 3
4 : 9
20:12:27
The second number = 177/(20+12+27) * 15 = 45
Answer is C #### C
QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 6300
interest only for the period. The principal amount borrowed by her was
options: A)Rs. 2000 B)Rs. 17500 C)Rs. 15000 D)Rs. 20000 E)None of these
SOLUTION:Explanation :
Principal = Rs. (100×6300 / 12×3)
=> Rs. 17500.
Answer : B #### B
QUESTION:A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
options: A)525 B)665 C)412 D)235 E)856
SOLUTION:Answer: Option B
8 * 84 = 672 – 7 = 665 #### B
QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 500. What is the manager's monthly salary ?
options: A)Rs.16003 B)Rs.16029 C)Rs.1288 D)Rs.16108 E)Rs.12000
SOLUTION:Explanation:
Manager's monthly salary Rs. (2000 * 21 - 1500 * 20) = Rs.12000.
Answer: E #### E
QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ?
options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6
SOLUTION:Given ratio is 7:6;
let weight before and after reduction be 7x and 6x respectively.
A/Q
7x=56.7
=> x=56.7/7
=> x= 8.1
Reduced weight= 6x= 6*8.1= 48.6;
hence reduced weight= 48.6
ANSWER:B #### B
QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?
options: A)30sec B)45sec C)36sec D)29sec E)52sec
SOLUTION:Speed of the train = 50*5/18 = 250/18 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(250/18) = 500*18/250 = 36sec
Answer is C #### C
QUESTION:A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 375,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
options: A)a) 500 B)b) 750 C)c) 1,000 D)d) 1,250 E)e) 1,500
SOLUTION:Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 375,000 = 93,750
So required ratio = 93,750/75 =1,250
Answer D #### D
QUESTION:If the sum of 7 consecutive negative integers is -70, what is the value of the 2nd number in the sequence?
options: A)8 B)-9 C)-8 D)9 E)6
SOLUTION:if sum is -70, the average = median = -70/7 = -10 = which is the middle in the sequence.
7/2 = 3.5. When rounded up = 4. So -10 is the 4th in the sequence.
4th - 2nd = 2 numbers away.
-10 + 2= -8
Answer: C #### C
QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
options: A)3.4 B)3.8 C)4 D)4.2 E)4.6
SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E #### E
QUESTION:A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
options: A)30 B)60 C)75 D)90 E)105
SOLUTION:Answer : A
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 160
16x = 160
x = 10.
Hence, total number of notes = 3x = 30. #### A
QUESTION:A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process?
options: A)4.15 B)4.21 C)4.52 D)4.81 E)4.93
SOLUTION:X is the initial quantity of salt in the water.
After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X
Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination.
So we have:
X1=1/3 X
X2=1/3 X1
X3=1/3 X2
By multiplying both ends of the equations we get:
X1*X2*X3 = (1/3)^3 X*X1*X2
Simplification leaves us with:
X3 = (1/3)^3 X
X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3)
In this case, given X was: X=5 g
So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81
Answer: D #### D
QUESTION:A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
options: A)25 B)37 C)36 D)29 E)21
SOLUTION:Explanation:
From the information provided we know that,
Principal + 8% p.a. interest on principal for n years = 180 …….. (1)
Principal + 4% p.a. interest on principal for n years = 120 ……… (2)
Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60.
Now, we can substitute this value in equation (2),
i.e Principal + 60 = 120
= Principal = Rs.60.
We know that SI = , where p is the principal, n the number of years and r the rate percent of interest.
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 =(60*n*4)/100
=> n = 100/4 = 25 years.
Answer: A) 25years #### A
QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is?
options: A)Rs. 3900 B)Rs. 4900 C)Rs. 4980 D)Rs. 5000 E)Rs. 5900
SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5 x.
2
15x + 2y = 4000
15x + 2 x 5 x = 4000
2
20x = 4000
x = 200.
So, y = 5 x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
A) #### A
QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6?
options: A)5 B)4 C)3 D)2 E)1
SOLUTION:Let's test out some values of p and q that satisfy the given information.
p leaves are remainder of 2 when divided by 6
So, p COULD equal 8
q leaves are remainder of 3 when divided by 6
So, q COULD equal 3
What is the remainder when p – q is divided by 6?
So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5
Answer: A #### A
QUESTION:A school’s annual budget for the purchase of student computers increased by 70% this year over last year. If the price of student computers increased by 30% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
options: A)30% B)30.77% C)36% D)37% E)38%
SOLUTION:Pick numbers.
Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $170, price = $1.3 --> the number of computers purchased = 170/1.3 = ~130.77
Increase in the number of computers purchased = 30.77%.
Answer: B. #### B
QUESTION:Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Six years ago Jim was 7 times as old as Sam. How old is Jim now?
options: A)8 B)12 C)16 D)20 E)24
SOLUTION:We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 2 years younger than Fred
3) Six years ago, Jim was 7 times as old as Sam.
let's TEST Answer D: 20
IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 8 years old
6 years ago, Jim was 14 and Sam was 2, so Jim WAS 7 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
D #### D
QUESTION:A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.46 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.54 In what ratio should he mix the water and milk?
options: A)1:20 B)1:10 C)1:8 D)1:45 E)6:11
SOLUTION:water = w (liter)
Milk = m (liter)
==> Cost = Price x Quantity = 0.46m
==> Revenue = Price x Quantity = 0.54(m + w)
==> Profit =0.54(m+w) - 0.46m = 0.2*(0.46m)[20% of cost]
==> 0.54m + 0.54w - 0.46m = 0.092m
==> 0.012m = 0.54w
==> m/w = 0.54/0.012 = 45
--OR--
w/m = 1/45
D is correct. #### D
QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 2. Find his average after 17th inning.
options: A)36 B)39 C)42 D)45 E)None of the above
SOLUTION:Let the average after 17th inning = x.
Then, average after 16th inning = (x – 2).
∴ 16(x – 2) + 87 = 17x or x = (87 – 32) = 55.
Answer E #### E
QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
options: A)12% B)19% C)15% D)14% E)22%
SOLUTION:Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:A #### A
QUESTION:What comes next in the series?
16 72 38 94 50 __
options: A)11 B)25 C)17 D)19 E)16
SOLUTION:E
16
Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit. #### E
QUESTION:power windows: 60%
anti-lock brakes: 25%
CD player: 45%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
options: A)25 B)8 C)11 D)3 E)0
SOLUTION:Answer: B
Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.
If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation:
45=15+22+x
x=8, choice B. #### B
QUESTION:A group of tourists wants to visit at least three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.
options: A)24 B)36 C)48 D)60 E)64
SOLUTION:The number of ways to choose three cities is 4C3=4.
The number of itineraries for each group of 3 cities is 3!.
So the number of itineraries to three cities is 4*3!=24.
The number of ways to choose four cities is 4C4=1.
The number of itineraries for the group of 4 cities is 4!.
So the number of itineraries to four cities is 4!=24.
The total number of itineraries is 24+24=48.
The answer is C. #### C
QUESTION:If -1 < x < 0, which of the following must be true?
I. x^4 < x^3
II. x^6 < 1 – x
III. x^5 < x^2
options: A)I only B)II only C)III only D)II,III only E)I,II,III only
SOLUTION:Answer : E #### E
QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
Q=z-x = x+9-x= 9
Ans:D #### D
QUESTION:Find the missing in the series: 70, 56, 45, 41,___
options: A)22 B)287 C)2679 D)276 E)2771
SOLUTION:Answer:D #### D
QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table?
options: A)11*10! B)9*8! C)8*7! D)7*6! E)6*5!
SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=12
(n-1)!=11!=11*10!
Ans:A #### A
QUESTION:A project scheduled to be carried out over a single fiscal year has a budget of $12,000, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,540. By how much was the project over its budget?
options: A) $380 B) $540 C) $1,050 D) $1,380 E) $1,430
SOLUTION:Difficulty level: 600
Each month's budget = 12000/12 = 1000
Budget for 4 months = 4*1000 = 4000
Actual amount spent = 4540
Amount spent over the budget = 4540 - 4000 = 540
Answer (B),
Regards, #### B
QUESTION:Which of the following is closer to (3!+2!)+(3!-2!)?
options: A)8 B)22 C)10 D)14 E)12
SOLUTION:(3!+2!)+(3!-12!)=6+2+6-2
= 12
Answer: E #### E
QUESTION:The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 50 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?
options: A)55 B)56 C)57 D)58 E)59
SOLUTION:20x + 50 = 21(x – 5)
X=55
ANSWER:A #### A
QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages.
options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12
SOLUTION:Explanation:
Let the present ages of A and B be 'a' and 'b' respectively.
3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1)
a-b = 5 -------(2) Solving (1) and (2) we get b=8
Substituting b = 8 in second equation, we get a= 13. Answer : C
=> 2a = 32 => a = 16.
Answer: C #### C
<<<Examples ends
QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr?
options: A)25 B)30 C)99 D)88 E)61
SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr.
= 72 * 5/18 = 20 m/sec.
Time taken to pass the man = 500 * 1/20 = 25 sec.
Answer: A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Which of the following points is symmetric with y=x at (2,3)?
options: A)(-2,-1) B)(-2,1) C)(2,1) D)(3,2) E)(-1,2)
SOLUTION:We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.
(2,3) would become (3,2).
Answer (D). #### D
QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ?
options: A)95 B)110 C)20 D)None of these E)Cannot be determined
SOLUTION:Solution
2/5of 350 - 4/7of 210 = 20.
Answer C #### C
QUESTION:At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $8 on candy, how much did John spend at the supermarket?
options: A) $60 B) $80 C) $90 D) $120 E) $180
SOLUTION:Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.
We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $8 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:
(1/2)T + (1/3)T + (1/10)T + 8 = T
To get rid of the fractions we can multiply the entire equation by 30, and we obtain:
15T + 10T + 3T + 240 = 30T
28T + 240 = 30T
240 = 2T
T = 120
John spent $90 at the supermarket.
Answer: D #### D
QUESTION:A company D has 15 percent of the employees are secretaries and 45 percent are salespeople. If there are 50 other employees of Company D, how many employees does Company D have?
options: A)200 B)125 C)180 D)152 E)250
SOLUTION:Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 45%
% of of employees other than secretaries and salespeople = 100 - 60 = 40%
But this number is given as 50
so 40% of x = 50
x = 125
Therefore there a total of 125 employees in the company D
Correct answer - B #### B
QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water.
options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20
SOLUTION:Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate of current = 1/2(a-b)
Rate in still water = 1/2(a+b)
=> Rate of current = 1/2(30-10) = 10 kmph
=> Rate in still water = 1/2(30+10) = 20 kmph
Option E #### E
QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min
SOLUTION:A
20 hours 30 min
1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours #### A
QUESTION:Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?
options: A)40 B)50 C)70 D)80 E)90
SOLUTION:L+M=M+N-40 / N=2L+10
40=M+N-L-M
40=N-L
40=2L+10-L
30=L
2(30)+10=70
C #### C
QUESTION:The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is:
options: A)2200 B)5500 C)3054.9 D)1100 E)4400
SOLUTION:Cylinder volume = πr(power2)h
= 22/7 × 9 × 9 × 12
= 3054.9 m(power3)
Answer is C. #### C
QUESTION:Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for r dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?
options: A)x/(y - r) B)x/(r - y) C)x D)x/r E)x/y
SOLUTION:Two ways...
1) let t be the total number, so cost = t*y+x and selling price=t*r..
No profit no loss....t*y+x=t*r.....T=x/(r-y)...
B #### B
QUESTION:Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
options: A)129 B)128 C)189 D)187 E)112
SOLUTION:CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
Answer: C #### C
QUESTION:y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
options: A)-512 B)-257 C)-256 D)-513 E)128
SOLUTION:As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form of ax^2+bx+c=0,
The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b
512 can be expressed as product of two numbers in the following ways:
1 * 512
2 * 256
4 * 128
8 * 64
16 *32
The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513.
The least value possible for b is therefore -513.
D #### D
QUESTION:Which of the following is non-negative number?
options: A)(a-0.9)(a-1) B)(a+1)(a-1) C)(a+0.9)(a+1) D)(a-0.6)(a-0.6) E)a(a+1)
SOLUTION:5-sec approach:
D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative.
Answer: D. #### D
QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150?
options: A)15 B)75 C)25 D)18 E)12
SOLUTION:A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (150 - 75) = 75 points to C.
Answer:B #### B
QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
options: A)877m B)180m C)786m D)165m E)456m
SOLUTION:Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B #### B
QUESTION:Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment?
options: A)1200 B)3000 C)1000 D)3600 E)2400
SOLUTION:Let the additional invested amount for 8% interest be x;
Equation will be;
2400+0.05*2400+x+0.08x = 2400+x+0.08(2400+x)
0.05*2400+0.08x = 0.06x+0.08*2400
0.02x = 2400(0.08-0.05)
x = 2400*0.03/0.02 = 3600
Ans:D #### D
QUESTION:Can you deduce the pattern and find the next number in the series?
3, 24,81, 192, __?
options: A)276 B)277 C)278 D)279 E)375
SOLUTION:Solution:
375
Explanation:
3 = 1^1^1 + 1^1^1 + 1^1^1
24 = 2^2^2 + 2^2^2 + 2^2^2
81 = 3^3^3 + 3^3^3 + 3^3^3
192 = 4^4^4 + 4^4^4 + 4^4^4
Thus the next number will be
375 =5^5^5 + 5^5^5 + 5^5^5
Answer E #### E
QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?
options: A)36 B)66 C)132 D)264 E)364
SOLUTION:12 * 396 = 36 * x
x = 132
ANSWER:C #### C
QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58?
options: A)2784 B)2287 C)2977 D)2668 E)1298
SOLUTION:Let the side of the square plot be a ft.
a2 = 144=> a = 12
Length of the fence = Perimeter of the plot = 4a = 48 ft.
Cost of building the fence = 48 * 58 = Rs. 2784.
Answer:A #### A
QUESTION:In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter?
options: A)15 B)25 C)30 D)45 E)60
SOLUTION:This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...
We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats.
Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as...
15X/7X
When we add the 16 cats and factor in the 'ending ratio', we have an equation....
15X/(7X+16) = 15/11
Here we have 1 variable and 1 equation, so we can solve for X....
(15X)(11) = (7X+16)(15)
(X)(11) = (7X+16)(1)
11X = 7X + 16
4X = 16
X = 4
With this X, we can figure out the initial number of dogs and cats...
Initial dogs = 15X = 15(4) = 60
Final Answer: D #### D
QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is?
options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400
SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4
Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C
QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof?
options: A)38. B)40. C)42. D)44. E)45.
SOLUTION:Let the width= x
x*4x=900
x^2= 225
x= 15
Length= 4*15= 60
difference= 60-15= 45
E is the answer #### E
QUESTION:Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 4 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
options: A)60 B)72 C)84 D)90 E)216
SOLUTION:E is the answer....
D = TS where D=distance, T=Time and S=Speed
To travel half distance, (2+4T) = 9T ==> T = 2/5 ==> 24 minutes
To travel double distance, 2(2+4T) = 9T ==> 4 ==> 240 minutes
Difference, 216 minutes
E #### E
QUESTION:one kilo gram coffee is Rs. 126 and Rs. 135 are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the 3rd variety per kilo gram is?
options: A)150 B)133 C)175.5 D)178 E)190
SOLUTION:Since first and second varieties are mixed in equal proportions.
So, their average price = Rs. 126 + 135 = Rs. 130.50
2
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind
Rs. 130.50 Mean Price
Rs. 153 Rs. x
(x - 153) 22.50
x - 153 = 1
22.50
x - 153 = 22.50
x = 175.50
C #### C
QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is :
options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these
SOLUTION:Solution
Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C
QUESTION:Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 2 screws and 4 nails?
options: A)a. 4 B)b. 5/2 C)c. 2 D)d. 3/2 E)e. 5/4
SOLUTION:let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 2s and 4n= 2s+4*2s=10s..
ratio= 15s/10s=15/10=3/2
D #### D
QUESTION:A train 250 m long is running at a speed of 58 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
options: A)5 sec B)9 sec C)12 sec D)18 sec E)15 sec
SOLUTION:Answer : D.
Speed of the train relative to man = (58 - 8) kmph
= (50* 5/18) m/sec = (125/9)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 250 m at 125/9 m / sec = 250 *9/ 125 sec = 18sec #### D
QUESTION:Two consecutive traffic signals each show either red or green. How many different arrangements of the two signals are possible? (Note: “Red-green” is different from “green-red.”)
options: A)10 B)9 C)8 D)7 E)4
SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 2 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 2 signals are possible.
Total Options: 4
Final Answer:
E #### E
QUESTION:There are 100 wine glasses. I offered my servant to 3 paise for every broken glass to be delivered safely and forfeit 9 paisa for every glass broken at the end of day. He recieved Rs.2.40 .how many glass did he break.
a. 20 b. 73 c. 5 d. 8
options: A)22 B)281 C)29 D)28 E)191
SOLUTION:Answer:B #### B
QUESTION:9886 + x = 13200, then x is ?
options: A)3327 B)3237 C)3337 D)2337 E)None of these
SOLUTION:Answer
x = 13200 - 9886 = 3314
Option: E #### E
QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day?
options: A)10 B)41 C)31 D)21 E)22
SOLUTION:Explanation:
1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12
1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16
1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48
Let ‘x’ be the No. of boys required.
Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1
= (4 + 3 + x)/48 = 1
i.e. 7 + x= 48 and x = 41.
Answer: Option B #### B
QUESTION:Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour?
options: A)The average speed is 1/5 miles per hour. B)The average speed is 1/3 miles per hour. C)The average speed is 2/5 miles per hour. D)The average speed is 2/3 miles per hour. E)The average speed is 3/5 miles per hour.
SOLUTION:We know the average speed and must find the fraction of time taken at a particular speed.
t1/t2 = (A2 – Aavg)/(Aavg – A1)
t1/t2 = (60 – 50)/(50 – 30) = 1/2
So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3.
ANSWER (B) #### B
QUESTION:How many positive integers less than 254 are multiple of 4 but NOT multiples of 6?
options: A)20 B)31 C)42 D)43 E)64
SOLUTION:252/4=63
Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0
240/12=20
63-20=43
Answer: D #### D
QUESTION:Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
options: A)15hrs B)20hrs C)25hrs D)30hrs E)32hrs
SOLUTION:Part filled by A in 1 hour = 1/50
part filled by B in 1 hour = 1/75
Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30
Both the pipes will together will fill the tank in 30 hours.
Answer is D #### D
QUESTION:Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next?
options: A)52 B)56 C)96 D)128 E)None
SOLUTION:Explanation: This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.
Answer: Option B #### B
QUESTION:In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg?
options: A)16 : 30 B)30 : 14 C)16 : 31 D)31 : 15 E)15 : 31
SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (31.50 - 23.75) / (23.75 - 20) = 31/15
ANSWER:D #### D
QUESTION:If a+b+c=13, a2+b2+c2=69, then find ab+bc+ca
options: A)50 B)30 C)20 D)94 E)25
SOLUTION:(a+b+c)2= a2+b2+c2+2(ab+bc+ca)
2(ab+bc+ca)= (a+b+c)2- a2+b2+c2
=169-69
=100
ab+bc+ca=50
ANSWER A 50 #### A
QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
options: A)38 B)2767 C)245 D)277 E)232
SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer:C #### C
QUESTION:The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
options: A)81 : 121 B)81 : 127 C)81 : 191 D)81 : 161 E)81 : 182
SOLUTION:Explanation:
Ratio of the sides = ³√729 : ³√1331 = 9 : 11
Ratio of surface areas = 92 : 112 = 81 : 121
Answer: Option A #### A
QUESTION:A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days,then B alone could do it in :
options: A)15 days B)20 days C)25 days D)30 days E)None of these
SOLUTION:Solution
(A +B)’s 1 day’s work =1/50; C's 1 day's work = 1/50
(A+B+C)’s 1 day’s work = (1/10+1/50)=6/50=3/25…..(i)
Also,A’s 1 day’s work =(B +C)’s 1 day’s work ……(ii)
From (i) and (ii),we get : 2 × (A’s 1 day’s work) =3/25
⇒ A’s 1 day’s work = 3/50
∴ B’s 1 day’s work = (1/10-3/50)=2/50=1/50
So, B alone could do the work in 25 days.
Answer C #### C
QUESTION:If 0 < m < 1 < n< 7, which of the following must be less than 1? I.m/n II. mn III. n - m
options: A)II,III only B)I,III only C)I only D)III only E)II only
SOLUTION:n > 1. So, option II, III is not possible.
So, Option I is correct.
Answer : C #### C
QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr
SOLUTION:Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12
--> 2x = 20
--> x = 10.
--> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr.
Answer : C. #### C
QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 82. How many points altogether did the team score?
options: A)662 B)672 C)652 D)646 E)721
SOLUTION:8 * 82 = 656 – 10 = 646
ANSWER:D #### D
QUESTION:Find the highest common factor of 36 and 84.
options: A)4 B)6 C)12 D)18 E)19
SOLUTION:36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.
Answer: Option C #### C
QUESTION:The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday?
options: A)X. B)X/2. C)2X/3 D)X/3 E)X/4.
SOLUTION:Given the value of stock is X dollars.
Then on Sunday the stock's value is increased by half i.e. X + X/2 = 3X/2 ( this is the new value)
Then on Monday its value dropped by 1/3 of new value = 1/3(3X/2) = 3X/6
Then 3X/2 - 3X/6 = 6X/6 = 6. (new value - 1/3 value)
Ans: A is correct option.. #### A
QUESTION:How many digits are in (12×10^14)(10×10^15)?
options: A)24 B)25 C)26 D)27 E)32
SOLUTION:The question simplfies to (12×10^14)(10^16)
=> 12*10^30
=> Will contain 30 zeros +2 digit 12
=>32
Ans E #### E
QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?
options: A)11 B)12 C)22 D)24 E)44
SOLUTION:22 times in a day.
12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes)
ANSWER:C #### C
QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money?
options: A)1489 B)6845 C)2598 D)1875 E)2600
SOLUTION:P = 75(100/20)5 => P = 1875
Answer: D #### D
QUESTION:The market value of a certain machine decreased by 20 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
options: A) $8,000 B) $5,600 C) $3,200 D) $2,400 E) $4,800
SOLUTION:E.
Market value in 1982= $ 8000
Market value in 1983 = $ 8000- ($ 8000 x 20/100) = 8000-1600= $ 6400
Market value in 1984 = Market value in 1983 - (20 % of $8000)= 6400-1600 = $4800 #### E
QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $8,200 less if they could find two more equal investors. How much is the total investment in the new business?
options: A)$61,500 B)$54,000 C)$21,000 D)$ 5,400 E)$ 3,600
SOLUTION:Total Investment between 5: (x/5)
Total investment including 8200 less between 3 people(x-(8200*3))/3
Set both eq. equal to each other.
61,500
Answer A) #### A
QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years?
options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11
SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320
C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5
Difference = (360.5 - 320) = Rs. 40.5
Answer: C #### C
QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy
SOLUTION:Payment of a week for 2 days a week = $2x
Payment of 4 weeks for 2 days a week = $2x*4 = $8x
Payment of a week for y days overtime a week = $3x+$2xy
Payment of 3 weeks for y days overtime a week = ($3x+$2xy)*3
Total Earnings = $8x + ($3x+$2xy)*3 = 17x+6xy
Answer: option E #### E
QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling?
options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr
SOLUTION:Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*50 = 2500m = 2.5km
Speed = 60*2.5=150km/hr
Answer is D #### D
QUESTION:A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
options: A)40.4 sec B)40.5 sec C)50.4 sec D)50.5 sec E)60.4
SOLUTION:Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 770 m
Time = Distance / Speed
= 770 x 18 / (5 x 55)
= 50.4 sec
correct Answer: option a #### A
QUESTION:Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
options: A)A)35 B)B)28 C)C)45 D)D)25 E)E)26
SOLUTION:Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Eight years ago, P was half of Q in age
=> 2(3x – 8) = (4x – 8)
=> 6x – 16 = 4x – 8
=> 2x = 8
=> x = 4
7x=7*4=28
Answer: Option B #### B
QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam?
options: A)52% B)64% C)72% D)76% E)80%
SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A
QUESTION:Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?
options: A)1/18 B)64/4032 C)63/64 D)1/9 E)1/4
SOLUTION:Explanation :
No of ways of selecting two squares from 64 squares on the chess board is 64C2.
Three cases arise:
case 1: when first square is any of the four corner ones
In this case second square can be chosen in 2 ways
no of ways of selecting two squares: 4*2 = 8
case2: when first square is any of the 24 squares on the side of the chess board other than the corner ones
the second square can be chosen in 3 ways
no of ways of selecting two squares: 24*3 = 72
case 3: the first square is any of the 36 remaining squares
the second square can be chosen in 4 ways
no of ways of selecting two squares: 36*4 = 144
Total no of ways of selecting two adjacent squares = 8 + 72 + 144 = 224
So required probability = 224/64C2 = 224/4032 = 1/18
Answer : A #### A
QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct?
options: A)120 B)130 C)110 D)150 E)180
SOLUTION:let x be the correct answer and y be the wrong answer
so the total number of questions is (x+y)=150
=>4x-2y=480
=>6x=780
hence x=130
ANSWER:B #### B
QUESTION:Find the value of 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
options: A)800 B)3200 C)900 D)1600 E)None
SOLUTION:Answer
4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
= 4 x [(36 x 48 x 250) / (12 x 9 x 5)]
= 4 x 4 x 4 x 50 = 3200
Correct Option: B #### B
QUESTION:An apple orchard grows red and green apples. On the first day of harvest, 496 apples are collected. There are three times as many red apples as there are green apples. How many green apples were harvested?
options: A)99 B)112 C)118 D)124 E)130
SOLUTION:Let x be the number of green apples.
There were 496 total apples; there are three times as many red apples as green apples. Therefore,
x + 3x = 496
4x = 496
x = 124
Answer: D #### D
QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7
SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7
Answer: B #### B
QUESTION:Find the one which does not belong to that group ?
options: A)237 B)232 C)223 D)426 E)111
SOLUTION:Explanation:
525 => 5 52,
39 => 3 32,
24 => 2 22,
636 => 6 62. The above pattern is not followed in 426.
Answer: D #### D
QUESTION:A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
options: A)20 B)24 C)25 D)26 E)30
SOLUTION:Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways #### A
QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?
options: A)50 B)55 C)60 D)45 E)40
SOLUTION:Given :-
Violets - C/2
Carnations - C
Tulip - C/4
Rose - C/4
Total flowers in terms of C = C/2+C+C/4+C/4 = 2C
Percentage of Carnations = C/2C *100 =50%
Answer A #### A
QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
options: A)2789 B)2772 C)1991 D)6725 E)2099
SOLUTION:CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
Answer: D #### D
<<<Examples ends
QUESTION:The length of a rectangle is halved, while its breadth is tripled. What is the % change in area?
options: A)30% B)40% C)50% D)60% E)65%
SOLUTION:Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value W of 100th term?
options: A)126 B)192 C)232 D)252 E)342
SOLUTION:(1~99) 19, (100~199) 19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer W is 342. The correct answer is E. #### E
QUESTION:The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
options: A)Rs.70 B)Rs.75 C)Rs.50 D)Rs.60 E)None of these
SOLUTION:2C + 3T = 1300 --- (1)
3C + 3T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T - C = 100
ANSWER:E #### E
QUESTION:19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
options: A)286 B)342 C)422 D)540 E)618
SOLUTION:2*19C2 = 2*171 = 342
The answer is B. #### B
QUESTION:A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h
SOLUTION:Ans.(A)
Sol. Total distance = 67 × 8 = 536 km
Now speed = 536/6 = 89.33 km/h #### A
QUESTION:We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy?
options: A)A)36 B)B)90 C)C)40 D)D)42 E)E)44
SOLUTION:Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=600.
6(85-G)+7G=600.
510-6G+7G=600.
G=600-510=90.
The answer is B. #### B
QUESTION:How much water should be added to 15 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters
SOLUTION:Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=15+x)))
2=5%*(15+x)-------->x=25
Ans A #### A
QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct?
options: A)120 B)130 C)110 D)150 E)180
SOLUTION:let x be the correct answer and y be the wrong answer
so the total number of questions is (x+y)=150
=>4x-2y=480
=>6x=780
hence x=130
ANSWER:B #### B
QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage.
options: A)4 B)2 C)1 D)3 E)None of them
SOLUTION:cost price=rs27.50, sp=rs 28.50
gain=rs(28.50 –27.50)=rs1.10
so gain%={(1.10/27.50)*100}=4%
Answer is A. #### A
QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse?
options: A)27 B)98 C)27 D)80 E)71
SOLUTION:CP = SP + 1CP = SP - g
620 + x = 860 - 2x
3x = 240 => x = 80
Answer:D #### D
QUESTION:The triplicate ratio of 1:3 is?
options: A)1:0 B)1:8 C)1:27 D)1:2 E)1:1
SOLUTION:13: 33 = 1:27
Answer: C #### C
QUESTION:What is the HCF of 2/3, 4/15 and 6/5
options: A)7/45 B)2/45 C)4/15 D)8/45 E)2/15
SOLUTION:Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 15, 5) = 2/15
Answer: Option E #### E
QUESTION:A,B,C can complete a piece of work in 24,8,12 days. Working together, they complete the same work in how many days?
options: A)4 B)4/5 C)7/9 D)10 E)24/7
SOLUTION:A+B+C 1day work = 1/24 + 1/8 + 1/12 = 6/24 = 1/4
A,B,C together will complete the job in 4 days
Answer is A #### A
QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities?
options: A)48 B)72 C)96 D)120 E)192
SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance Q to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E #### E
QUESTION:Determine the value of 62/54 divided by 62/54
options: A)0 B)1 C)2 D)3 E)none
SOLUTION:Solution:
Each number divided by itself equals 1.
Answer B #### B
QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females?
options: A)16% B)25% C)30% D)40% E)52%
SOLUTION:We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 45 are employed males, hence 19% are employed females.
(employed females)/(total employed people)=19/64=30%
Answer: C. #### C
QUESTION:Solve 8x – 4 = 4x + 11
options: A)5(1/3) B)6(1/3) C)7(1/3) D)3(3/4) E)9(1/3)
SOLUTION:Sol.
8x – 4 = 4x + 11
=> 8x – 4x = 11 + 4
=> 4x = 15 => x = 15/3 = 3(3/4).
Answer D #### D
QUESTION:In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive?
options: A)None B)One C)Two D)Three E)Four
SOLUTION:Non - Negative ( zero to positive infinity )
Solution to the question :
-4,-3,-2,-1,0 , 1,2,3
Hence ans is 3 ..option D #### D
QUESTION:Insert the missing number
..., 4, 8, 16, 32, 64, 128, 256
options: A)6 B)5 C)2 D)3 E)8
SOLUTION:series is 2* Previous Number.
ANSWER:C #### C
QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit
SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1
[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1
[(5.4 + 2.4 + 1.8)/8] - [8/8]
+1.6/8
+20%
answer is D #### D
QUESTION:Given two fair dice, what is the probability E that the sum of their numbers is 4 if exactly one die shows a 3?
options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5
SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.
E=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A
QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1
SOLUTION:1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: C #### C
QUESTION:Varma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8)
options: A)6/k B)8/k C)83k D)2/k E)1/k
SOLUTION:Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 8 minutes =8/k.
Answer: B #### B
QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these
SOLUTION:Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
ANSWER:D #### D
QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph
SOLUTION:Speed downstream = 55 + 20
= 75 kmph
Speed upstream = 55 - 20
= 35 kmph
Answer: C #### C
QUESTION:The average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher.
options: A)40 yrs B)42 yrs C)45 yrs D)46 yrs E)47 yrs
SOLUTION:The average age of 30 boys of a class is equal to 14 yrs:
i.e Sum of all boys:30*14
include class teacher:31 candidates in a class
& avg age is:15 yr
i.e. sum of all:31*15(include class teacher)=465
so,the age of the class teacher:465-420=45yr
answer will be 45 yrs
ANSWER:C #### C
QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils?
options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44
SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 90 - 90p = 40p --> p = 9/13.
(cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44.
Answer: E. #### E
QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)?
options: A)102 B)103 C)111 D)120 E)201
SOLUTION:Explanation :
Number of days from 26-Jan-1996 to 15-May-1996 (both days included)
= 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111
Answer : Option C #### C
QUESTION:At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day?
options: A) 100 B) 1,800 C) 1,090 D) 200 E) 1,000
SOLUTION:Let the total number of sunlasses produced be x
% of high quality sunglasses = 70%
% of low quality sunglasses = 25%
% of sunglasses defective = 100% - 95% = 5%
But this number is given as 50
so 5% of x = 50 and x = (50)(100/5))
x = 180
Therefore there a total of 1,000 sunglasses made per day.
Correct answer - E #### E
QUESTION:In the simple subtraction problem below, some single digits (not necessarily distinct) are replaced by letters. Find the value of 2*A + 2*B + 4*C*D.
A9C5
- 2B79
--------------
633D
options: A)50 B)52 C)66 D)48 E)46
SOLUTION:A9C5
-2B79
----------
6336 since,15-9=6. from there,D=6 and solving all,we get A=8,B=5,C=1.
So 2*8+2*5+4*1*6=50
ANSWER:A #### A
QUESTION:The average of 35 students in a class is 18 years. The average age of 25 students is 20. What is the average age of remaining 10 students?
options: A)17 years B)16 years C)15 years D)14 years E)13 years
SOLUTION:Sum of the ages of 14 students
= (18 * 35) - (20 * 25) = 630 - 500 = 130
Required average = (130/10) = 13 years.
Answer:E #### E
QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5)
SOLUTION:3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5.
Answer: D. #### D
QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?
options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1
SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40 => x = 20.
Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3
Answer:B #### B
QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
options: A)25 B)34 C)50 D)67 E)100
SOLUTION:Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 6 oz can = 300 oz/6 oz = 50
Answer C, 50 cans #### C
QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P?
options: A)20% B)40% C)50% D)60% E)80%
SOLUTION:65% is 15%-points below 80% and 10%-points above 55%.
So the ratio of solution P to solution Q is 2:3.
Mixture P is 2/5 = 40% of the volume of mixture PQ.
The answer is B. #### B
QUESTION:A monkey starts climbing up a tree of 20 feet tall. Each hour it hops 3 feet and slips back 2 feet. How long monkey will take to reach the top of the tree?
options: A)16 hours. B)19 hours. C)12 hours. D)18 hours. E)13 hours.
SOLUTION:The monkey hops 3 feet and slips down 2 feet. So for the first hour it climb 1 feet.
Then for 2 hours 2 feet. Continuing the same till 17 hours, the monkey might have reached 17 feet.
In 18th hour monkey hops 3 feet and reach the 20 feet. Hence the answer is 18 hours.
Answer D #### D
QUESTION:Find the odd man out. 18, 7, 12, 24, 48, 34, 46
options: A)16 B)46 C)24 D)11 E)7
SOLUTION:Explanation :
7 is the only odd number in the given series
Answer : Option E #### E
QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area?
options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2
SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm.
Area of the triangle
= 1/2 * 36 * 15
= 270 cm^2
Answer: E #### E
QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 7.
options: A)18 B)20 C)17.5 D)30 E)32
SOLUTION:Solution
Average = (7+14+21+28)/4)
= 70 / 4
= 17.5.
Answer C #### C
QUESTION:In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat?
options: A)4! B)5! C)7! D)8! E)9!
SOLUTION:There are seven positions to be filled.
The first position can be filled using any of the 7 letters contained in PROBLEM.
The second position can be filled by the remaining 6 letters as the letters should not repeat.
The third position can be filled by the remaining 5 letters only and so on.
758
Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways.
C #### C
QUESTION:How many even multiples of 45 are there between 449 and 901?
options: A)5 B)6 C)9 D)10 E)11
SOLUTION:450 = 10*45
900 = 20*45
The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B. #### B
QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to
options: A)1/35 B)3/35 C)5/37 D)2/35 E)None
SOLUTION:Answer
We have, m x n = 6 x 210 = 1260
∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35
Correct Option: D #### D
QUESTION:The ratio of boys to girls is 6:4.60% of the boys and 40% of girls take lunch in the canteen.What % of class takes lunch?
options: A)51% B)52% C)53% D)54% E)55%
SOLUTION:let total no of students 100, boy 60 and girl 40, so lunch taken by boy and girl respectively 60* 60/100=36 and 40* 40/100=16
so total 52 students takes lunch out of 100 students..so required % is 52%
ANSWER:B #### B
QUESTION:When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y?
options: A)96 B)75 C)50 D)25 E)12
SOLUTION:Guys, one more simple funda.
5/2= 2.5
now .5 x2 =1 is the remainder
25/4 = 6.25
now .25x4=1 is the remainder
32/5=6.4
now.4x5 = 2 is the remainder
given x/y = 6.12 and remainder is 6
So .12 X y = 6
hence y= 50
Ans C #### C
QUESTION:If the speed of the boat in still water is 12km/hr and the speed of the stream is 5km/hr. Find the time taken to travel 34kms down stream.
options: A)4 hrs. B)1 hrs. C)3 hrs. D)2 hrs. E)5 hrs.
SOLUTION:DS =speed of the boat + speed of the stream 5+12 =17km/hr. Time taken to cover 34km down stream =34/17 =2hrs. Answer : D #### D
QUESTION:How many pieces of 0.85 metres can be cut from a rod 42.5 metres long?
options: A)30 B)40 C)50 D)60 E)70
SOLUTION:Number of pieces = 42.5/0.85
= 42.50/0.85
= 4250/85
= 50.
ANSWER:C #### C
QUESTION:Which number is the odd one out?
159
248
963
357
951
852
options: A)154 B)248 C)536 D)645 E)135
SOLUTION:B
248
In the rest there is the same difference between each digit, eg: 8 (–3) 5 (–3) 2. #### B
QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1
SOLUTION:Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer:A #### A
QUESTION:There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
options: A)90 B)120 C)675 D)180 E)200
SOLUTION:Number of ways of selecting 2 fiction books = 10C2
Number of ways of selecting 2 non fiction books = 6C2
10C2 * 6C2 = 45 * 15 = 675
Answer: C #### C
QUESTION:The average of first four prime numbers greater than 30 is?
options: A)38 B)20 C)30 D)40 E)50
SOLUTION:31 + 37 + 41 + 43 = 152/4 = 38
ANSWER:A #### A
QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ?
options: A)2150 B)2200 C)2100 D)2250 E)2300
SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10.
Investment x time.
Kala = 9 x 12 = 108.
Sudha = 12 x 12 = 144.
Githa = 10 x 9 = 180.
Or Kala : Sudha : Githa => 6 : 8 : 5.
Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a.
Difference between the profits received by Kala and Sudha
6a – 8a = 2a = 840 or a = 420.
Githa = 5a = 5 x 420 = Rs.2100.
Option C #### C
QUESTION:4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 2 professor, how many ways can this committee be formed?
options: A)36 B)64 C)72 D)80 E)100
SOLUTION:you count up combinations twice.
4*9*8... and let me name 6 with students A,B,C,..,F
after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.
I don't think that's the only mistake.
64 is a factor of = 2^2*4^2
144 is a factor of = 2^4*3^2.
These are very different numbers and you cannot divide 144 with something to get to 64. #### B
QUESTION:In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 6 metres then what will be the area of the square so formed?
options: A)Cannot be determined B)2600 cm2 C)5184 cm2 D)3025 cm2 E)None of these
SOLUTION:Let the side of the square be x m.
∴ Perimeter of the square = 48 × 6 = 4x ∴ x = 72 m
∴ Area = (72)2 = 5184 m2
Answer C #### C
QUESTION:A club wants to mix 15 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
options: A)20 B)30 C)40 D)50 E)60
SOLUTION:Let number of pounds of 5$ candy to be used be w
6 = (15*8 + 5*w)/(15 +w)
=>90 + 6w = 120 + 5w
=> w = 30
Answer B #### B
QUESTION:A circle graph shows how the budget of a certain company was spent: 60 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
options: A)18° B)36° C)54° D)72° E)90°
SOLUTION:The percent of the budget for transportation is 100 - (60+9+5+4+2)= 20%
100% of the circle is 360 degrees.
Then (20%/100%)*360 = 72 degrees
The answer is D. #### D
QUESTION:Look at this series: V, VIII, __, XIV, XVII, XX, ... What number should fill the blank?
options: A)IX B)XXIII C)XV D)XI E)None
SOLUTION:Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: D #### D
QUESTION:In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had?
options: A)10.7% B)20% C)25% D)33 1/3 E)58 1/3
SOLUTION:No of bank customers in 1985 = 60 x .45 = 27
No of bank customers in 1987 = 144 x .25 = 36
increase in % = 100 X 9/27 = 100/3 or 33 1/3
D is the correct answer #### D
QUESTION:Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt?
options: A)1/216 B)5/216 C)7/216 D)1/36 E)5/36
SOLUTION:The total number of ways the dice can land is 6*6*6=216.
Bob must get a score of 18=6+6+6.
There is only 1 way to do this.
P(Bob wins)=1/216
The answer is A. #### A
QUESTION:There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is:
options: A)9 B)13 C)15 D)12 E)19
SOLUTION:Explanation:
abc/bcd=385/1001=>a/d=5/13
So d = 13
Option B #### B
QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train?
options: A)299 B)277 C)276 D)370 E)281
SOLUTION:Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 150)/26 = 20
x = 370 m.
Answer: D #### D
QUESTION:30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?
options: A)15% B)20% C)80% D)70% E)90%
SOLUTION:Explanation :
Let number of men = 100.
Then, 80 men are less than or equal to 50 years old i.e 20 men are greater than 50 years of age.
Now, the number of men above 50 years who play football = 20% of 20 = 4.
20% of all men play football i.e total no. of men who play football = 20, out of which 4 men are above 50 years old.
So, 20 - 4 = 16 men are less than or equal to 50 years old.
Therefore, percentage of football players less than or equal to 50 years = (16/20) x 100 = 80% .
Answer : C #### C
QUESTION:A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the difference of the numerator and denominator of the original fraction?
options: A) 49 B) 9 C) 28 D) 26 E) 21
SOLUTION:x/y = 2/5 -> 1
(x+4)/2y = 1/3 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 6/5
=> 5x = 3x + 12
=> x = 6
=> y = 5/2 * 6 = 15
so x - y = 9
The answer is B #### B
QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price
options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/-
SOLUTION:100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
A #### A
QUESTION:The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?
options: A)0.03 B)0.04 C)0.048 D)0.05 E)0.12
SOLUTION:Probability of Brand A defective is x
Probability of Brand B defective is 0.06 which 6/100. Which tells you there are 2 defective piece in a lot of 33, for 35 lot it is approx - 2.12
Probability of Brand C defective is 0.08 which 8/100. Which tells you there are 2 defective piece in a lot of 25
Total = 40 + 25 + 25 = 100
Probability of having defective piece in a lot of 100 ( All brands ) = 0.053
Hence 5.3 defective piece out 100 lot.
So 40x + 2.12 + 2 = 5.3
x = 0.03
ANSWER :Opt A. #### A
QUESTION:The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
options: A)2197 B)1267 C)1750 D)2267 E)1262
SOLUTION:Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8) = Rs. 1750
Answer:C #### C
<<<Examples ends
QUESTION:Find the missing in the series: 70, 56, 45, 41,___
options: A)22 B)287 C)2679 D)276 E)2771
SOLUTION:Answer:D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?
options: A)11 B)12 C)22 D)24 E)44
SOLUTION:22 times in a day.
12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes)
ANSWER:C #### C
QUESTION:There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men?
options: A)1932 B)1933 C)1934 D)1935 E)1936
SOLUTION:(5c3*11c3)+(5c4*11c2)+(5c5*11c1)
1936
ANSWER:E #### E
QUESTION:A hall 36m long and 15m broad is to be paved with stones, each measuring 8dm by 5 dm. The number of stones required is:
options: A)180 B)1800 C)18 D)18000 E)1350
SOLUTION:Area of the hall= 3600*1500
Area of each stone= (80*50)
Therefore, number of stones= (3600*1500/ 80*50)= 1350
ANSWER:E #### E
QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours?
options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44)
SOLUTION:Explanation:
Here clock-wise and anti-clockwise arrangements are same.
Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}}
Answer: C) 18!(6 x 24) #### C
QUESTION:What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 145° each?
options: A)96 cm B)108 cm C)120 cm D)132 cm E)154.28 cm
SOLUTION:Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 145*n
from here
n = 10.28
So perimeter becomes 15*10.28= 154.28
Answer: E #### E
QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm.
options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm²
SOLUTION:AB² = AC² - BC²
= 15² - 12²
= 225 - 144
= 81
Therefore, AB = 9
Therefore, area of the triangle = ¹/₂ × base × height
= ¹/₂ × 12 × 9
= 54 cm²
ANSWER : C #### C
QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers.
options: A)28 B)30 C)32 D)34 E)36
SOLUTION:Given:
Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6)
Average = Sum of Quantities/Number of Quantities
= [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27
Simplifying we get, x = 24
Therefore,
Largest number = (x + 6) = (24 + 6) = 30
Smallest number = 24
ANSWER IS B #### B
QUESTION:In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are finance majors?
options: A)3 B)5 C)8 D)11 E)17
SOLUTION:pqrs = 1365 = 3* 5 *7 * 13
Since 1< p < q < r < s, the number of students who are finance majors is q = 5.
The answer is B. #### B
QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen?
options: A)1.34 B)2.84 C)3.84 D)4.34 E)5
SOLUTION:40*(40/100) = 16 --- 50
? --- 12 => Rs.3.84
Answer: C #### C
QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible?
options: A)18 B)20 C)54 D)84 E)120
SOLUTION:the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total S=84 outcomes
D #### D
QUESTION:Lisa earns a profit of $3 on each ribbon that she sells, and $5 on each bracelet. If at the end of the day Lisa has earned $120 and she has sold at least 10 pieces of each item. At least how many bracelets she has sold?
options: A)2 B)5 C)9 D)12 E)15
SOLUTION:Since Lisa has sold at least 10 pieces for each item, let us say Lisa sells (10 + r) number of ribbons and (10 + b) number of bracelets, her profit for the day = 3(10 + r) + 5(10 + b)
=> 3(10 + r) + 5(10 + b) = 120
=> 30 + 3r + 50 + 5b = 120
=> 3r + 5b = 120 - 30 - 50 = 40
=> 5b = 40 - 3r
=> b = 8 - (3/5)r
To minimize b, we need to maximize r and it will be a multiple of 5.
r = 5, b = 8 - (3/5)5 = 5
r = 10, b = 8 - (3/5)10 = 2
Beyond that b will become -ve. So Lisa has sold at least 10 + 2 = 12 bracelets.
Answer: D #### D
QUESTION:he L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
options: A)30 B)40 C)38 D)36 E)39
SOLUTION:Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 48 or x = 8
The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40. Answer: Option B #### B
QUESTION:Calculate the ratio between x and y if 30% of x equal to 50% of y?
options: A)4 : 5 B)3 : 5 C)3 : 7 D)3 : 2 E)4 : 5
SOLUTION:Explanation:
30 x = 50 y
x: y = 30: 50 = 3 : 5
Answer:B #### B
QUESTION:In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can?
options: A)52 B)56 C)60 D)64 E)68
SOLUTION:Let C be the capacity of the can.
(5/8)*(C-20)+20=(3/4)*C
5C-100+160=6C
C=60
The answer is C. #### C
QUESTION:How many different subset of the set of the 12 Calendar Month will not have the Month of March.
options: A)1951 B)1948 C)1953 D)1947 E)1949
SOLUTION:This is a combination solution
Since we have 11 different Month other than the Month of March we can take any Month from the set of 11 Months to make a subset.
11C1 +11C2 + 11C3 + 11C4 + 11C5 + 11C6 + 11C7 + 11C8 + 11C9 + 11C10 + 11C11 = 1948
Plus the one set that is null that is the Set having no element in it which is 11C0 =1
= 1948 + 1 = 1949
E = 1949 #### E
QUESTION:The HCF of two numbers is 42 and the other two factors of their LCM are 11 and 12. What is the largest number.
options: A)462 B)450 C)480 D)504 E)555
SOLUTION:Explanation:
HCF of the two numbers = 42
HCF will be always a factor of LCM
42 is factor of LCM
other two factors are 11 & 12
Then the numbers are (42 11) and (42 x 12)
= 462 and 504
Answer: Option D #### D
QUESTION:At what rate percent per annum will a sum of money double in 16years?
options: A)10.6% B)3.65% C)6.25% D)8.32% E)11%
SOLUTION:Let principle = P
S.I. = P
T = 16yrs
Rate = 100*P/P*16 = 25/4% = 6.25%
Answer is C #### C
QUESTION:The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
options: A)7 B)4 C)5 D)3 E)1
SOLUTION:Explanation:
P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.
Answer:B #### B
QUESTION:The cost of 3 kg of sugar is $30. What will the cost of 8 kg of sugar be?
options: A)20 B)40 C)80 D)160 E)180
SOLUTION:3 kg costs $30
1 kg costs $10
8 kg costs $80
The answer is C. #### C
QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6
SOLUTION:Explanation:
40*(48/100) = 19.2 --- 64
? --- 12 => Rs.3.6
Answer: D #### D
QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?
options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10
SOLUTION:(p-2)(p-4) = q
p = 3 for this to be true, so
1/10
Ans :B #### B
QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double (5,5)?
options: A)1/24 B)1/36 C)1/12 D)1/18 E)1/3!
SOLUTION:total no. in two dice (1,1) ,(2,2) .....(6,)
Total number of events= 6*6
Total events of getting same pair(5,5) = 6
Probability= 6/6*6= 1/6=1/3!
E #### E
QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
options: A)12 B)18 C)22 D)24 E)none of these
SOLUTION:Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x 27 * x = 36 * 18
x = (36 * 18)/27
x = 24.
Answer is D. #### D
QUESTION:3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
options: A)33 B)77 C)26 D)12 E)99
SOLUTION:Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps 4 : 3 :: 8 : x
Days 1 : 2
4 x 1 x x = 3 x 2 x 8
x = (3 x 2 x 8)
(4)
x = 12.
Answer:D #### D
QUESTION:If the product of 2 integers is negative, at most how many of the integers can be negative?
options: A)1 B)3 C)4 D)5 E)6
SOLUTION:The product of 2 integers is negative
Thus an odd number of integers need to be negative to have a negative product
We are asked at most how many are required.
So, the highest odd integer before 6,i.e. 1
Correct Option : A #### A
QUESTION:For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 2/7, what are the odds of it burning out during the period from 6months to 1 year following its purchase?
options: A)5/27 B)2/9 C)1/2 D)4/9 E)2/3
SOLUTION:P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period)
P(of burning out in 1st 6 mnth)= 2/7
--->P( of not burning out in 1st 6 mnth)=1-2/7=5/7
---->P(of not burning out in a six mnth period)=1/2 *5/7=1/3
--->P(of burning out in a six mnth period)=1-1/3=2/3
now
P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)*P(of burning out in a six mnth)
=5/7 * 2/3=1/2
Ans C #### C
QUESTION:If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ?
options: A)3653 B)3657 C)2977 D)3957 E)2711
SOLUTION:Explanation:
Given :
Letter : T I E R B A N
Code : 7 1 9 3 2 4 5
Thus, the code for RENT is 3957.
ANSWER:D #### D
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
options: A)11% B)25% C)87% D)19% E)12%
SOLUTION:800 --- 200
100 --- ? => 25%
Answer: B #### B
QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But
whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11
mornings and 12 afternoons. How many days did they stay there totally?
options: A)16 B)18 C)20 D)13 E)14
SOLUTION:Explanation :
Clearly 11 mornings and 12 afternoons = 23 half days
=> Since 13 days raining means 13 half days.
=> So 23-13 =10 halfdays ( not effecetd by rain )
=> So 10 halfdays =5 fulldays
Hence ,
Total no. of days = 13+5 =18 days
Answer : B #### B
QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M?
options: A)278 B)2890 C)270 D)2702 E)1050
SOLUTION:504/M = 384/800
(504 * 800) / 384 = M
M = 1050
Answer:E #### E
QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?
options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n
SOLUTION:C is the answer.
To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.
Given
- tank was already 1/3 full.
- When n ltr added, it became 5/9
So 1/3 + n = 5/9
n = 5/9 - 3/9
n = 2/9
capacity of the tank is full fraction . i.e. 1 i.e. 9/9
so the question is 9/9 is how much times n
= 9/9 = 1 = xn
so x = 9/2
and total = 9/2n #### C
QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is?
options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2
SOLUTION:A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:B #### B
QUESTION:A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday
SOLUTION:This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.
To show the correct time, it has to gain 5 min.
So the correct time will be shown on wednesday at 7:20 PM
Answer: B #### B
QUESTION:The population of a town is 7500. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
options: A)9300 B)8000 C)8500 D)9500 E)10000
SOLUTION:Formula :
( After =100 denominator
Ago = 100 numerator)
7500 × 100/90 × 100/90 = 9259
A) #### A
QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 11 people all together .how many people can sit in a bus?
options: A)52 B)92 C)95 D)88 E)66
SOLUTION:Right Side =15 seat
Left Side =15-3 (3 few seat in right side)= 12 seat
Total= 15+12= 27
People can seat in 27 seat= 27*3=81
People can seat in Last Seat = 11
Total People can seat= 81+11=92
ANSWER:B #### B
QUESTION:what is the least number by which 15,625 must be divided to get a number perfect square
options: A)21 B)25 C)24 D)40 E)45
SOLUTION:15,625/25=625
625=(25)^2
Ans-25
ANSWER:B #### B
QUESTION:What was the day of the week on, 18th July, 1776?
options: A)Thursday B)Wednesday C)Monday D)Saturday E)SUNDAY
SOLUTION:16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days)
Total number of odd days = (0 + 4) = 4.
Required day was 'Thursday'.
Answer:A #### A
QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet?
options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec
SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (36 + 36)*5/18 = 4*5 = 20 mps.
The time required = d/s = 100/20 = 5 sec.
Answer : C #### C
QUESTION:The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)
options: A)200π B)240π C)300π D)480π E)1,200π
SOLUTION:Distance traveled in 1 revolution = 2πr= 2π10/5280
Revolutions in one second= 1320
Revolutions in 60 seconds (one minute)= 1320*60
Total distance traveled= total revolutions *distance traveled in one revolution
1320*60 *2π10/5280= 300π
C is the answer #### C
QUESTION:Find the unit's digit in the product 2467 153 * 34172?
options: A)1 B)3 C)2 D)5 E)7
SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172
Now 7 4 gives unit digit 1
7 152 gives unit digit 1
7 153 gives 1*7=7.Also 172 gives 1
Hence unit's digit in the product =7*1=7.
Option A #### A
QUESTION:What is the place value of 7 in the numeral 2734?
options: A)450 B)500 C)700 D)800 E)840
SOLUTION:Option 'C'
7 * 100 = 700 #### C
QUESTION:Cara picked a number of pears, each of which she sold, canned, or poached. If she canned 40 percent more than she poached, and she poached 80 percent less than she sold. If there were a total of 111 pears, then how many pears did she sell?
options: A)69 B)72 C)75 D)78 E)81
SOLUTION:Let x be the amount of pears that she sold.
Then she poached 0.2x.
Then she canned 1.4*0.2x=0.28x.
The total amount of pears is x+0.2x+0.28x=1.48x
The fraction of pears that she sold is 1/1.48=100/148=25/37.
The number of pears she sold is (25/37)*111=75.
The answer is C. #### C
QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph
SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10)
= 50 kmph.
Answer:B #### B
QUESTION:Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged?
options: A)6 B)48 C)36 D)24 E)12
SOLUTION:Dhoni have to sit at either of the ends.
If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24
David can also sit on the other end, then another 4! ways we can arrange.
So total number of ways = 24+24 = 48
Answer : B #### B
QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
options: A)299 B)267 C)269 D)400 E)276
SOLUTION:2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D #### D
QUESTION:Amol was asked to calculate Arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged the 2 digits, say a and b,in one of these 10 integers. As a result, his answer for the Arithmetic mean was 1.8 more than what it should have been. Then b - a equals
options: A)1 B)2 C)3 D)4 E)None of these
SOLUTION:Explanation :
Arithmetic mean is more by 1.8 means sum is more by 18.
So, ba – ab = 18.
b > a because sum has gone up, e.g. 31 – 13 = 18.
Hence, b – a = 2.
Answer : B #### B
QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube.
options: A)36 B)48 C)45 D)360 E)55
SOLUTION:16200 = 23 * 34 * 52
A perfect cube has a property of having the indices of all its prime factors divisible by 3.
Required number = 32 * 5 = 45.
ANSWER:C #### C
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)267 B)240 C)166 D)111 E)121
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300
= 540 ==> x
= 240 m.
Answer: B #### B
QUESTION:The average of first 18 even numbers is?
options: A)19 B)18 C)16 D)11 E)17
SOLUTION:Sum of 18 even numbers = 18 * 19 = 342
Average = 342/18 = 19
Answer:A #### A
QUESTION:If a : b = 5 : 9 and b : c = 4: 7, find a : b : c
options: A)63:36:20 B)36:20:63 C)20:63:36 D)20:36:63 E)None of them
SOLUTION:a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4
a:b:c = 5:9:63/4 =20:36:63.
Answer is D. #### D
QUESTION:Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
options: A)1 years B)7 years C)6 years D)8 years E)9 years
SOLUTION:Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) = 42 years.
Required difference = (42 - 36) = 6 years.
Answer: C #### C
QUESTION:A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be
options: A)7744 B)2388 C)3778 D)2992 E)2888
SOLUTION:Explanation:
length of wire = {\color{Blue}2 \Pi r}= 2 *(22/7 )*56 = 352 cm
side of the square = 352/4 = 88cm
area of the square = 88*88 = 7744sq cm
Answer: A) 7744 #### A
QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph
SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (26 - 18)/2 = 4 kmph
Answer:B #### B
QUESTION:In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 30 ducks and in the larger pond there are 50 ducks. If 20% of the ducks in the smaller pond are green and 12% of the ducks in the larger pond are green, then what percentage of ducks are green?
options: A)13% B)14% C)15% D)16% E)17%
SOLUTION:Number of ducks in small pond = 30
green ducks in small pond = 20 % of 30 = 6 ducks
Number of ducks in large pond = 50
green ducks in large pond = 12 % of 50 = 6 ducks
Total number of ducks = 30 + 50 = 80
total number of green ducks = 6 + 6 = 12 ducks
percentage of green ducks = 12/80 * 100 = 15%
Answer: C #### C
QUESTION:A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item
options: A)Rs. 480 B)Rs. 760 C)Rs. 860 D)Rs. 960 E)None of these
SOLUTION:Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 600
= 80/100 * 600
= 480
Option A #### A
QUESTION:If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number?
options: A)20 B)22 C)27 D)28 E)30
SOLUTION:Given Ratio => 2:3
2x - 10 : 3x - 10 = 2 : 4
4[2x - 10] = 2[3x - 10]
8x - 40 = 6x - 20
8x - 6x = 40 - 20
x = 10
Then biggest number is = 3x
3x = 30
Ans = E #### E
QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
options: A)200 B)300 C)500 D)600 E)700
SOLUTION:Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: Option C #### C
QUESTION:The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
options: A)3:4 B)3:0 C)3:1 D)7:3 E)3:7
SOLUTION:Let the present ages of A and B be 4.5x and 3x years respectively.
Then, (4.5x - 4)/(3x + 4) = 1/1
1.5x = 8 => x = 5.33
Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: D #### D
QUESTION:In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
options: A)65 B)44 C)86 D)29 E)26
SOLUTION:Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: B #### B
QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
options: A)5/16 B)5/12 C)5/19 D)5/17 E)5/15
SOLUTION:Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer: B #### B
QUESTION:If f(x)=x^2 and x is a natural number, what CANNOT be the solution to f(f(f(x)))?
options: A)16384 B)65536 C)6561 D)256 E)1
SOLUTION:Answer A is equal to 4^7 and cannot be a solution because f(f(f(x)) is equivalent to x^8 and 4^7 cannot equal to anything to the power of 8. #### A
QUESTION:A survey was sent to 90 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
options: A)2% B)6% C)14% D)28% E)63%
SOLUTION:case 1: (7/90)=x/100
x=8%
case 2: (9/63)=y/100
y=14%
So percent increase is =(y-x)=(14-8)%=6%
Answer is B #### B
QUESTION:There are 8 magazines lying on a table; 4 are movie magazines and the other 4 are education magzines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the movie magazine will be selected?
options: A)9/14 B)11/14 C)13/14 D)1/14 E)3/14
SOLUTION:1- (4c3/8c3) = 13/14
Answer : C #### C
QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train?
options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph
SOLUTION:D = 100 + 250 = 350
T = 7
S = 350/7 * 18/5 = 180 kmph
Answer:D #### D
<<<Examples ends
QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph.
SOLUTION:DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Evaluate:55- 12*3*2 =?
options: A)42 B)47 C)62 D)72 E)82
SOLUTION:According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
55 - 12*3*2 = 55- 8 = 47
correct answer B #### B
QUESTION:The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
options: A)16 seconds B)34 seconds C)14 seconds D)18 seconds E)15 seconds
SOLUTION:Speed of the boat downstream = 9 + 3 = 12 kmph
= 12 * 5/18 = 10/3 m/s
Hence time taken to cover 60 m = 60*3/10
= 18 seconds.
Answer: D #### D
QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea?
options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None
SOLUTION:Solution: 1st Method:
Let the original price of tea be Rs. x/kg.
After reduction the price becomes = x -10% of x = 9x/10 per kg.
Now,
(22500/(9x/10))-22500/x = 25
Or, 22500[10/9x- 1/x] = 25
Or, 25*9x = 22500;
Or, x = (22500/2589) = Rs. 100.
Hence, new price = 90 per kg.
Thought process Method:
Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg.
After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg.
So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea.
Answer: Option C #### C
QUESTION:A sum of 11,500 amounts to 13,500 in 5 years at the rate of simple interest. What is the rate of interest?
options: A)2% B)3% C)6% D)5% E)8%
SOLUTION:B
3%
S.I. = (13500 - 11500) = 2000.
Rate = (100 x 2000)/(11500x5)% = 3% #### B
QUESTION:A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
options: A)15 sec B)16 sec C)18 sec D)20 sec E)25 sec
SOLUTION:Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec
ANSWER: D #### D
QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $500 per sq. metre.
options: A)$10312.50 B)$13512.50 C)$16512.50 D)$14512.50 E)$18512.50
SOLUTION:Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $500
Hence, total cost
=5.5×3.75×500= $10312.50
A #### A
QUESTION:On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4*[sqrt(t-9)] for t>9, where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?
options: A)17 B)21.25 C)12.25 D)14.05 E)18
SOLUTION:radius=7mm.
So dia= 14mm.
putting D=14 in equation we can easily calculate
t=21.25
ANSWER:B #### B
QUESTION:A sequence contains y numbers of alternating positive and negative numbers, If the first number is postive and y is an even number, how many negative numbers are in it?
options: A)(y+1)/2 B)(y-1)/2 C)y/(2+1) D)y/(2-1) E)y/2
SOLUTION:Lets put values for y, say y=8 since it's even
and first number is positive so sequence will be {pos,neg,pos,neg,pos,neg,pos,neg} we can see that it has 4 negative terms
so putting y=8 in the options,
option E = y/2 => 8/2 = 4 , the number of negative integers
So, E is the answer #### E
QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls?
options: A)12 B)32 C)5 D)28 E)30
SOLUTION:number of kids playing with white color balls = 26
total number of kids in the play school = 35
number of kids playing with both white and yellow color balls = 19
we have to find,
number of kids playing with yellow color balls
35 = 26 + n(B) - 19
35 + 19 - 26 = 28
Hence, Answer is 28 kids play with yellow color
balls. ANSWER D #### D
QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there?
options: A)20 coins B)30 coins C)40 coins D)60 coins E)None of these
SOLUTION:Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 105
⇒ 1.75x = 105 ⇒ x = 60 coins
Answer D #### D
QUESTION:If a < b < c , which of the following must be true?
(I) a < b^2
(II) a < c - b
(III) a^2 < b^2 < c^2
options: A)None B)I only C)II only D)III only E)II and III
SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: A. #### A
QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments.
options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3
SOLUTION:The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:21.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6.
ANSWER:A #### A
QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00?
options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00
SOLUTION:For retail price = $25
First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5
Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14
Answer: Option A #### A
QUESTION:Anderson has a phone plan that charges a
monthly rate of $50 for the first 1,000 minutes
plus $0.25 for each additional minute.
Which of the following functions models
Anderson’s plan for all m > 1,000, with m as
the number of minutes per month and f(m)
as the monthly charge?
options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000
SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee
based on the number of minutes used plus a flat rate of $50. With this information, you can
create the following function:
f(m) = Usage fee + 50
The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So
the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify:
f(m) = 0.25(m – 1,000) + 50
f(m) = 0.25m – 250 + 50
f(m) = 0.25m – 200
correct answer C)f(m) = 0.25m – 200 #### C
QUESTION:If x is an integer, then x(x - 1)(x - k) must be evenly divisible by three when k is any of the following values except
options: A)-4 B)-6 C)-1 D)2 E)5
SOLUTION:if we put k=-1 we get:
X(x-1)(X+1) rearrange:(x-1)X(X+1)
so it looks like a sequenc,
if we assume that X =2 and put number from the answer then we get:
(x – 1)x(x – k)
k=5 =1.2.-3
k=2 =1.2.0
k=-1 =1.2.3
k=-4 =1.2.6
but when we put
k=-6 =1.2.8 not satisfied
so,answer is B #### B
QUESTION:A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball?
options: A)5⁄7 B)10⁄21 C)2⁄7 D)11⁄21 E)None of these
SOLUTION:Reqd probability = 5C2/7C2=5×4/7×6=10/21
Answer B #### B
QUESTION:Today Joelle opened an interest-bearing savings account and deposited $5,000. If the annual interest rate is 4 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?
options: A)$5200 B)$5408 C)$5208 D)$5608 E)$5808
SOLUTION:Interest for 1st year = 5000*4/100 = 200
Interest for 2nd year = 5200 *4/100 = 208
Total =5000+200+208 = 5408
Answer : B #### B
QUESTION:Evaluate: 20 - 12÷12×2 =
options: A)A)4 B)B)8 C)C)12 D)D)16 E)E)20
SOLUTION:According to order of operations, 12÷12×2 (division and multiplication) is done first from left to right
12÷12×2 = 1 × 2 = 2
Hence
20 - 12÷12×2 = 20 - 12 = 8
correct answer is B) 8 #### B
QUESTION:Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age?
options: A)12 years B)13 years C)15 years D)14 years E)18 years
SOLUTION:Let MTomy's present age be 'x' years.
x+ 16 = 3(x- 4)
=> 2x = 28 => x = 14 years.
D #### D
QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
options: A)16 B)24 C)32 D)28 E)54
SOLUTION:after 7 girls left remaining 7 girls
now boys 14 are twice as many as remaining girls.
initially boys=14 and girls=14.
ANSWER:D #### D
QUESTION:A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
options: A)24 kmph B)22 kmph C)21 kmph D)28 kmph E)29 kmph
SOLUTION:A
24 kmph
Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph #### A
QUESTION:Out of a classroom of 6 boys and 5 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions?
options: A)2/33 B)4/33 C)2/165 D)4/165 E)7/165
SOLUTION:The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 5C3=10.
P(only girls are chosen)=10/165=2/33
The answer is A. #### A
QUESTION:Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 2/3 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
options: A)1/16 B)7/8 C)9/64 D)5/64 E)3/64
SOLUTION:P(Xavier will solve)=1/4
P(Yvonne will solve)=2/3
P(Zelda will NOT solve) = 1- 5/8 = 3/8.
Now, we need to multiply all this Ps to find an answer:
p= (1/4)*(2/3)*(3/8) = 1/16.
Ans. A. #### A
QUESTION:Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought?
options: A)20 B)18 C)24 D)26 E)28
SOLUTION:Smallest gumballs = (19-16) + (19-14) +19= 27
Largest gumballs = (25-16) + (25-14) +25= 45
Difference = 45 - 27 = 18
B #### B
QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
options: A)18 B)24 C)42 D)81 E)28
SOLUTION:Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
ANSWER:B #### B
QUESTION:In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
options: A)150 B)750 C)1,250 D)1,500 E)2,500
SOLUTION:Given 150 deers were caught and they are tagged in the first slot.
In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged.
Given this 10% approximates the percentage of tagged deer in the forest..here number is 150..
then 100% is 1500.. is the number of deers population in the forest..
Answer: D is correct answer.. #### D
QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
options: A)Rs.12:29 B)Rs.18:90 C)Rs.16.28 D)Rs.16.50 E)Rs.82.09
SOLUTION:Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer:D #### D
QUESTION:A Pharmacy company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 8 hrs and a machine of type S does the same job in 4 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
options: A)3 B)4 C)2 D)9 E)12
SOLUTION:Rate of machine R =1/8
Rate of machine S =1/4
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/8 +x/4 =1/2
3x/8=1/2
x=8/6=1.3=2
So no of machine R is 2
Answer C #### C
QUESTION:If e is an integer, what is the greatest possible value for e that would still make the following statement true: 11*10^e < 1/10 ?
options: A) –4 B) –3 C) –2 D) –1 E) 0
SOLUTION:Just putting values, the LHS becomes
e=0 --> 11
e=-1 --> 11/10
e=-2 --> 11/100
e=-3 --> 11/1000
Anything lower will be smaller than 11/1000. e=-2, equality does not hold but it does for e=-3.
Answer is B. #### B
QUESTION:1100 boys and 700 girls are examined in a test; 31% of the boys and 23% of the girls pass. The percentage of the total who failed is ?
options: A)A)63.3% B)B)52.4% C)C)81.2% D)D)75.4% E)E)72.11%
SOLUTION:Total number of students = 1100+700 = 1800
Number of students passed = (31% of 1100+23% of 700) = 341+161 = 502
number of failures = 1298*100/1800= 72.11%
Answer is E #### E
QUESTION:The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides.
options: A)12, 9 B)18, 3 C)15.16, 6 D)12, 12.37 E)12, 15.16
SOLUTION:CM=3
AREA=PM*CM/2, thus PM=12
By Pythagorean Theorem, we can now find the value of PC.
D is the correct option. #### D
QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is:
options: A)233 B)37 C)25 D)27 E)11
SOLUTION:Explanation:
Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: C #### C
QUESTION:Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2500. then his monthly salary is
options: A)Rs. 12500 B)Rs. 1000 C)Rs. 8000 D)Rs. 6000 E)Rs. 15000
SOLUTION:Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 2500
⇔ 20 / 100x = 2500
⇔ x = 2500 × 5 = 12500.
Answer A #### A
QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between?
options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p
SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p.
2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate.
1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound.
So range is 5p to 10p.
Answer C. #### C
QUESTION:If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
options: A)1/4 B)1/2 C)3/4 D)3/5 E)None of these
SOLUTION:The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer : B #### B
QUESTION:A single discount equivalent to the discount series of 20%, 15% and 8% is?
options: A)37.4 B)31.8 C)31.6 D)31.3 E)31.1
SOLUTION:100*(80/100)*(85/100)*(92/100)
= 62.6
100 - 62.6 = 37.4
Answer:A #### A
QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
options: A)388 B)299 C)266 D)400 E)2871
SOLUTION:2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400.Answer: D #### D
QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers?
options: A)56% B)57% C)58% D)45% E)35%
SOLUTION:let assume he sells 1 buffet daily,
now
then 300*1 = revenue (eq -1)
if he reduced his price by 20% then ,
240*(customer) = 125/100*revenue
customer = 1.25*300/240 = 1.56
means 56 % increase in customer.
ANSWER:A #### A
QUESTION:(469 + 174)(power 2) - (469 - 174)(power 2) / (469 x 174) = ?
options: A)174 B)178 C)171 D)176 E)170
SOLUTION:Formula = (a + b)(power 2) - (a - b)(power 2) / ab
= 4ab/ab
= 4 (where a = 469, b = 174.)
Answer is A. #### A
QUESTION:A boat running up stram takes 6 hours to cover a certain distance, while it takes 9 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
options: A)2 : 3 B)5 : 1 C)4 : 5 D)7 : 1 E)8 : 1
SOLUTION:Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
6(x+y) = 9(x-y)
6x+6y = 9x-9y
15y = 3x
5y = x
x/y = 5/1
5 : 1
Answer: Option B #### B
QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C?
options: A)2250 B)3000 C)3018 D)3019 E)3012
SOLUTION:60*5:36*6:75*3
100: 72: 75
75/247 * 7410 = 2250
Answer: A #### A
QUESTION:Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
options: A)15hrs B)20hrs C)25hrs D)30hrs E)32hrs
SOLUTION:Part filled by A in 1 hour = 1/50
part filled by B in 1 hour = 1/75
Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30
Both the pipes will together will fill the tank in 30 hours.
Answer is D #### D
QUESTION:What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.?
options: A)Rs. 8908.42 B)Rs. 9720 C)Rs. 10123.20 D)Rs. 10483.20 E)None
SOLUTION:Amount = [22000 * (1 + 12/100)3]
= 22000 * 28/25 * 28/25 * 28/25 = Rs. 30908.42
C.I. = (30908.42 - 22000) = Rs. 8908.42
ANSWER:A #### A
QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 7:00 a.m., at what time was it one-eighth full?
options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m.
SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 7:00 a.m -1 hour = 6:00 a.m.
Answer: C. #### C
QUESTION:A shipment of 8 TV sets contains 6 black and white sets and 2 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?
options: A)1/7 B)1/4 C)5/14 D)11/28 E)27/28
SOLUTION:2/8 * 1/7 = 2/56
1-(2/56) = 54/56 = 27/28
Answer E #### E
QUESTION:Annie has 100 cards numbered 1 through 100. If she deals four cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers?
options: A)95!/100! B)96!/100! C)(95! X 5!)/100! D)(96! X 5!)/100! E)(97! X 4!)/100!
SOLUTION:Alex to get 4 consecutive cards in ascending order, to have 4 consecutive at the end is good enough.
There are 97 consecutive numbers in 100: {1, 2, 3, 4, }, {2, 3, 4, 5}, ..., { 97, 98, 99, 100};{4!*97!}{100!}.
Answer: E. #### E
QUESTION:The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this triangle.
options: A)15° ,45° ,110° B)15° ,45° ,130° C)15° ,45° ,110° D)15° ,35° ,110° E)25° ,45° ,110°
SOLUTION:Solution
If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
x = 15
The measures of the three angles are
x = 15°
3x = 3 × 15 = 45°
8x = 8 × 15 = 120°
ANSWER IS C #### C
QUESTION:If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r?
options: A)2 B)3 C)4 D)5 E)Cannot be determined
SOLUTION:\frac{15^r( 1+ 15)}{4^y} = 15^y
(15^r . 4^2 ) / 4^y = 15^y. 4^0
15^r . 4^(2-y) = 15^y. 4^0
Equating the powers, r = y; 2-y = 0; So r = y = 2=A #### A
QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages.
options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these
SOLUTION:Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 136
20x = 160 => x = 8
Their present ages are 32, 56 and 72 years respectively.
ANSWER:D #### D
QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
options: A)230 B)783 C)291 D)112 E)221
SOLUTION:Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer:A #### A
QUESTION:A large box contains 21 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
options: A)250 B)350 C)450 D)550 E)525
SOLUTION:The number of chocolate bars is equal to
21 * 25 = 525
correct answer E #### E
QUESTION:For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| =
options: A)ab-4+b B)2b-ab-4 C)ab+4 D)ab-2b+5 E)4-ab
SOLUTION:Given: |ab| = ab and |a| = -a
Question: |b-3| + |ab-b| = ?
**** Looking at |ab| = ab tells us that a and b are either both positive or negative
**** Looking at |a| = -a tells us that a must be negative
**** Combine two observations: a and b are both negative values
Let a=-1 and b=-1
|b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5
Test a) ab-4 = (-1)(-1)-4 = -5
Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7
Test c) ab+4 = 1 + 4 = 5
Answer: C #### C
QUESTION:For how many integers n is 1^n+2 = (n+2)^1?
options: A)0 B)1 C)2 D)None of these E)3
SOLUTION:If n=0
1^0+2 = (0+2)^1
1^2 = 1 ; 2^1 =2 not ok
If n=1
1^1+2 =1 ; (1+2)^1=3^1=3 not OK
So, Answer : D #### D
QUESTION:Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint?
options: A)10 B)20 C)28 D)14 E)19
SOLUTION:number of statues=all the paint÷amount used per statue
=7/8 ÷ 1/16
=7/8*16/1
=112/8
=14.
Answer is D. #### D
QUESTION:Let B represent a set of four distinct prime numbers. If the sum of the numbers in B is even and x is a member of B, then what is the least possible value that x can be?
options: A)1 B)2 C)3 D)5 E)7
SOLUTION:We are told that B is a set of four distinct prime numbers, and the sum of the numbers in B is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of B must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number. #### C
QUESTION:If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF
options: A)13 - 11 - 9 - 7 - 8 B)13 - 11 - 9 - 7 - 6 C)13 - 11 - 9 - 7 - 7 D)13 - 11 - 9 - 7 - 3 E)13 - 11 - 9 - 7 - 1
SOLUTION:MLIGF = 13 - 11 - 9 - 7 - 8
Note: this is a dummy question. Dont answer these questions
Answer:A #### A
QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence?
options: A)−164 B)0 C)16 D)32 E)64
SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term)
sum of 64 terms = 32
ANSWER:D #### D
QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils?
options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44
SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 90 - 90p = 40p --> p = 9/13.
(cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44.
Answer: E. #### E
QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number
x + y = 16
x - y = 4
options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2
SOLUTION:Solution
Let x be the first number. Ley y be the second number
x + y = 16
x - y = 4
Solve the system of equations by elimination
Adding the left sides and the right sides gives:
x + x + y + -y = 16 + 4
2x = 20
x = 10
Since x + y = 16, 10 + y = 16
10 + y = 16
10 - 10 + y = 16 - 10
y = 6
The numbers are 10 and 6
Answer A #### A
QUESTION:Sheena has a pet frog and it is growing fast and eating more flies each day. When she first brought it home on Monday it ate 3 flies, Tuesday it ate 6, Wednesday it ate 9, and Friday it ate 15.
How many flies did her frog eat on Thursday?
options: A)12 B)14 C)10 D)11 E)13
SOLUTION:A) 12. The frog started eating 3 more flies each day.
3 +3 =6
6+3=9
9+3=12
12+3=15 #### A
QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine?
options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4
SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine"
The above statement is NOT clear
Still a solution:
For 8 students we have 3 posts
one post can be occupied by only one member
no two posts can be occupied by the same member
probability(P) for a member getting selected for particular 2 of the 3 posts=
probable outcomes=1(Caine)+1(Abel)=2
total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8
=2/8=1/4
Probability required for the given case= 1-P=1-1/4=3/4
Answer: E #### E
QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8?
I. x^2
II. y^2
III. xy
options: A)I only B)II only C)III only D)I and II only E)I, II and III
SOLUTION:4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is C #### C
QUESTION:The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Ans: E - 4 pairs
(xˆ2)(yˆ2) = 900 [square root both sides]
xy = 30
20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15
Cancel the repeats
This leaves us with exactly 4 options.
Hence, E #### E
QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article?
options: A)2777 B)2987 C)1200 D)1240 E)1671
SOLUTION:CP* (50/100) = 620
CP= 12.4 * 100 => CP = 1240
Answer: D #### D
<<<Examples ends
QUESTION:There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division?
options: A)22 B)35 C)37 D)20 E)75
SOLUTION:D
20
29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30 = 20. #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases?
options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc
SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips
The answer is C. #### C
QUESTION:curie bakes 5 cookies for 5 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:curie made 5*5 cookies = 25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends.
9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same.
The nearest multiple of 2 is 8.
9-8=1
A is the correct answer #### A
QUESTION:2+2^2+2^+......+2^9=?
options: A)2044 B)1022 C)1056 D)1065 E)None of them
SOLUTION:This is a G.P. in which a=2, r=2^2/2=2 and n=9
S^n=a(r^n -1)/(r-1)
=2x(2^9-1)/(2-1)
=2x(512-1)=2x511
=1022
Answer is B #### B
QUESTION:What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10?
options: A)5 B)7 C)4 D)9 E)3
SOLUTION:30,40,50,60,70
total 5
Answer is A #### A
QUESTION:A ladies hostel had provision of food for 300 women for 45 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is:
options: A)38.89 B)39.18 C)38.78 D)38.0 E)38.18
SOLUTION:Explanation :
After 10 days : 300 women had food for 35 days.
Suppose 275 women had food for x days.
Now, Less women, More days (Indirect Proportion)
275 : 300 :: 35 : x
=> 275 x x = 300 x 35
=> x = 300 x 35 / 275
=> x = 38.18
Answer : E #### E
QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days
SOLUTION:B = 1/4 – 1/20 =0.2 days
ANSWER:E #### E
QUESTION:The simple interest on a sum of money will be Rs.1000 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
options: A)8981 B)3799 C)1200 D)2693 E)2000
SOLUTION:P --- 10 ---- 1000
P --- 5 ----- 500
3P --- 5 ----- 1500
------
=> 2000
Answer: E #### E
QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is?
options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25
SOLUTION:The number of exhaustive events = 50C1 = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50
= 17/25.
Answer: E #### E
QUESTION:If S = {1, 2, 3, 4, 5, 6, 7}, how much less is the mean of the numbers in S than the median of the numbers in S?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Mean = (1 + 2 +3 + 4 + 5 + 6 + 7)/7 = 4
Median = 4
Difference = 4-4 = 0
Option A #### A
QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1
SOLUTION:1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: C #### C
QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 10800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
options: A)9000 B)98000 C)60000 D)11000 E)12000
SOLUTION:100 % - 10 % = 90 %
54%-36%=18%
18% ------> 10800 ( 18 × 600 = 10800)
100% -------> 60000 votes (100 × 600 = 60000)
C #### C
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform?
options: A)338 B)240 C)287 D)400 E)191
SOLUTION:Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m.
Answer: D #### D
QUESTION:A number is missing from the number series below.
Can you find it ?
84, 155, ?, 399 , 584, 819.
options: A)275 B)350 C)399 D)258 E)449
SOLUTION:D
The missing number is 258.
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
399 = 7^3 + 7^2 + 7
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9
Thus,
258 = 6^3 + 6^2 + 6 #### D
QUESTION:If the two hands in a clock are 15 minutes divisions apart,then the angle between them is
options: A)3° B)18° C)24° D)90° E)None of these
SOLUTION:In a clock, each minute makes 6°
∴ 15 minutes will make 6 × 15 = 90°
Answer D #### D
QUESTION:Replace X with the appropriate number in
2 , 4 , 6 , 30 , 32 , 34 , X
options: A)38 B)8 C)5 D)36 E)37
SOLUTION:D
list of consecutive numbers that does not contain a 'e' in the spelling #### D
QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is:
options: A)4884 B)5340 C)5342 D)5345 E)5356
SOLUTION:Divisor = (5 * 44) = 220
= 10 * Quotient = Divisor
=> Quotient = 220/10 = 22
Dividend = (Divisor * Quotient) + Remainder
Dividend = (220 * 22) + 44 = 4884.
A #### A
QUESTION:If the price of rice rises from Rs. 6 per kg to Rs. 8 per kg, to have no increase in his expenditure on rice, a person will have to reduce his consumption of sugar by
options: A)12 % B)19 % C)25 % D)32 % E)36 %
SOLUTION:Explanation:
Let original consumption = 100 kg and consumption = y kg.
So, 100 x 6 = y x 8
y = 75 kg
Reduction in consumption = 25 %.
ANSWER: C #### C
QUESTION:Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
options: A)a) 66.67-x B)b) 40-x C)c) 80-2x D)d) 120-x E)e) 40-x/2
SOLUTION:Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of:
R = (100 mi)/(1.5) = 66.67 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is x, and let's call the other y. We want y.
x + y = 66.67
y = 66.67 - x
Answer =(A) #### A
QUESTION:If the price of petrol increases by 44, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
options: A)25% B)20% C)16.67% D)33.33% E)None of these
SOLUTION:Explanation :
let us assume before increase the petrol will be Rs. 100.
After increase it will be Rs (100+44) i.e 144.
Now, his consumption should be reduced to :-
=(144−100)/144 ∗ 100.
Hence, the consumption should be reduced to 30.6%.
Answer : E #### E
QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x?
options: A)16 B)28 C)15 D)13 E)18
SOLUTION:HCF x LCM = Product of Numbers
2 x 144 = 16 x x
x = (2 x 144) / 16
x = 18
ANSWER : E #### E
QUESTION:What is the smallest number which when diminished by 20, is divisible 15, 30, 45 and 60?
options: A)200 B)220 C)240 D)322 E)342
SOLUTION:Required Number
= (LCM of 15, 30, 45 and 60) + 20
= 180 + 20 = 200
Option A #### A
QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x?
options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1
SOLUTION:x^2 > x^3 > x^1
1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x.
This can be possible only if the base is negative; therefore, the variable, x, must be a negative number.
2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1.
With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B
QUESTION:From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 27 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
options: A)20 B)10 C)30 D)50 E)40
SOLUTION:Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+27) and number of girls were 5x
Hence, 2(5x) = x + 27
=> 10x = x + 27
=> x = 3
Number of girls in the beginning = (5x + 15) = (5×3 + 15) = 30
Answer is C. #### C
QUESTION:a bank was to give a loan out to a newly married couple for 800,000 with no interest for 2 years and raise the price to 900,000 after 2 years. what is the interest rate?
options: A)17% B)13% C)12% D)7% E)6%
SOLUTION:for 0 years = (900,000- 800,000) = 100,000.
for 2 years = (100,000 x 2)/2= 100,000
Principal = (800,000 - 100,000) = 700,000.
Hence, rate = (100 x 100,000)/(700,000x2) = 7% ANSWER: D #### D
QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer?
options: A)55 B)25 C)85 D)45 E)35
SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer.
Therefore 0+1+3+4+5+6+7+9=35
Answer is E #### E
QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed?
options: A)104 B)130 C)298 D)269 E)213
SOLUTION:520/4 = 130 kmph
Answer:B #### B
QUESTION:A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
options: A)4 B)5 C)6 D)7 E)8
SOLUTION:The rate of the pump + leak = 5/14
1/2 - leak's rate = 5/14
leak's rate = 1/2 - 5/14 = 1/7
The leak will empty the tank in 7 hours.
The answer is D. #### D
QUESTION:What is the place value of 7 in the numeral 2734?
options: A)450 B)500 C)700 D)800 E)840
SOLUTION:Option 'C'
7 * 100 = 700 #### C
QUESTION:What is the remainder when 1274 * 1275 * 1277 *1285 is divided by 12?
options: A) 0 B) 6 C) 11 D) 9 E) 7
SOLUTION:1271*1275*1277*1285 = (1272 - 2)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-2)(3)(-7)(1) = 42. Thus the question becomes: what is the remainder upon division of 42 by 12? The answer to this question is 6.
Answer: B #### B
QUESTION:The sum of three consecutive odd natural numbers, each divisible by 3 is 90. What is the largest among them?
options: A)21 B)24 C)27 D)33 E)45
SOLUTION:Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 = 90
3X = 81
X = 27
The numbers are 27, 30, 33
Therefore the largest number is 33
Answer D. #### D
QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book?
options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20
SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = 2p
p = p
Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.
With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E
QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse?
options: A)27 B)98 C)27 D)80 E)71
SOLUTION:CP = SP + 1CP = SP - g
620 + x = 860 - 2x
3x = 240 => x = 80
Answer:D #### D
QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D?
options: A) 1 B) 8 C) 19 D) 20 E) 27
SOLUTION:I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.
C #### C
QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph
SOLUTION:Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer:A #### A
QUESTION:If 2994 ÷ 14.5 = 171, then 29.94 ÷ 1.45 = ?
options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.2
SOLUTION:29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ]
= 171/10
= 17.1
Answer is A. #### A
QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house?
options: A)25 B)49 C)3 D)87 E)36
SOLUTION:Aravind can select one or more than one of his 8 gang.
=> Required number of ways = 2^2 – 1= 3.
C #### C
QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ?
options: A)87 B)95 C)99 D)100 E)103
SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.
Answer: C. #### C
QUESTION:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
options: A)88 B)90 C)96 D)98 E)102
SOLUTION:2 multiples-choice questions can be answered in = 4 x 4 = 16 ways
3 true-false questions can be answered in = 2x2x2 = 8 ways
But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers
Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways
Total ways to answer the quiz = 16 x 6 = 96
Answer C #### C
QUESTION:The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is
options: A)35.22 B)36.12 C)36.22 D)36.42 E)None
SOLUTION:Solution
Correct sum = (36x50+44-23)
= 1821.
∴ Correct mean = 1821 / 50
= 36.42.
Answer D #### D
QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is?
options: A)8 B)9 C)7 D)62 E)2
SOLUTION:2x * x = 162 => x= 9
Answer: B #### B
QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3?
options: A)9 B)10 C)11 D)12 E)14
SOLUTION:A number will be divisible by 3 if sum of all the digits of the number is divisible by 3
Here the Possible sum of the two distinct digits can be 3, 6, 9 and 12 only in order to satisfy the given condition
If sum of Digits = 3, No. = 12, 21 --- 2 Cases
If sum of Digits = 6, No. = 15, 24, 42, 51 --- 4 Cases
If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases
If sum of Digits = 12, No. = 57, 75 --- 2 Cases
Total Cases = 2+4+6+2 = 14 cases
Answer: option E #### E
QUESTION:9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day?
options: A)18 B)9 C)10 D)8 E)11
SOLUTION:We have, M1D1H1 = M2D2H2
So, 9*12*4= 6*D2*8
D2 = 9*12*4/6*8 = 9
ANSWER:B #### B
QUESTION:The sum of two consecutive number is 109. Which is the larger number?
options: A)42 B)43 C)44 D)45 E)55
SOLUTION:Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=109
2x+1=109
2x=108
x=54
Therefore larger number is x+1=55
ANSWER:E #### E
QUESTION:How many ways are there for 4 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
options: A)48 B)12 C)72 D)100 E)720
SOLUTION:So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 4 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 4! different ways, so total 2*4!=48.
Answer A. #### A
QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/9 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
options: A)11/30 B)29/60 C)17/30 D)13/18 E)11/15
SOLUTION:Let s assume the platinum card spending limit =x
Gold card spending limit will be =x/2
balance on gold card is =x/2*1/3=x/6
Platinum card unspent limit is= x-1/9x=8/9x
So if gold card balance is transferred then the rest unspent will be
8/9x-x/6=13/18x
So the ans is D #### D
QUESTION:If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it?
options: A)22 B)38 C)60 D)88 E)90
SOLUTION:Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
\inline \fn_jvn \therefore 10:36 ::25:x \inline \fn_jvn \Leftrightarrow (10 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{10}=90
Hence, 10 men can do it in 90 hours.
Answer: E) 90 #### E
QUESTION:40% of x is greater than 1/3rd of x by 110.what is x?
options: A)1100 B)2100 C)1300 D)1650 E)1400
SOLUTION:4x/10-x/3=110
1x/15=110
x=1650
ANSWER:D #### D
QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
options: A)400 B)197 C)278 D)270 E)279
SOLUTION:2000 ---- 50
2000 ---- 40
x ----- 50
x*50 = 2000*40
x=1600
2000
-------
400
Answer: A #### A
QUESTION:The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica?
options: A)48 B)47 C)46 D)49 E)52
SOLUTION:let their ages are 9x,15x and 25x respectively.
difference between the ages of Patrick and Monica = 25x-9x=16x where
49x=147 or x=3
so diff in ages = 16x=16*3=48 yrs
ANSWER:A #### A
QUESTION:If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC?
options: A)9 B)18−3√3 C)18 D)18+3√3 E)27
SOLUTION:The altitude of an equilateral triangle is side*√3/2.
As perimeter of triangle ACD is 9+3√3, AC + CD + AD =
(side+side/2+side*√3/2) = 9 + 3√3 or side =6.
Perimeter of equilateral triangle, ABC is 3(side) or 18.
Answer:(OptionC) #### C
QUESTION:A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails?
options: A)1/8 B)1/4 C)3/8 D)1/2 E)9/16
SOLUTION:We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.
Using the binary formula and defining a head as a success,
P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2
t= 6/16
= 3/8
The answer is therefore (C) #### C
QUESTION:A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
options: A)(320 - y)/(5x) B)(y +220)/(5x) C)5(80 - y)/(4x) D)(y + 400)/(4x) E)(4y + 320)/(5x)
SOLUTION:Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20 = 65 houses per week
total time they took = (40/20) + (40/65) = 2.6 weeks
Putting the values of x and y in equation B
(y +220)/(5x) = (40+220)/5*20 = 260/100 = 2.6 #### B
QUESTION:In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
options: A)2.5 sec B)4.25 sec C)3.75 sec D)12.5 sec E)6 sec
SOLUTION:Speed = 144 * 5/18 = 40 m/sec
Time taken = 150/40 = 3.75 sec.
ANSWER:C #### C
QUESTION:If x = 3^9 and x^x = 3^k, what is k?
options: A)3^11 B)3^13 C)3^25 D)3^27 E)3^81
SOLUTION:Solution:
We know that x=3^9
which implies x^x = (3^9)^(3^9) = 3^(9 * 3^9) [because (x^y)^z = x^(y*z))]
so 3^(3^2 * 3^9) = 3^(3^(2+9)) [because x^a * x^b = x^(a+b)]
therefore x^x = 3^(3^11)
Given that x^x=3^k
so 3^(3^11) = 3^k
Since the base is same the exponent will also be same
therefore k = 3^11
Answer: A #### A
QUESTION:What is the value of x if (64^2)-(36^2)=20*x?
options: A)120 B)100 C)140 D)130 E)115
SOLUTION:20*x=(64+36)(64-36)
20*x=100*28
x=(100*28)/20
x=5*28
x=140
Option C #### C
QUESTION:A train 150 m long running at 72 kmph crosses a platform in 28 sec. What is the length of the platform?
options: A)410 m B)354 m C)450 m D)350 m E)250 m
SOLUTION:A
410
A = (72 * 5/18)*28-150 = 410 #### A
QUESTION:The volume of a rectangular box is 330 square inches. The length on one side of the top is 11
inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing
may help you with this one.)
options: A)100 B)130 C)120 D)110 E)101
SOLUTION:3 x 11 = 33
V = 33 x missing measure
V is 330
330 ÷ 33 = 10 which is the missing
measure of the side of the box top
10 x 11 = 110 sq. ft. which is area
of the top of the box.
correct answer D #### D
QUESTION:In a dairy farm, 20 cows eat 20 bags of husk in 20 days. In how many days one cow will eat one bag of husk?
options: A)1 B)40 C)20 D)26 E)30
SOLUTION:Explanation :
One bag of husk = 20 cows per day
⇒ 20 × 1 × 20 = 1 × 20 × x
For one cow = 20 days
Answer : C #### C
QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college?
options: A)13680 B)13885 C)14005 D)14280 E)14680
SOLUTION:dana borrows 6000 and returns 2% per month.
so returns 120 per month. and 1440 per year.
so dana owes 6000-1440=4560 per year.
after 3 years she will owe 13680.
Ans (A) #### A
QUESTION:A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
options: A)14 years B)18 years C)20 years D)22 years E)16 years
SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 20) + 2 = 2(x + 2)
x + 22 = 2x + 4
x = 18.
answer :B #### B
QUESTION:9, 35, 91, 189, 341, ?
options: A)502 B)521 C)559 D)611 E)712
SOLUTION:Explanation :
13 + 23 = 9
23 + 33 = 35
33 + 43 = 91
43 + 53 = 189
53 + 63 = 341
63 + 73 = 559
Answer : Option C #### C
QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
options: A)7 B)6 C)5 D)4 E)3
SOLUTION:Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:7
Webs 7:1
1 x 7 x x = 7 x 1 x 7
=> x= 7
Answer is 7 #### A
QUESTION:8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged?
options: A)A.1296 B)B.1850 C)C.2880 D)D.3546 E)E.4200
SOLUTION:Glue milk and water bottlestogether: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: C. #### C
QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business?
options: A)$11,000 B)$50,000 C)$16,500 D)$ 6,600 E)$ 3,600
SOLUTION:Total Investment between 5: (x/5)
Total investment including 2200 less between 3 people(x-(2200*3))/3
Set both eq. equal to each other.
16,500
Answer C) #### C
<<<Examples ends
QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each?
options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7
SOLUTION:Explanation:
Let the present ages of Anand and Bala be 'a' and 'b' respectively.
Given a - 2b = 1 --- (1)
a+b = 7----(2) =>b =7-a
Substituting b = 7-a in first equation,
3a-14 = 1 => a = 5
=> b = 2
Answer: B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area?
options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2
SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm.
Area of the triangle
= 1/2 * 36 * 15
= 270 cm^2
Answer: E #### E
QUESTION:In a apartment, 70% of the people speak English, 10% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
options: A)1/3 B)2/3 C)2/5 D)1/2 E)2/9
SOLUTION:P (E) = 70 / 100 = 3 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E ∩ H) = 30 / 100 = 3 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (7 / 10) + (1 / 10) - (3 / 10) = 3 / 10 = 1/2
D #### D
QUESTION:In a two digit number, the digit in the units place is two times the digit in ten's place and sum of the digits is equal to 6. What is the number?
options: A)24 B)28 C)32 D)36 E)38
SOLUTION:Solution
Let the ten digits be x. Then,units digit=2x
Therefore x + 2x = 6
‹=›3x = 6
‹=›x= 2.
So, ten's digit = 2, unit's digit = 4.
Hence, the required number is 24.
Answer A #### A
QUESTION:5020−(502÷100.4)=?
options: A)15 B)20 C)5015 D)25 E)35
SOLUTION:Explanation:
=5020−(502/1004×10)
=5020−5=5015
Option C #### C
QUESTION:Which of the following is(are) true for a@b=b@a?
I. a@b=b+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ
SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A
QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
options: A)19 B)18.7 C)19.9 D)21.7 E)22.8
SOLUTION:Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 36 Paise is given as tax
=> Total tax incurred = 36 Paise = Rs.36/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−36/100−x)6/100 = 36/100
⇒ 6(25 −0.36 −x) = 36
⇒ (25 − 0.36 − x) = 6
⇒ x = 25 − 0.36 − 6 = 18.7
B) #### B
QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125
options: A)134 B)154 C)166 D)178 E)189
SOLUTION:28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C #### C
QUESTION:In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was:
options: A)2500 B)2520 C)3000 D)3100 E)None of these
SOLUTION:Explanation :
Number of valid votes = 70% of 9000
= 6300.
Valid votes polled by other candidates = 40% of 6300
(40/1006300)
= 2520.
Harsh Mishra a year ago
0 upvotes
Answer : B #### B
QUESTION:A watch was sold at a loss of 10%. If it was sold for Rs.196 more, there would have been a gain of 4%. What is the cost price?
options: A)s:1000 B)s:1067 C)s:1278 D)s:1028 E)s:1400
SOLUTION:90%
104%
--------
14% ---- 196
100% ---- ? =>
Rs:1400
Answer: E #### E
QUESTION:A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
options: A)66 2/3 % B)33 7/3 % C)33 1/3 % D)33 5/8 % E)34 1/3 %
SOLUTION:The total number of mangoes bought by the shopkeeper be 15.
If he buys 5 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 5
Profit = SP - CP = 5 - 3 = 2
Profit Percent = 2/3 * 100 = 66 2/3 %
Answer: A #### A
QUESTION:P and Q entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by:
options: A)Rs.2400 B)Rs.3000 C)Rs.3600 D)Rs.4800 E)Rs.3800
SOLUTION:A : B : C = (16000 x 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)
= 147 : 189 : 126 = 7 : 9 : 6.
Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22
= Rs.3600
ANSWER:C #### C
QUESTION:A store sells four different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:4C2=6.
The answer is B. #### B
QUESTION:Pipe A can fill the tank in 30 minutes and pipe B in 20min and pipe C can empty the tank in 90 minutes. How long it will take to fill the tank if three of the pipes are operating together?
options: A)10.55 B)12.0 C)13.1 D)13.85 E)15.2
SOLUTION:Pipe A fills 1/30th of the tank in a minute and pipe B, 1/20th. Pipe C empties in 90min
(1/30)+(1/20)-(1/90)=(1/x)
13/180=1/x => x=180/13 => x=13.85 minutes
Answer: D #### D
QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used?
options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7
SOLUTION:Rate of machine R =1/50
Rate of machine S =1/20
since same no of machines used for R and S to do the same work in 5 hrs
So collective rate needed to finish the work in 5 hrs= 1/5
Let the no of machine be x
So, x/50 +x/20 =1/5
(2x+5x)/100=1/5
7x=20
x=20/7
So no of machine R is 20/7
Answer E #### E
QUESTION:In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is-
options: A)42 B)32 C)48 D)28 E)38
SOLUTION:X/63 = 24.
X = 24 *63.
So correct answer would be,
(24 *63) /36 = 42.
ANSWER : A #### A
QUESTION:In how many different ways can the letters of the word "LEADING" be arranged in such a way that the vowels always come together.
options: A)W8 B)789 C)279 D)277 E)191
SOLUTION:Answer:D #### D
QUESTION:The ratio between a two-digit number and the sum of the digits of that
number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number?
options: A)47 B)36 C)58 D)25 E)14
SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3).
Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3.
11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3.
Hence, required number = 11x + 3 = 36.
Answer is B. #### B
QUESTION:The perimeter of one face of a cube is 40 cm. Its volume will be:
options: A)125cm3 B)400cm3 C)250cm3 D)1000cm3 E)None of these
SOLUTION:Explanation:
Edge of cude = 40/4 = 10 cm
Volume = a*a*a = 10*10*10 = 1000 cm cube
Option D #### D
QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required?
options: A)34 B)40 C)68 D)88 E)26
SOLUTION:We have: l = 20 ft and lb = 60 sq. ft.
So, b = 3 ft.
Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft.
ANSWER:E #### E
QUESTION:If (2/3)^n=(3/2)^3, what is the value of n?
options: A)-3 B)-2 C)-1 D)0 E)1
SOLUTION:(2/3)^n = (3/2)^3
= (2/3)^-3
n = -3 (Answer = A) #### A
QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
options: A)7 cm B)6 cm C)4 cm D)3 cm E)9 cm
SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h
= 9 cm
Answer: E #### E
QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51 kmph, find the speed of the stream?
options: A)12 kmph B)13 kmph C)14 kmph D)15 kmph E)17 kmph
SOLUTION:The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 51/3 = 17 kmph
ANSWER:E #### E
QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have?
options: A)27 B)32 C)43 D)54 E)77
SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys
49 - 5 = 44 for Tom and Bob
If distributed equally, each one will have
44 / 2 = 22 toys
Bob has 5 more toys than Tom, so Bob has
22 + 5 = 27 toys
correct answer A #### A
QUESTION:A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English?
options: A)55 B)66 C)77 D)44 E)None of these
SOLUTION:Given student scores 55% marks in english in 8 papers of 100 marks each.
so,his total marks are (55*800)/100 =>440
15% of his 440 marks is 440*(15/100)=>66
so,he scored 66 marks in english.
ANSWER:B #### B
QUESTION:One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met?
options: A)38.07 B)40 C)42 D)39 E)40.07
SOLUTION:Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows
9t + 8(t + 1) = 80
9t + 8t + 8 = 80
17t = 72
T = 4.23 (hours)
Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A. #### A
QUESTION:What is the smallest number which when diminished by 24, is divisible 5, 10, 15 and 20?
options: A)276 B)84 C)88 D)90 E)342
SOLUTION:Required Number
= (LCM of 5, 10, 15 and 20) + 24
= 60 + 24 = 84
Option B #### B
QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $25. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
options: A)9/(25xy) B)xy/225 C)225/(xy) D)225xy E)25xy/9
SOLUTION:The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 25 / (xy/9) = 225/(xy).
The answer is C. #### C
QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share?
options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164
SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) .
x + 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs.145
B #### B
QUESTION:A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 12 multiples of 14, how many multiples of 7 are there in Q?
options: A)20 B)21 C)22 D)23 E)24
SOLUTION:Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 12+11 = 23.
The answer is D. #### D
QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is?
options: A)36.7 B)36.1 C)36.5 D)36.9 E)36.3
SOLUTION:Correct sum
= (36 * 50 + 48 - 23)
= 1825.
Correct mean = 1825/50
= 36.5
Answer:C #### C
QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water?
options: A) 16 B) 72 C) 112 D) 128 E) 144
SOLUTION:Solution:
We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water.
2x + 16x = 162
18x = 162
x = 9
Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water.
Answer E. #### E
QUESTION:Sum of Rs.4000 is given out in 2 pieces, one at 8% S.I. and the other at 10% S.I. If the annual interest is Rs 352, the sum is given at 8% is
options: A)2000 B)2200 C)2300 D)2400 E)None of these
SOLUTION:Explanation :
i) Given the total sum = Rs. 4000
If the sum given at 8% be Rs.a
ie) P = a , n=1, R = 8%
(aX18/100) = (8a/100)
If the addition given at 10% be Rs. 4000 – a
P = 4000-a , n=1, R = 10%
(4000 – aX1X10)/(100) = (40000-10a)/100
Given Annual interest is Rs. 352
(8a/100) + (40000-10a)/100 = 352
8a – 10a = 35200 – 40000
-2a = -4800
X = (4800/2)= Rs.2400/-
Answer : D #### D
QUESTION:Divide $ 1162 among A, B, C in the ratio 35 : 28 : 20.
options: A)490,490,490 B)360,392,460 C)490,382,280 D)260,160,60 E)492,390,280
SOLUTION:Sum of ratio terms = (35 + 28 + 20) = 83.
A's share = $ (1162 x (35/83))= $ 490; B's share = $ (1162 x(28/83))= $. 392;
C's share = $ (1162 x (20/83))= $ 280.
Option C #### C
QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
options: A)288 B)165 C)881 D)1277 E)121
SOLUTION:Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 25 = 375 m.
Let the length of the platform be x m . Then,
(x + 375)/36 = 15 => x = 165 m.
Answer: B #### B
QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
options: A)38 B)41 C)30 D)31 E)29
SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: C #### C
QUESTION:In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A?
options: A)2 B)3 C)5 D)6 E)8
SOLUTION:I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have A=2*3*5*7 = 840
Thus, answer B #### B
QUESTION:Tough and Tricky questions: Word Problems.
If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money Y would he earn per month?
options: A)$700 B)$754 C)$770 D)$782 E)$893
SOLUTION:OFFICIAL SOLUTION:
(C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as:
$812 = 1.16S, where S is his current salary.
Then S = $812/1.16 = $700.
Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be:
Y=$700 + $70 = $770.
The correct answer is choice (C). #### C
QUESTION:Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged?
options: A)6 B)48 C)36 D)24 E)12
SOLUTION:Dhoni have to sit at either of the ends.
If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24
David can also sit on the other end, then another 4! ways we can arrange.
So total number of ways = 24+24 = 48
Answer : B #### B
QUESTION:The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?
options: A)21/55 B)28/55 C)34/55 D)5/8 E)139/220
SOLUTION:Prob of selecting one blue and two green is (4*8*7/12*11*10)
one blue and two green can be arranged in 3!/2! ways
hence the prob becomes 3*4*8*7/12*11*10=28/55
Correct answer is B #### B
QUESTION:Mangala completes a piece of work in 10 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
options: A)8 days B)10 days C)20/3 days D)14 days E)16 days
SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 20/30 = 20/3 days
C) #### C
QUESTION:There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
options: A)300 B)T=400 C)T=500 D)600 E)None of these
SOLUTION:{Managers} = {Female Managers} + {Male Managers};
We are told that the total number of managers in the company is 2/5 of all the employees , thus {Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively.
Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200;
Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500.
Answer: C. #### C
QUESTION:There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?
options: A)36 B)77 C)88 D)99 E)22
SOLUTION:Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1)
Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get
=> 2r = 72 => r = 36.
Answer: A #### A
QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 40 pints of Perfect Pink paint?
options: A)9 B)16 C)21 D)25 1/3 E)28 1/2
SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
40 pints will require 9/17 * 40= 21 pints..
C #### C
QUESTION:The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is
options: A)112 B)22 C)56 D)27 E)35
SOLUTION:Explanation:
Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 16 and 28.
L.C.M. of 16 and 28 = 112.
Answer: Option A #### A
QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water
options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr
SOLUTION:still in water=1/2(98+10)km/hr
=54km/hr
correct option is :B #### B
QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10
SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 5*4*1=20.
P(dispensing one of each color)=20/120=1/6.
The answer is D. #### D
QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years?
options: A)12300 B)12350 C)12100 D)12500 E)12600
SOLUTION:Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 110/100 × 110/100 = 12100
C #### C
QUESTION:John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 : 1/4 : 1/5 . What is the minimum no. of pencils that the person should have?
options: A)65 B)68 C)70 D)77 E)80
SOLUTION:Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.
D) #### D
QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
options: A)109 B)119 C)129 D)139 E)149
SOLUTION:45 + 23 + 15 = 83%
100 – 83 = 17%
700 * 17/100 = 119
The answer is B. #### B
QUESTION:When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ?
options: A)11 B)44 C)24 D)25 E)22
SOLUTION:the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44
0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44.
Only option A-11 satisfies this
for remainder 11,
A=236 and B=25
Ans - D #### D
QUESTION:Calculate the HCF of 64, 318, 250
options: A)6 B)5 C)4 D)3 E)2
SOLUTION:Explanation:
Lets solve this question by factorization method.
64=2 x 2 x 2 x 2 x 2 x 2,
318=2 × 3 × 53,
250=2 × 5 × 5 × 5
So HCF will be minimum term present in all three, i.e.
2×32=18
Answer: Option E #### E
QUESTION:From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
options: A)16 B)24 C)60 D)120 E)150
SOLUTION:Answer=E=150
No of 4 person committees that can be formed=5C2*6C2=150
Answer E #### E
QUESTION:21 goats eat as much as 15 cows. How many goats eat as much as 35 cows?
options: A)49 B)32 C)36 D)41 E)45
SOLUTION:Explanation:
15 cows ≡ 21 goats
1 cow ≡ 21/15 goats
35 cows ≡ 21×35/15 goats
≡ 21×7/3 goats
≡ 7 × 7 goats
≡ 49 goats
Answer: Option A #### A
QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480
SOLUTION:Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 × (1/8) = 400
Answer : Option D #### D
QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train?
options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph
SOLUTION:D = 100 + 250 = 350
T = 7
S = 350/7 * 18/5 = 180 kmph
Answer:D #### D
QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?
options: A)8/35 B)34/35 C)27/35 D)21/32 E)33/35
SOLUTION:Solution:
P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35
ANSWER IS A #### A
QUESTION:What is the units digit of (52^5)(37^3)(71^9)?
options: A)3 B)4 C)6 D)7 E)8
SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2.
The units digit of 37^3 is the units digit of 7^3 which is 3.
The units digit of 71^9 is the units digit of 1^9 which is 1.
The units digit of 2*3*1 is 6.
The answer is C. #### C
QUESTION:Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries?
options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140
SOLUTION:Probability of basket = 3/5
Probability of no basket = 2/5
Required probability=3* 3/5*2/5*2/5
=36/125
A is the answer . #### A
QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
options: A)3630 B)3637 C)3630 D)3631 E)3635
SOLUTION:6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer: A #### A
QUESTION:The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year?
options: A)12300 B)12350 C)12000 D)12500 E)12600
SOLUTION:Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 = 12000
C #### C
QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d?
options: A)2 B)8 C)10 D)11 E)14
SOLUTION:1155 = 3 * 5 * 7 * 11
a = 11
d = 3
a - d = 8
Answer is B #### B
QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
options: A)Rs.6620 B)3378 C)2768 D)2999 E)2771
SOLUTION:A = 20000(11/10) 3
= 26620
= 20000
----------
6620
Answer: A #### A
QUESTION:A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
options: A)22 B)28 C)25 D)82 E)34
SOLUTION:M = 20
S = 5
DS = 20 + 5 = 20.Answer:C #### C
QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
options: A)$5 B)$15 C)$50 D)$100 E)$105
SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
1,000(1.10)^2 = 1,000(1.21) = 1,210
and Lana would have
2,000(1.05)^2 = 2,000(1.1025) = 2,205
Thus, Tim earned 210 dollars, while Lana earned 205 dollars
The difference is $5 and the answer is A. #### A
<<<Examples ends
QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A.
options: A)256 B)388 C)379 D)277 E)122
SOLUTION:Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 672 = 256
Answer: A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec
SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 100 + 280 = 380m.
The time required = d/s = 380/20 = 19 sec.
Answer:E #### E
QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00?
options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00
SOLUTION:For retail price = $25
First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5
Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14
Answer: Option A #### A
QUESTION:A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
options: A)5/7 B)9/14 C)13/21 D)17/28 E)23/35
SOLUTION:P(no red balls) = 6/8*5/7*4/6 = 5/14
P(at least one red ball) = 1 - 5/14 = 9/14
The answer is B. #### B
QUESTION:Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 9 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
options: A)7/4 B)32/9 C)15/4 D)10/3 E)17/5
SOLUTION:Rate(1)=1/6
Rate(2)=1/9
Combined = 5/18
Work done in 2 days=5/9
Work left = 4/9
Rate * Time = Work left
1/8 * Time = 4/9
Time=32/9
B #### B
QUESTION:How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits?
options: A) 48 B) 52 C) 66 D) 68 E) 84
SOLUTION:Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
2 5 5
Number of possibilities = 3*4*4 = 48.
Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52.
Answer: B #### B
QUESTION:A pharmaceutical company received $3 million in royalties on the first $25 million in sales of and then $9 million in royalties on the next $130 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $25 million in sales to the next $130 million in sales?
options: A)8% B)15% C)35% D)42% E)56%
SOLUTION:(9/130)/(3/25) = 15/26 = 57.7% it means that 9/130 represents only 57.7%. Therefore a decrease of 42%.
Answer D #### D
QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction?
options: A)10% B)5% C)12% D)6% E)4%
SOLUTION:In such a case there is always a loss
Loss% = (20/10)^2 = 4%
Answer is E #### E
QUESTION:In the set of positive integers from 1 to 80, what is the sum of all the odd multiples of 5?
options: A)180 B)245 C)320 D)260 E)270
SOLUTION:reduce to 1 - 80
5 - 15 - 25 - 35 - 45--55--65--75 are valid multiples. Add them --> 320
C #### C
QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
options: A)610 B)720 C)825 D)920 E)650
SOLUTION:Explanation:
The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).
Hence we can assume total letters as 5 and all these letters are different.
Number of ways to arrange these letters
=5!=5×4×3×2×1=120=5!=5×4×3×2×1=120
All the 3 vowels (OIA) are different
Number of ways to arrange these vowels among themselves
=3!=3×2×1=6=3!=3×2×1=6
Hence, required number of ways
=120×6=720
ANSWER IS B #### B
QUESTION:If square-root of 15 is 3.87. Then find the value of square-root of (5/3)
options: A)1.29 B)1.39 C)1.49 D)1.59 E)1.69
SOLUTION:=> root 5/ root 3 = (root 5/ root 3)*(root 3/ root 3)
= root 15/ root 9
= 3.87/3
= 1.29
ANSWER:A #### A
QUESTION:hree 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
options: A)1/39 B)1/36 C)1/32 D)1/287 E)1/29
SOLUTION:It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer: B #### B
QUESTION:Tough and Tricky questions: Ratios
1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?
options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5
SOLUTION:let total no. of students be 30
students left on a field trip = 1/5(30) =6
thus 24 students left behind
1/3(24)=8 students did not want to go. thus 16 students want to go on the trip
1/2(16)=8 were able to join the other students on the field trip.
thus total number of students that went on a field trip =6+8 =14
thus required fraction = 14/30 =7/15
C #### C
QUESTION:The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ?
options: A)6 years B)7 years C)8 years D)9 years E)None
SOLUTION:Answer
Let the age of youngest child be y.
so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12
⇒ 4y + 24= 48
∴ y = 6 years
Correct Option: A #### A
QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?
options: A)80.5 B)82 C)81.5 D)85 E)81.25
SOLUTION:Weighted mix method is best here....
Ratio is 1:10 for 88:80.5...
So the answer required = 80.5+ (88-80.5)*1/10=80.5+7.5*1/10
80.5+0.75=81.25
E #### E
QUESTION:Find the greatest number which on dividing 6215 and 7373, leaves a reminder of 23 and 29 respectively
options: A)125 B)127 C)129 D)131 E)144
SOLUTION:Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (6215 - 23) and (7373 -29)
= HCF (6192, 7344) = 144
Option E #### E
QUESTION:A certain Maroon paint contains 70 percent blue pigment and 30 percent red pigment by weight. A certain green paint contains 10 percent blue pigment and 90 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
options: A)1.5 B)2 C)2.5 D)3 E)3.5
SOLUTION:10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.3 =1.5 Grams of red pigment #### A
QUESTION:If one of the followings is the product of the two 3-digit integers 8K5 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be
options: A) 478,823 B) 511,913 C) 531,875 D) 538,424 E) 569,114
SOLUTION:To know the unit digit you can multiply both digit number: 5 x 5 = 25
This eliminates A, B, D, and E, because the number must end with a 5
So the answer is C #### C
QUESTION:What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
options: A)20(2/3)% B)20% C)21% D)22(2/3)% E)None of these
SOLUTION:Explanation :
Total numbers = 70
Total numbers in 1 to 70 which has 1 in the unit digit = 7
Total numbers in 1 to 70 which has 9 in the unit digit = 7
Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14
Required percentage = (14/70) × 100 = 140/7 = 20%
Answer : Option B #### B
QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
options: A)150 B)152 C)154 D)158 E)144
SOLUTION:D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158 #### D
QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour?
options: A)181 B)211 C)241 D)271 E)301
SOLUTION:In 2/5 of an hour there are 24*60 = 1440 seconds
The number of 6-second intervals = 1440/6 = 240
After the first flash, there will be 240 more flashes for a total of 241.
The answer is C. #### C
QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water?
options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3
SOLUTION:G = 10W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
10W+5Wx = x+1 * 6W
10+5x = 6(x+1)
x = 4
Ratio of gold with copper = 1:4 = 1:4
Answer is B #### B
QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9
SOLUTION:72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B #### B
QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct?
options: A)120 B)130 C)110 D)150 E)180
SOLUTION:let x be the correct answer and y be the wrong answer
so the total number of questions is (x+y)=150
=>4x-2y=480
=>6x=780
hence x=130
ANSWER:B #### B
QUESTION:What is the area of a square field whose diagonal of length 12 m?
options: A)288 B)72 C)200 D)112 E)178
SOLUTION:d2/2 = (12 * 12)/2
= 72
Answer: B #### B
QUESTION:A machine P completes a certain amount of work in 12 hrs and machine Q completes the same work in x hrs if both machines works together to complete the same work in 8 hrs then what is x?
options: A)12 hrs B)18 hrs C)24 hrs D)32 hrs E)34 hrs
SOLUTION:Explanation:
P’s 1hr work = 1/12
Q’s 1 hr work = 1/x
(A+B)’s 1 hr work = 1/8 = 1/12+1/x
=> x = 24 hrs
Answer: Option C #### C
QUESTION:Convert 50miles into yards?
options: A)25630 yards B)35200 yards C)88000 yards D)42560 yards E)41520 yards
SOLUTION:1 mile = 1760 yards
50 miles = 50*1760 = 88000 yards
Answer is C #### C
QUESTION:Pomes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
options: A)40 minutes. B)1 hour and 30 minutes. C)1 hour. D)1 hour and 40 minutes. E)2 hours and 15 minutes.
SOLUTION:Rate =Output/Time
Pomes Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min #### C
QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is?
options: A)39yr B)42yr C)45yr D)32yr E)50yr
SOLUTION:Let B's present age = x years
Then A's present age = x+9 years
x+9+10 = 2(x-10)
x + 19 = 2x - 20
x = 39years
Answer is A #### A
QUESTION:A university cafeteria offers 1 flavors of pizza - pepperoni. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
options: A)4 B)8 C)12 D)1 E)32
SOLUTION:1 flavours * 1 choices = 1C1*1C1 = 1*1=1=D #### D
QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
options: A)8 B)9 C)6 D)5 E)1
SOLUTION:2x * x = 128 => x
= 8
Answer:A #### A
QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ?
options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these
SOLUTION:Explanation:
Part filled by A in 1 hour = 1/6
Part filled by B in 1 hour = 1/18
Part filled by C in 1 hour = 1/36
Part filled by (A+B+C) in 1 hour =
1/6+1/18+1/36=9/36
So all pipes will fill the tank in 4 hours.
Option C #### C
QUESTION:The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages.
options: A)20,35,45 B)8,20,28 C)16,28,36 D)16,28,46 E)None of these
SOLUTION:Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 76
20K = 100
K = 5
Therefore, then present ages are 20,35,45.
ANSWER:A #### A
QUESTION:The number 0.8 is how much greater than 1/2 ?
options: A)½ B)3/10 C)1/50 D)1/500 E)2/500
SOLUTION:let x be the difference
then
.8-1/2=x
8/10-1/2=x
x= 3/10
ans B #### B
QUESTION:A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
options: A)32 B)55 C)6 D)78 E)81
SOLUTION:S = (100 + 300)/45 = 400/45 * 18/5
= 32
Answer: A #### A
QUESTION:9886 + x = 13200, then x is ?
options: A)3327 B)3237 C)3337 D)2337 E)None of these
SOLUTION:Answer
x = 13200 - 9886 = 3314
Option: E #### E
QUESTION:One type of liquid contains 10% of water and the second type of liquid contains 15% of water. A glass is filled with 5 parts of 1st liquid and 2 parts of 2nd liquid. The percentage of water in the new mixture in the glass is?
options: A)5.6% B)11.4% C)15.6% D)21.3% E)18.9%
SOLUTION:Required percentage = (10% of 5 + 15% of 2)/5+2 *100
= 0.8/7 * 100 = 11.4%
Answer is B #### B
QUESTION:Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
options: A)9 B)10 C)12 D)20 E)8
SOLUTION:Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =(9/54x 60)min = 10 min.
Answer :B #### B
QUESTION:A,B and C started a business by investing Rs.800/- , Rs.1,000/- and Rs.1,200/- respectively for two years.
Total profit is Rs.1000/-. Find the C's share?
options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 800 E)Rs. 900
SOLUTION:Solution: A : B : C = (800 * 2) : (1,000 * 2) : (12,000 * 2) = 4 : 5 : 6.
So C's share = Rs. (1000 * 6/15) = Rs. 400.
Answer: Option C #### C
QUESTION:Which of the following is satisfied with |x-4|+|x-3|<6?
options: A)1<x<5 B)2<x<5 C)0.5<x<6.5 D)0.5<x<4 E)3<x<4
SOLUTION:--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5
Therefore, the answer is C. #### C
QUESTION:If Aaron is now twice as old as Bailey was 5 years ago, and B is Bailey's current age in years, which of the following represents the sum of Aaron and Bailey's ages 4 years from now?
options: A)3B B)3B-1 C)3B-21 D)3B-11 E)3B-2
SOLUTION:B is Bailey's current age.
Let Aaron's current age be A.
given A = 2(B-5).
four years from now Aaron's age will be = 2(B-5) + 4 = 2B-6
four years from now Bailey's age will be = B+4
Sum of ages of Mason and Gunther's after 4 years = 2B-6+B+4 = 3B-2
Ans : E #### E
QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is?
options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5
SOLUTION:36 * 5/18 = 12.5
20:25 => 4:5
Answer: E #### E
QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
options: A)76 B)55 C)44 D)12 E)91
SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1}
From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12.
Answer:D #### D
QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre?
options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6
SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8 Ratio of water and milk = 4 : 8 = 1 : 2
Answer:B #### B
QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is
options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12
SOLUTION:Explanation:
Given numbers are 1.08 , 0.42 and 0.90
H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F]
therefore H.C.F of given numbers = 0.06
Answer: C) #### C
QUESTION:In a throw of dice what is the probability of getting number greater than 5
options: A)1/7 B)1/6 C)1/11 D)1/13 E)2/9
SOLUTION:Number greater than 5 is 6, so only 1 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 1/6
B) #### B
QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number R of different possible seating arrangements for the group?
options: A)5 B)10 C)24 D)32 E)120
SOLUTION:Circular arrangements= (n-1)!
Hence (4!) = 24=R
Answer is C #### C
QUESTION:What should come in place of the question mark (?) in the following equation?
45789+ 34567 = 610+ ?
options: A)96543 B)13678 C)23456 D)56789 E)79746
SOLUTION:45789+ 34567 = 610+ ?
45789+ 34567 – 610 = 79746
Answer E #### E
QUESTION:The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes?
options: A)5! B)10!/(5!5!) C)10!/5! D)10! E)10!*5!
SOLUTION:Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations R of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B #### B
QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:
options: A)276 B)299 C)322 D)345 E)395
SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12).
Larger number = (23 x 12) = 276.
Answer: Option A #### A
QUESTION:If points A and B are (6-1) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
options: A)I only B)II only C)III only D)I and II only E)I and III only
SOLUTION:I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A. #### A
QUESTION:One-third of 1200 is what percent of 236 ?
options: A)169.49 B)30 C)120.32 D)125.32 E)15.152
SOLUTION:Answer
Let one-third of 1200 is N% of 236.
∵ 1200/3 = (N x 236)/100
∴ N = (400 x 100) / 236= 169.49
Correct Option: A #### A
QUESTION:A contractor undertook to finish a job in 150 days and employed 200 men. After 50 days he found that only 1/4 of work was finished. How many extra days are needed if he employs 50 more men?
options: A)20 B)25 C)30 D)35 E)45
SOLUTION:work part A=25% and work part B= 75%
25% work done by 200 people in 50 days
if only one employee works then he takes 200*50=10000 days
and if work(B) is triple more ten he will take =10000*3 =30000 days
if employees are 250 then days = 30000/250=120days
then total days = 50+120 = 170 days
how many extra days taken = 170-150 = 20 days
ANSWER:A #### A
QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0
options: A)-1 B)1 C)2 D)3 E)4
SOLUTION:a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A #### A
QUESTION:If a and b are positive integers of C such that a/b=2.86, which of the following must be a divisor of a?
options: A)10 B)B.13 C)18 D)26 E)50
SOLUTION:The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).
The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 143
B = 50
143/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Final Answer:
B #### B
QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples?
options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24
SOLUTION:The cost of one apple=20/12=1.67
The cost of twenty apples= 1.67x20= $ 33.33
Answer: B #### B
QUESTION:Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed?
options: A)10 pm B)1 pm C)2 pm D)3 pm E)4 pm
SOLUTION:Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the Printer were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm
B #### B
QUESTION:Yesterday's closing prices of 2,640 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
options: A) 484 B) 726 C) 1,100 D) 1,320 E) 1,440
SOLUTION:Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 2640 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1)(2) to get H = 1440.
E is my answer. #### E
QUESTION:The area of a triangle is with base 18m and height 6m?
options: A)88 m2 B)10 m2 C)66 m2 D)54 m2 E)31 m2
SOLUTION:1/2 * 18 * 6 = 54 m2
Answer: D #### D
QUESTION:If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/10
II. 1/9
III. 1/11
options: A)None B)I only C)III only D)II and III only E)I, II, and III
SOLUTION:Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us B as the only possible answer. #### B
QUESTION:A bat is bought for Rs.400 and sold at a gain of 30% find its selling price?
options: A)s.460/- B)s.480/- C)s.500/- D)s.520/- E)s.540/-
SOLUTION:100 % ------> 400 (100 * 4 = 400)
130 % ------> 520 (130 * 4 = 520)
Selling price = Rs.520/-
Option 'D' #### D
QUESTION:In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 2/3 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight
options: A)1/6 B)1/8 C)1/4 D)3/4 E)7/8
SOLUTION:Good question.
So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).
we're told that 2/3 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/3 are yellow. We're also told there is an equal probability of straight or curved, 1/2.
We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).
So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 1/3 * 1/2 = 1/6, or A. #### A
QUESTION:For how many integers n is 1^n+2 = (n+2)^1?
options: A)0 B)1 C)2 D)None of these E)3
SOLUTION:If n=0
1^0+2 = (0+2)^1
1^2 = 1 ; 2^1 =2 not ok
If n=1
1^1+2 =1 ; (1+2)^1=3^1=3 not OK
So, Answer : D #### D
QUESTION:A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
options: A)155 m B)150 m C)187 m D)177 m E)186 m
SOLUTION:Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y
= x/15
(x + 100)/25
= x/15
=> x = 150 m.
Answer: B #### B
QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.
options: A)12sec B)20sec C)15sec D)18sec E)10sec
SOLUTION:Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec
Answer : E #### E
<<<Examples ends
QUESTION:One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
options: A)4 B)6 C)0 D)9 E)19
SOLUTION:Answer: Option D
x/2 – x/3 = 6 => x =6
3 + 6 = 9 #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is:
options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these
SOLUTION:Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (45 x 2) = 90 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv)
Subtracting (i) from (iv), we get : B = 35.
B’s weight = 35 kg.
Answer: D #### D
QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680?
options: A)1500 B)2777 C)2889 D)27670 E)2771
SOLUTION:1680 = P [1 + (5*12/5)/100]
P= 1500.Answer:A #### A
QUESTION:The H.C.F. of two numbers is 12 and their difference is 12. The numbers are :
options: A)66, 78 B)70, 82 C)94, 106 D)84, 96 E)None of these
SOLUTION:Explanation:
Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96.
ANSWER IS D #### D
QUESTION:Imagine John has 2 blue balls, 3 green balls, 1 black ball and 4 red balls. How many ways can he arrange the balls lining them up?
options: A)10!/(2!)2 1! B)10!/2! 1! 3! 1! C)10!/4! 4! D)9!/4! 3! 2! E)10!/4! 3! 2!
SOLUTION:n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
John has 10 balls which are 4 red balls, 3 green balls, 2 blue balls and 1 black ball.
Number of arrangements = 9!/(2!)2 3!
Answer: E #### E
QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is?
options: A)1 B)4 C)5 D)6 E)7
SOLUTION:4.5 4.5
45% 55%
45% ----- 4.5
55% ------? => 5.5 - 4.5 = 1 ml
ANSWER:A #### A
QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
options: A)47/5 B)13 C)17 D)21 E)23
SOLUTION:Let A contains A, B contains B liters
so, (A-4)/(B+4)= 1/3.......(1)
again, (B-5)/(A+5)= 1/2..........(2)
from (1)(2) we find A= 47/5
ans: (A) #### A
QUESTION:Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 249 marks in the second test and failed by 66 marks in that test. Find the pass mark in the first test?
options: A)768 B)243 C)246 D)280 E)224
SOLUTION:Let the maximum mark in each test be M.
The candidate failed by 66 marks in the second test.
pass mark in the second test = 249 + 66 = 315
45/100 M = 315
Pass mark in the first test = 40/100 M = 40/45 * 315 = 280.
Answer:D #### D
QUESTION:A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 550 ?
options: A)249 B)498 C)676 D)823 E)274
SOLUTION:slope of 2 and a y-intercept of 2
y-coordinate is 550
y = 2x + 2
548 = 2x
x = 274
Answer:
E. 274 #### E
QUESTION:Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48.
options: A)240/1587 B)240/1545 C)240/1547 D)240/1542 E)240/1512
SOLUTION:P : 2/13 = 5/34 : 7/48
As the product of the means is equal to the product of the extremes.
P*7/48 = 2/13 * 5/34
P*7/48 = 10/442
P = 480/3094 => P = 240/1547
Answer: C #### C
QUESTION:Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side?
options: A)20,25 B)21,25 C)27,23 D)28,25 E)30,25
SOLUTION:Let the two parallel sides of the trapezium be a cm and b cm.
Then, a-b = 4 ------ (1)
And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2)
Solving 1 and 2, we get: a=27,b=23
So, the two parallel sides are 27 cm and 23 cm.
C #### C
QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
options: A)42 6/9% B)42 3/7% C)42 7/7% D)42 6/7% E)22 6/7%
SOLUTION:SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D #### D
QUESTION:A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is:
options: A)90 cm B)6 dm C)1 m D)1.1 cm E)None of these
SOLUTION:Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (160 - x)] = 8000 × 1000
=> 320 × 250 × (160 - x) = 8000 × 1000
=> (160 - x) = 8000×1000/320=
100
=> x = 60 cm = 6 dm.
Answer: B #### B
QUESTION:The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares
options: A)22 cm B)24 cm C)26 cm D)28 cm E)None of these
SOLUTION:Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 10*10 - 8*8
= 36 cm
So side of third square = 6 [because area of square = side*side]
Perimeter = 4*Side = 4*6 = 24 cm
Option B #### B
QUESTION:In how many ways can the letters of the word CAVERN be arranged in a row so that the vowels appear in alphabetic order?
options: A)360 B)720 C)620 D)180 E)36
SOLUTION:Two letters can be arranged in 2! ways.
only one combination EIU is required.
6 letters can be arranged in 6! ways.
thus 6!/ 2! * 1 = 360.
A #### A
QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long?
options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec
SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec
time = (360+140)/25/2
= 500*2/25
=40sec
ANSWER:A #### A
QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES
SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 .
Number of pages typed by Kumar in 1 hour = 40/5 = 8.
Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 .
Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours
= 8 hours 15 minutes. ANSWER : E #### E
QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce
options: A)100 B)65 C)25 D)11 E)18
SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 10
So, x = 10.
Hence 6x = 6*10 = 60 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/60
= 18
Hence option (E). #### E
QUESTION:If p is the product of the integers from 1 to 38, inclusive, what is the greatest integer k for which 3^k is a factor of p?
options: A)13 B)15 C)17 D)19 E)21
SOLUTION:38! has 3, 6, 9,....30, 33, 36 as factors, which are 12 multiples of 3.
We need to add 5 more to these 12 because of 9, 18, 27, and 36.
The greatest integer of k is 17.
The answer is C. #### C
QUESTION:The digit in unit's place of the product 81 ×82×.....×89 is
options: A)0 B)2 C)6 D)8 E)4
SOLUTION:Solution
Required digit = Unit digit
=(1×2×3×4×5×6×7×8×9) =0.
Answer A #### A
QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full?
options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes
SOLUTION:1/20 - 1/40 = 1/40
40 minutes
Answer:C #### C
QUESTION:A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?
options: A)80 B)288 C)4^4 D)576 E)288^2
SOLUTION:The condition that TWO boys or TWO girls cannot be together means they should be alternate..
Total five means 3 of one and 2 of other..
1) choose 3 girls and arrange them... 4C3*3! = 4!= 24
2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C2*2!= 12
Total ways = 24*12 = 288..
2) same as above.. 2 girls and 3 boys.. 288
Total 288*2=576
ANS:D #### D
QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen?
options: A)6 B)24 C)36 D)66 E)72
SOLUTION:Try using the formula for combinations:
n!/r!(n-r)!
12!/2!(12-2)!
12!/2!*10!
12*11/2*1
=66
ANSWER:D #### D
QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856
SOLUTION:(900*3*3)/100 = 81
920 + 81 = 1001
ANSWER:B #### B
QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 7 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
options: A)0.07 B)0.049 C)0.7 D)0.49 E)4.9
SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*49*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 490/10,000 = 49/1000 = 0.049 ft
The answer is B. #### B
QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None
SOLUTION:Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1250 x 2/5) = Sterling 500.
Answer: Option C #### C
QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm
SOLUTION:33 + 43 + 53 = a3 => a = 6
ANSWER:D #### D
QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
options: A)12 B)15 C)16 D)18 E)14
SOLUTION:Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
10 +8 - 4 = 14
E) #### E
QUESTION:Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3
SOLUTION:26^2+26^3 = 26^2(1+26)=27*26^2
The answer is C. #### C
QUESTION:At what rate of interest is an amount doubled in two years, when compounded annually?
options: A)41.4% B)43.4% C)31.4% D)30% E)21.4%
SOLUTION:Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4%
ANSWER:A #### A
QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long?
options: A)65sec B)70sec C)74sec D)80sec E)85sec
SOLUTION:Speed = 240/24 = 10 m/sec.
Required time = (240 + 500)/10 = 74 sec.
Answer:C #### C
QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu?
options: A)10 B)20 C)40 D)80 E)100
SOLUTION:Q=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C #### C
QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
options: A)15 kmph B)10 kmph C)12 kmph D)12.5 kmph E)None of these
SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
ANSWER:D #### D
QUESTION:If you are given $5, and the amount doubles every day, how much money will you have after 4 days?
options: A)$256 B)$512 C)$1024 D)$625 E)$720
SOLUTION:5^4=625
The answer is D #### D
QUESTION:A, B and C enter into a partnership. They invest Rs. 70,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
options: A)21 : 32 : 4 B)21 : 26 : 4 C)21: 12 : 1 D)21: 16 : 28 E)none
SOLUTION:Sol.
A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =252 : 192 : 336 = 21: 16 : 28
Answer D #### D
QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
options: A)Rs. 4980 B)Rs. 4991 C)Rs. 4996 D)Rs. 4997 E)Rs. 5000
SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
B) #### B
QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet?
options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge
SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location.
In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle.
Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate.
The correct answer is (E). #### E
QUESTION:If two letters are chosen at random (without replacement) from the word COMPUTER, what is the probability that none of the letters are vowels?
options: A)2/7 B)3/7 C)3/14 D)5/14 E)11/28
SOLUTION:The number of ways to choose two letters is 8C2 = 28
The number of ways to choose two consonants is 5C2 = 10.
P(no vowels) = 10/28 = 5/14
The answer is D. #### D
QUESTION:A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings?
options: A)16 B)56 C)112 D)28 E)38
SOLUTION:In 8 different toppings, selecting 2 diff toppings = 8c2
formula is n!/(n-c)!
n = total number of toppings
C = number chosen in a grouping.
n=8 and c=2 so we get
8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1)
= 8*7 =56
ANSWER:B #### B
QUESTION:At what rate percent per annum will a sum of money double in 16years?
options: A)10.6% B)3.65% C)6.25% D)8.32% E)11%
SOLUTION:Let principle = P
S.I. = P
T = 16yrs
Rate = 100*P/P*16 = 25/4% = 6.25%
Answer is C #### C
QUESTION:In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?
options: A)25 B)30 C)45 D)20 E)50
SOLUTION:6p2 = 6 x 5 = 30
B) #### B
QUESTION:if (p/q)-(q/p)=21/10
then what ia the value of(4p/q)+(4q/p)
options: A)58/5 B)59/5 C)121/105 D)101/105 E)1/2
SOLUTION:p/q =a then q/p = 1/a
a+1/a=21/10
by solving this we get a=5/2
then 4*5/2+4*2/5 = 58/5
ANSWER:A #### A
QUESTION:Find the perimetri of trapezium with sides 4,6,12 and distance between two parallel side is 3.
options: A)27 B)26 C)28 D)25 E)24
SOLUTION:1/2*(6+12)*3=27
ANSWER:A #### A
QUESTION:Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 18 hours. If all the three pipes are opened together, then the tank will be filled in?
options: A)3 9/97 hrs B)4 2/4 hrs C)3 9/17 hrs D)3 9/27 hrs E)3 9/19 hrs
SOLUTION:Net part filled in 1 hour = 1/9 + 1/6 - 1/18
= 4/18
The tank will be full in 18/4 hrs, i.e., 4 2/4 hrs.
Answer:B #### B
QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water?
options: A) 16 B) 72 C) 112 D) 128 E) 144
SOLUTION:Solution:
We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water.
2x + 16x = 162
18x = 162
x = 9
Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water.
Answer E. #### E
QUESTION:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 100 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
options: A)250 B)300 C)350 D)400 E)500
SOLUTION:Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.
Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 100 meters, thus the circumference is 200 + 100 = 300 meters.
Answer: B. #### B
QUESTION:864.942 - ? + 45.76 = 547.905
options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these
SOLUTION:Explanation:
362.797
Answer: Option D #### D
QUESTION:In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers?
options: A)26 B)27 C)28 D)29 E)30
SOLUTION:8/7 * 24 = 27.4
The answer is B. #### B
QUESTION:1.5, 2.3, 3.1, 3.9, ..?
options: A)0.6 B)0.8 C)0.4 D)0.24 E)0.15
SOLUTION:1.5+0.8=2.3
2.3+0.8=3.1
3.1+0.8=3.9
3.9+0.8=4.7
ANSWER:B #### B
QUESTION:In the first 12 overs of a cricket game, the run rate was only 4.5. What should be the run rate in the remaining 38 overs to reach the target of 360 runs?
options: A)9.55 B)6.25 C)6.75 D)8.05 E)7.25
SOLUTION:Required run rate = 360 - (4.5 x 12) /38 = 306/38 = 8.05 Option D #### D
QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110
SOLUTION:A+B+C = 400
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 400
----------------
C = 150
Answer:A #### A
QUESTION:The value of (34.31*0.473*1.5)/(0.0673*23.25*7.57) is close to
options: A)2 B)1.15 C)2.01 D)2.06 E)2.35
SOLUTION:(34.31*0.473*1.5)/(0.0673*23.25*7.57) = 24.343/11.845
= 2.06
ANSWER:D #### D
QUESTION:At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes?
options: A)2150 B)2600 C)3120 D)1500 E)1895
SOLUTION:Winner votes = 100-30 = 70
polled votes = [(100*1000)/2*70-100]+100 = 2600
Answer is B #### B
QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red?
options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15
SOLUTION:P(Both are red),
=6C213C2=6C213C2
=5/26
C #### C
QUESTION:If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips?
options: A)1/4 B)1/8 C)1/2 D)1/16 E)1/32
SOLUTION:(1/2) * (1/2) * (1/2) * (1/2) = 1/16 Answer: D #### D
QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages.
options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these
SOLUTION:Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 136
20x = 160 => x = 8
Their present ages are 32, 56 and 72 years respectively.
ANSWER:D #### D
QUESTION:The price for a loaf of bread in April was $1.20, in May the price was $1.27, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period?
options: A)$1.18 B)$1.17 C)$1.16 D)$1.15 E)$1.14
SOLUTION:Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(120) + 127x + (4x/3)(108) / (2x/3 + x + 4x/3) =
(80 + 127 + 144) / (3) = 351/3 = $1.17
The answer is B. #### B
QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer
SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/10 * 480 =48
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 48-68 =20>>> therfore answer is 20 greater
A #### A
QUESTION:In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
options: A)12 Years B)12.6 Years C)13.6 Years D)14 Years E)14.5 Years
SOLUTION:Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years \
B #### B
QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
options: A)18 cm B)20 cm C)22 cm D)24 cm E)26 cm
SOLUTION:2(l + b) = 5
b 1
2l + 2b = 5b
3b = 2l
b = 2 l
3
Then, Area = 216 cm2
l x b = 216
l x 2 l = 216
3
l2 = 324
l = 18 cm.
A) #### A
QUESTION:A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5760. What is the average monthly balance maintained by John in his
account during the year?
options: A) 2840 B) 28800 C) 6840 D) 7540 E) 28400
SOLUTION:bank balance is doubled with accumulation of interest tp 5760..
this means INTEREST is 5760/2=2880 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 28800..
B #### B
QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively
options: A)19 B)17 C)13 D)9 E)18
SOLUTION:Explanation:
Answer will be HCF of (28-10, 128-2, 147-3)
HCF of (18, 126, 144) = 18
Option E #### E
QUESTION:Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.90?
options: A)426 B)430 C)443 D)480 E)486
SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 7.9$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.9 $ left. so we buy 1 pack of 50 for 1$. We now have 0.9$ left, so we buy 30 individual envelopes. If we add up the numbers, we get 400+50+30=480 envelopes. Answer D #### D
QUESTION:The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?
options: A)40 B)42 C)45 D)48 E)54
SOLUTION:1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
Thus for the 5th year = 50,
6th year = 50-5 = 45.
The correct answer is C. #### C
QUESTION:Which of the following is a prime number
options: A)9 B)2 C)4 D)8 E)7
SOLUTION:Explanation:
A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself.
So from above options 2 is that number
Option B #### B
<<<Examples ends
QUESTION:What is the area of a square field whose diagonal of length 20 m?
options: A)10 sq m B)200 sq m C)400 sq m D)500 sq m E)156 sq m
SOLUTION:Explanation:
d^2/2 = (20 * 20)/2 = 200 sq m
Answer : B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations?
options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10
SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others
C #### C
QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
options: A)150 B)152 C)154 D)158 E)144
SOLUTION:D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158 #### D
QUESTION:3889 + 13.952 - ? = 3854.002
options: A)48.95 B)49.75 C)45.97 D)47.59 E)45.79
SOLUTION:Let 3889 + 13.952 - x = 3854.002.
Then x = (3889 + 13.952) - 3854.002
= 3902.952 - 3854.002
= 48.95.
Answer is A #### A
QUESTION:The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number
options: A)400 B)256 C)120 D)490 E)None of these
SOLUTION:Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 14 * 5040
x = (14*5040)/144 = 490
Option D #### D
QUESTION:If n is the product of 3 consecutive integers, which of the following must be true about n?
I. n is a multiple of 2
II. n is a multiple of 3
III. n is a multiple of 4
options: A)I only B)II only C)III only D)I and II E)II and III
SOLUTION:n is the product of 3 consecutive integers.
So, according to the rule, n must be divisible by 3, 2 and 1
So, we already know that statements I and II must be true.
Do we need to check statement III? No.
Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D. #### D
QUESTION:What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21?
options: A)2327 B)2757 C)3147 D)3587 E)3997
SOLUTION:When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150
The answer is C. #### C
QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible?
options: A)90 B)79 C)64 D)57 E)36
SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible.
Total Options: 64
Final Answer:
C #### C
QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players?
options: A)45 B)56 C)64 D)78 E)90
SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players.
=> Required number of ways = 13C11
= 78
D #### D
QUESTION:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
options: A) 6x B) 4x C) 5x/3 D) 3x/2 E) 3x/5
SOLUTION:Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<D<5x --> only option B fits.
Answer: B. #### B
QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers?
options: A)1 B)5 C)7 D)8 E)9
SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6
y = mx + b => 12 2/3 = -22*5/6 + b => b = 31
y = -5x/6 + 31
Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point.
A #### A
QUESTION:If the height of a right cone C is 3 and the diameter of the base of C is 8, what is the distance from the apex of C to any point on the circumference of the base of C?
options: A)3√2 B)5 C)5√2 D)√(67) E)√(73)
SOLUTION:height of cone=3
radius of base=4
so the distance from the apex of C to any point on the circumference of the base of C will be a right angled triangle
Hence the distance is sqrt(3^2+4^2)= 5
ANSWER:B #### B
QUESTION:Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
options: A)$40,000 B)$56,000 C)$64,000 D)$66,667 E)$80,000
SOLUTION:Equation is correct, so math must be a problem.
0.12*40,000+0.2*(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000.
Answer: B. #### B
QUESTION:A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
options: A)(320 - y)/(5x) B)(y +220)/(5x) C)5(80 - y)/(4x) D)(y + 400)/(4x) E)(4y + 320)/(5x)
SOLUTION:Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20 = 65 houses per week
total time they took = (40/20) + (40/65) = 2.6 weeks
Putting the values of x and y in equation B
(y +220)/(5x) = (40+220)/5*20 = 260/100 = 2.6 #### B
QUESTION:The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds?
options: A)4 B)9 C)39 D)48 E)63
SOLUTION:Given: z=s^2+2s for 0≤s≤7
z(4) = 4^2 + 2*4 = 24
z(7) = 7^2 + 2*7 = 63
Therefore z(7) - z(3) = 63 - 24 = 39 km/hr
Option C #### C
QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
options: A)90. B)45. C)50. D)40. E)25.
SOLUTION:STREET-CAT DOMESTIC-Cat
70 130
(25gray+45other) 85gray+45other
Answer:B #### B
QUESTION:On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 60% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?
options: A)10.5% B)12.5% C)15% D)25% E)30%
SOLUTION:suppose there are X motorists.
10% of them exceeded the speed limit and received the ticket, i.e. X/10.
Again, suppose total no. of motorists who exceeded the speed limit are Y.
60% of Y exceeded the speed limit but didn't received the ticket, i.e. 3Y/5.
it means 2Y/5 received the ticket.
hence, 2Y/5 = X/10
or Y/X=1/4
or Y/X * 100= 1/4 * 100= 25%
D #### D
QUESTION:A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%?
options: A)7 B)6 C)5 D)9 E)8
SOLUTION:C
5
C.P. of 6 toffees = $ 1
S.P. of 6 toffees = 120% of $ 1 = $ 6/5
For $ 6/5, toffees sold = 6. For $ 1.
Toffees sold = 6 * 5/6 = 5 #### C
QUESTION:Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit?
options: A)1% B)2% C)3% D)4% E)5%
SOLUTION:A dozen toys cost $360, so each toy cost $30.
selling price / cost price = 30.60 / 30 = 1.02
The percentage profit is 2%.
The answer is B. #### B
QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11
SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10
Answer: D #### D
QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5
options: A)45 B)20 C)25 D)27 E)22
SOLUTION:Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5 = 20.
Answer:B #### B
QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face.
options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114
SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C #### C
QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate?
options: A)576 B)425 C)215 D)321 E)None of these
SOLUTION:Explanation :
In a circle, 5 boys can be arranged in 4! ways
Given that the boys and the girls alternate.
Hence there are 4 places for girls which can be arranged in 4! ways
Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A
QUESTION:There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?
options: A)15 B)30 C)120 D)240 E)256
SOLUTION:Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence C. #### C
QUESTION:Bob finishes the first half of an exam in one-thirds the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?
options: A)20 B)24 C)27 D)30 E)40
SOLUTION:Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/3's the time of the second half (3/3's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 1:5 and the second half is 3:5). With each fifth of an hour being 15 minutes (60/4), the first half of the exam would have taken 30 minutes. Correct answer is D. #### D
QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is?
options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m
SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
E #### E
QUESTION:What is the total surface area in square meters of a rectangular solid whose length is 9 meters, width is 8 meters, and depth is 5 meters?
options: A)152 m2 B)162 m2 C)180 m2 D)300 m2 E)314 m2
SOLUTION:Surface Area of a cuboid = 2(lb+bh+lh) = 2(9*8+8*5+9*5)=2(72+40+45)=2*157=314 m2
Answer : E #### E
QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least?
options: A)John B)Susan C)Sam D)Mark E)Lynn
SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 160% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.6*J)=0.8*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John.
Answer: B. #### B
QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make?
options: A)30% B)75% C)40% D)70% E)None of these
SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150
Profit(%) = (31150 - 17800)/17800* 100 = 75%
ANSWER:B #### B
QUESTION:A can do a piece of work in 13 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
options: A)15 10/11 days B)10 10/11 days C)12 10/11 days D)19 10/11 days E)13 10/11 days
SOLUTION:B
(x – 5)/13 + x/20 = 1
x = 10 10/11 days #### B
QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 2x+ 2y > 2z
III. yz > xz
IV. xy > y + z
options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only
SOLUTION:we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 2x+ 2y > 2z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B #### B
QUESTION:A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?
options: A)11:10:15 B)20:17:23 C)19:19:18 D)5:4:9 E)None of these
SOLUTION:Explanation:
A:B:CA:B:C =(25 lakhs××1)+(35 lakhs××2) :(35 lakhs××2+25 lakhs××1) :(30 lakhs××3)
= 95 lakhs : 95 lakhs : 90 lakhs =19:19:18=19:19:18.
ANSWER IS C #### C
QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream?
options: A)15 B)17 C)19 D)18 E)16
SOLUTION:The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 57/3 = 19 kmph.
Answer:C #### C
QUESTION:If p/q =4/5, then the value of 1/7 + {(2q - p) / (2q + p)} is ?
options: A)4 / 7 B)34 C)1 D)2 E)3
SOLUTION:Answer
Given Exp. = 4 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 1/7 + {2-p/q) / (2 + p/q)}
= 1/7 + {(2 - 4/5) / (2 + 4/5)}
= 1/7 + 6/14
= 1/7 + 3/7
=4/7
Correct Option: A #### A
QUESTION:A trade analyst announced 15% reduction in the unit price of bike. As a result, the sales volume went up by 15%. What was the net effect on the sales revenue?
options: A)no change B)decreases by 6.5% C)increases by 6.5% D)increases by 5.6% E)None of these
SOLUTION:Explanation :
Reduction of price = (100 -15)% = 85% = 0.85
Increase of sale = (100+15)% = 115% = 1.15
Total effect = 0.85 X 1.15 = 93.5%, Decreases by 6.5%
Answer :B #### B
QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
options: A)3002 B)3000 C)3018 D)3019 E)3012
SOLUTION:60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer: B #### B
QUESTION:From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond?
options: A)238/5525 B)176/5534 C)253/5523 D)234/5525 E)1/5525
SOLUTION:Solution
Let S be the sample space. Then,
n(S) = 52C3 = 22100
Let E = event of getting 1 face card.
n(E) = number of ways of choosing 1 face card out of 26
=13C1 * 13C2= 13*72 = 936
P(E) = n(E) / n(S) = 936 / 22100 = 234/5525
= 234/5525.
Answer D #### D
QUESTION:If n is a positive integer, then n(n+1)(n+2) is even without any condition
options: A)divisible by 3 only when n is odd B)divisible by 4 whenever n is even C)odd whenever n is odd D)even only when n is odd E)even only when n is even
SOLUTION:n*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 6,7&8)
B #### B
QUESTION:Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase?
options: A)3 B)4 C)6 D)9 E)10
SOLUTION:We have 5, 10, 10 and 20 to work with
From least to greatest, we have...
5 (the least)
10
15
20
25
30
35
40
45 (the greatest)
Total options = 9
Final Answer:D #### D
QUESTION:A car covers a distance of 630 km in 6 ½ hours. Find its speed?
options: A)105 kmph B)176 kmph C)298 kmph D)186 kmph E)268 kmph
SOLUTION:630/6
= 105 kmph
Answer:A #### A
QUESTION:What percent of a day is 15 hours?
options: A)37×1/2% B)16×1/2% C)18×2/3% D)22×1/2% E)None
SOLUTION:Solution
Required percentage = (15/24×100)%
= (75 / 2)%.
= 37×1/2%.
Answer A #### A
QUESTION:Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
options: A)8 kmph B)11 kmph C)12 kmph D)14 kmph E)16 kmph
SOLUTION:Explanation:
Let the distance travelled by x km.
Then, x/10-x/15=2
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr =60/10 hrs= 6 hrs.
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60/5kmph= 12 kmph
ANSWER IS C #### C
QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used?
options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7
SOLUTION:Rate of machine R =1/50
Rate of machine S =1/20
since same no of machines used for R and S to do the same work in 5 hrs
So collective rate needed to finish the work in 5 hrs= 1/5
Let the no of machine be x
So, x/50 +x/20 =1/5
(2x+5x)/100=1/5
7x=20
x=20/7
So no of machine R is 20/7
Answer E #### E
QUESTION:Find the smallest number which when divided by 12 and 15 leaves respective remainders of 8 and 11.
options: A)87 B)97 C)27 D)21 E)56
SOLUTION:Let 'N' is the smallest number which divided by 12 and 15 leaves respective remainders of 8 and 11.
Required number = (LCM of 12 and 15) - (common difference of divisors and remainders) = (60) - (4) = 56.
ANSWER:E #### E
QUESTION:The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is
options: A)62 kg B)60 kg C)64 kg D)72 kg E)None of these
SOLUTION:Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 8 kg
=> (96-x)/4 = 8
=> x = 64
Answer : C #### C
QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast?
options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2
SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes.
Answer: C. #### C
QUESTION:Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
options: A)15:8 B)15:5 C)15:9 D)15:2 E)15:3
SOLUTION:Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8
Answer:A #### A
QUESTION:Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L
options: A)1/3. B)1/2. C)3. D)2. E)6.
SOLUTION:Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2
C #### C
QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
options: A)1055 B)1050 C)1057 D)1060 E)1070
SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055.
A #### A
QUESTION:The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is
options: A)3 10 B)2 10 – 1 C)3 10 – 1 D)2 10 E)None of these
SOLUTION:Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions.
Hence, the number of all possible selections is 3 10 – 1.
Answer C #### C
QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
options: A)65 B)21 C)78 D)67 E)51
SOLUTION:Let the total number of workers be x. Then,
8000x = (12000 * 7) + 6000(x - 7)
= 2000x = 42000
= x = 21.
Answer: B #### B
QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?
options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31
SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 2/7 + 2/5 * 5/7
= 16/35
Answer:A #### A
QUESTION:The H.C.F. of two numbers is 18 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
options: A)270 B)300 C)299 D)322 E)345
SOLUTION:the numbers are (18 x 11) and (18 x 15).
Larger number = (18 x 15) = 270.
ANSWER :A #### A
QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ?
options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points
SOLUTION:A: B = 80 : 75, A : C = 80 : 65.
B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5
Therfore ,In a game of 60, B can give C 8 points.
Answer is E. #### E
QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour.
options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these
SOLUTION:Explanation:
We know Time = Distance/speed
So total time taken =
(120/60+160/80)=4hours
Time taken for 280 Km = 280/4=70.km/hr
Option A #### A
QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150?
options: A)15 B)75 C)25 D)18 E)12
SOLUTION:A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (150 - 75) = 75 points to C.
Answer:B #### B
QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+79)=?
options: A)4500 B)4250 C)4350 D)4800 E)4150
SOLUTION:Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 79=1+(n-1)2
=> n=40
Use value of n in (1)
then,
Sn = (40/2)(1+79) = 1600
Ans:- 3(Sn) = 4800
Answer : D #### D
QUESTION:How many Books each of Volume 100 meter cube can be packed into a crate of volume 3000 meter cube?
options: A)50 B)cannot be determined C)150 D)300 E)350
SOLUTION:Gud question with a simple concept.
In geo if we want to insert one shape into another we need to know the dimensions of the two shapes.
In above with volume given , we can come up with different shapes, so we cant know the answer
For ex :3000 m3 can be 300*10 or 30*100 or just 3000*1 we don't know , so we cant calculate
Answer : B #### B
QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525
SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
A) #### A
QUESTION:Solve :
42 : 56 :: 110 : ?
options: A)121 B)111 C)132 D)143 E)158
SOLUTION:6*7=42
7*8=56
10*11=110
11*12=132
ans 42:56::110:132
ANSWER:C #### C
QUESTION:If x is an integer and 2.134 × 10^x is less than 21000, what is the greatest possible value for x?
options: A)7 B)6 C)5 D)4 E)3
SOLUTION:If x=4
2.134 × 10^4 = 21340 > 21000
So, x = 3
Answer : E #### E
QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.8 kg. the weight of the new student is ?
options: A)10.6 kg B)10.8 kg C)11 kg D)14.9 kg E)None
SOLUTION:Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.8 - 19 x 15) kg
= 11 kg.
Correct Option: C #### C
QUESTION:There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women?
options: A)8/12 B)6/16 C)4/16 D)6/10 E)4/10
SOLUTION:w = m+4
w+m = 20
m+4+m = 20
2m = 16
m = 8
w = 12
ratio:8:12
Ans: A #### A
QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
options: A)5729 B)5760 C)2889 D)3600 E)2799
SOLUTION:1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 2.5 = 3600.Answer: D #### D
QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:For: (2^(3x+3)+3)/3
Let n = 3x + 3
2^n
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, ....
Rule: x^(m+n) = (x^m)(x^n)
(2^(3x))(2^3)
Rule: x^(mn) = (x^m)^n
((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1.
Answer: B #### B
<<<Examples ends
QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double?
options: A)1/3 B)1/6 C)1/12 D)1/24 E)1/36
SOLUTION:ways you can get double - 6...as each dice showing any number from 1 to 6...
total ways = 6∗6=36.6∗6=36..
P=6/36=1/6
ANSWER: B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?
options: A)21 B)42 C)120 D)600 E)200
SOLUTION:Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel)
Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200
Answer E #### E
QUESTION:In a 500 m race Dishu beats Abhishek by 100 m or 5 seconds. In another race on the same track at the same speeds. Abhishek and Prashant start at one end while Dishu starts at the opposite end. How many metres would Abhishek have covered, by the time Dishu meets Prashant given that Dishu's speed is 10 m/sec more than that of Prashant.
options: A)250 m B)560 m C)100 m D)320 m E)240 m
SOLUTION:Explanation :
Abhishek's speed = 100/5=20 m/s.
Time taken by Abhishek to cover 500 m =500/20=25 seconds.
Dishu's speed = 500/20 or 25 m/s
Prashant's speed = 15 m/s
Time taken by Dishu to meet Prashant in 500m race in opposite direction:
Distance covered by Abhishek:
=>500/(15+25).
=>12.5 sec.
=>12.5(20)= 250 m.
Answer : A #### A
QUESTION:What is the area of a square with perimeter 12P ?
options: A) 16p^2 B) 4P C) 9P^2 D) P/16 E) P^2/16
SOLUTION:Each side is 3p
A = (3p)^2 = 9p^2
Answer C #### C
QUESTION:In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
options: A)50% B)40% C)20% D)30% E)10%
SOLUTION:Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 10) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/10) * 100 ---> 10%
Answer : E #### E
QUESTION:If points A and B are (6-1) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
options: A)I only B)II only C)III only D)I and II only E)I and III only
SOLUTION:I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A. #### A
QUESTION:The L.C.M of two numbers is 48. The numbers are in the ratio 1:2. The sum of numbers is:
options: A)28 B)30 C)40 D)50 E)72
SOLUTION:Let the numbers be 1x and 2x.
Then, their L.C.M = 2x. So, 2x = 48 or x = 24.
The numbers are 24 and 48.
Hence, required sum = (24 + 48) = 72.
ANSWER:E #### E
QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate?
options: A)100 B)50 C)Cannot be determined D)105 E)25
SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position.
Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C
QUESTION:16, 23, 19, 19, 22, 15, 25, ?
What number should replace the question mark?
options: A)13 B)11 C)16 D)18 E)19
SOLUTION:B
11
There are two alternate sequences: +3 and –4; #### B
QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at?
options: A)12 min B)17 min C)19 min D)11 min E)16 min
SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B
= 6 - 1 = 5 rounds per hour.
Time taken to complete one round at this speed
= 1/5 hr
= 12 min.
Answer: A #### A
QUESTION:A customer pays 50 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
options: A)70 B)80 C)90 D)50 E)60
SOLUTION:Solution
Let x be the original price.
x - 20 = 50
x - 20 + 20 = 50 + 20
x + 0 = 70
x = 70
Answer A #### A
QUESTION:If two numbers are in the ratio 4:5. If 10 is added to both of the numbers then the ratio becomes 5:6 then find the smallest number?
options: A)10 B)20 C)30 D)40 E)50
SOLUTION:Explanation:
4:5
4x + 10 : 5x + 10 = 5 : 6
6[4x + 10] = 5[5x + 10]
24x + 60 = 25x + 50
25x - 24x = 60 - 50
x = 10
Then smallest number is =4
4x = 40
Answer: Option D #### D
QUESTION:John purchased a house for Rs.45000 and a site for Rs.25000 respectively, if he sold the house for Rs.55000 and the site for Rs.16000, then find the resultant percentage of gain?
options: A)1.39% B)1.40% C)1.41% D)1.42% E)1.43%
SOLUTION:Sol.
Total CP = 70000 & total SP = 71000 ⇒ gain = SP/CP = 71000/70000 = 1.0142 = 1.42%.
Answer D #### D
QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
options: A)42 B)70 C)140 D)196 E)315
SOLUTION:Ans: 196
7C1 * 8C2
Answer D) #### D
QUESTION:For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation?
options: A)(-3)^2 B)2 C)3 D)4 E)5
SOLUTION:Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4
Step 2, For each number: subtract the Mean and square the result =
(1-4)^2=(-3)^2
(2-4)^2=(-2)^2
(3-4)^2 =(-1)^2
(4-4)^2=(.0)^2
(5-4)^2=(1)^2
Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options.
Hence A #### A
QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Let the sequence have N terms starting 18*K
--> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence.
The sum of the sequence is
---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2).
So the average is
153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*).
On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**).
By *), **) we have K=2, N=14.
Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms R which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C. #### C
QUESTION:A research team that must consists of 3 members is to be formed from a pool of 6 scientists. How many different teams are possible?
options: A)17 B)10 C)40 D)26 E)20
SOLUTION:Note that the team must consist of 3 members, not at least 3 members. Hence, all you have to do is 6C3 = 20
Answer (E) #### E
QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
options: A)13.5 B)14 C)15 D)12.5 E)None
SOLUTION:Solution:
At present the total age of the family = 5*20 =100.
The total age of the family at the time of the birth of the youngest member,
=[100−10−(10*4)]=50.
Therefore, average age of the family at the time of birth of the youngest member,
= 50/4 = 12.5.
Answer: Option D #### D
QUESTION:In a suite there are men and cats. In all, there are 15 heads and 40 feet. How many men and how many cats are in the suite?
options: A)8 men and 7 cats. B)7 men and 8 cats. C)6 men and 9 cats. D)10 men and 5 cats. E)11 men and 4 cats.
SOLUTION:10 men and 5 cats.
Let M = men and C = cats. We can come up with 2 equations.
M + C = 15
2M + 4C= 40
Solving the 2 equations will give 10 men and 5 cats.
Answer D #### D
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter
SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer:A #### A
QUESTION:What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”?
options: A)5 B)7 C)49 D)20 E)25
SOLUTION:The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum).
C #### C
QUESTION:John began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after John?
options: A)35 B)55 C)39 D)40 E)60
SOLUTION:Carla starts 30 minutes later and it takes 3 hr for carla to meet John
So John total time travelled = 3hr + 30 minutes
John distance = 30 * (3 1/2) = 105
so carla need to travle 105 to meet John in 3 hrs
speed of carla = 105/3 = 35 miles per hour
Answer is A #### A
QUESTION:The monthly income of Suman in the year 2009 was approximately what percentage of the monthly income of Jyothi in the year 2010?
options: A)22 B)27 C)26 D)29 E)21
SOLUTION:Answer:C #### C
QUESTION:A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
options: A)A.0.6 B)B.1 C)C.2.1 D)D.3 E)E.2.4
SOLUTION:30% of 6 = 1.8
50% of 6 = 3
shortage is 1.2
so we need to have 1.2/50% to get 50% alcohol content.
= 2.4 E #### E
QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C?
options: A)2250 B)3000 C)3018 D)3019 E)3012
SOLUTION:60*5:36*6:75*3
100: 72: 75
75/247 * 7410 = 2250
Answer: A #### A
QUESTION:62467 × 9998 = ?
options: A)624545037 B)627745452 C)624545077 D)624545066 E)625454211
SOLUTION:D
624545066
62467 × 9998 = 62467 × (10000 - 2)
= 62467 × 10000 - 62467 × 2
= 624670000 - 124934
= 624545066 #### D
QUESTION:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
options: A)17% B)24% C)30% D)32% E)79%
SOLUTION:take it as original output =100.
to meet demand increase by 10%, then output=110.
to meet holiday demand , new output increase by 10% then output equals 121
To restore new holidy demand output to original 100.
final -initial/final*100
=21/121*100=8/33*100=17% approxiamately.
option A is correct. #### A
QUESTION:After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
options: A)Rs.2989 B)Rs.5029 C)Rs.5000 D)Rs.5197 E)Rs.5029
SOLUTION:Given SP = Rs. 6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15)
= Rs. 8000
If SP = Rs. 8000, profit
60%
CP = [SP(100)]/(100 + 60)
= (8000 * 100)/160
= Rs.5000
Answer: C #### C
QUESTION:If two sides of a triangle have lengths 3 and 7, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19
options: A)None B)I only C)II only D)II and III only E)I, II, and III
SOLUTION:Let x be the length of the third side.
7-3 < x < 7+3
4 < x < 10
14 < perimeter < 20
The answer is D. #### D
QUESTION:On a map, 1 centimeter represents 17 kilometers. Two cities 663 kilometers apart would be separated on the map by how many centimeters?
options: A)15 B)27 C)39 D)270 E)480
SOLUTION:X=663/17= 39
Answer: C #### C
QUESTION:Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0
options: A)If x>y B)If x>=y C)If x<y D)If x<=y E)x=y or relationship cannot be established
SOLUTION:Solution:-
Solving we get X= -2/3 or -2
Y= 3/4 or 4
C) #### C
QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours.
Working together how long will it take both pipes to fill the tank ?
options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes.
SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour.
Pipe B has a rate of 400 liters per hour.
400 + 600 (A+B) = Together they have a rate of 1000 liters per hour.
1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes
Answer -E #### E
QUESTION:There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
options: A)50 B)23 C)108 D)28 E)45
SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand. #### C
QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
options: A)20 B)34 C)38 D)40 E)46
SOLUTION:We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 40
Hence answer is D #### D
QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)?
options: A)2 B)4 C)7 D)9 E)10
SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3.
Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9.
The answer is D. #### D
QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)
options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87
SOLUTION:Explanation:
Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer: A #### A
QUESTION:The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 20 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?
options: A)230/(30+10A) B)230/(30+60A) C)230/38A D)220/(30+10A) E)220/40A
SOLUTION:Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution.
Substitute A with 3.meaning tommy would have travelled a distance of ((160-20) + (160-70)) in 60 minutes.
230 Kms in 60 minutes ==> 3.8km/hr.
Substitute A with 3 in the answer options.
Option A #### A
QUESTION:If square-root of 15 is 3.87. Then find the value of square-root of (5/3)
options: A)1.29 B)1.39 C)1.49 D)1.59 E)1.69
SOLUTION:=> root 5/ root 3 = (root 5/ root 3)*(root 3/ root 3)
= root 15/ root 9
= 3.87/3
= 1.29
ANSWER:A #### A
QUESTION:What should be added to 4750 so that it may become a perfect square?
options: A)11 B)15 C)16 D)17 E)18
SOLUTION:69x69=4761
4761-4750 = 11
If added to 11 get perfect square
answer =A #### A
QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
options: A)610 B)720 C)825 D)920 E)650
SOLUTION:Explanation:
The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).
Hence we can assume total letters as 5 and all these letters are different.
Number of ways to arrange these letters
=5!=5×4×3×2×1=120=5!=5×4×3×2×1=120
All the 3 vowels (OIA) are different
Number of ways to arrange these vowels among themselves
=3!=3×2×1=6=3!=3×2×1=6
Hence, required number of ways
=120×6=720
ANSWER IS B #### B
QUESTION:A part of certain sum of money is invested at 16% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
options: A)5:4 B)1:4 C)3:1 D)3:5 E)3:4
SOLUTION:12:16
= 3:4
ANSWER:E #### E
QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
options: A)33 1/3% B)46 2/3% C)50% D)62 1/2% E)75%
SOLUTION:P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3%
Answer B #### B
QUESTION:In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number Q of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85?
options: A)144 B)189 C)234 D)279 E)309
SOLUTION:Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2.
Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant.
If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279.
(10x+18x) < 85.
28x < 85, i.e. 28x <= 84 (Since number of balls cannot be in fraction). Thus, x<=3.
(45x+48x) = 93x.
Max (93x) Q= 279.
Answer is D. #### D
QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
options: A)212 km B)214 km C)224 km D)216 km E)204 km
SOLUTION:50(x + 1) = 64x
X = 3.57
60 * 3.57 = 214 km
ANSWER:B #### B
QUESTION:Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be 7?
options: A)3/14 B)1/7 C)0 D)1/2 E)12/21
SOLUTION:METHOD-1
Probability that the number on first die is 7 = 0
Probability that the number on Second die is 7 = 1/7 [Because 1 out of 7 faces is 7]
Probability that Both Dice result in odd numbers = (0)*(1/7) = 0
Answer: Option C #### C
QUESTION:Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.
options: A)8 min B)3 min C)21 min D)23 min E)24 min
SOLUTION:3/4 tank is filled by A in 18 mins.
then balance 1/4 tank is filled by B in 32*1/4 = 8 mins.
ANSWER:A #### A
QUESTION:How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length?
options: A)18.9 sec B)88.9 sec C)22.9 sec D)30.00 sec E)72.0 sec
SOLUTION:D = 110 + 390 = 500 m
S = 60 * 5/18 = 50/3
T = 500 * 3/50 = 30 sec
Answer: D #### D
QUESTION:In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class?
options: A)1/2 B)1/3 C)2/3 D)1/4 E)3/4
SOLUTION:(1/2)G=(1/3)(B+G)
3G=2B+2G
G=2B
B/G=1/2.
The answer is A. #### A
QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
options: A)5729 B)5760 C)2889 D)3600 E)2799
SOLUTION:1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 2.5 = 3600.Answer: D #### D
QUESTION:If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod?
options: A)22.8 kg B)26.6 kg C)28 kg D)26.5 kg E)None of these
SOLUTION:Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 7 :: 42.75 : x
=> 11.25 x x = 7 x 42.75
=> x = (7 x 42.75) / 11.25
=> x = 26.6
Answer : B #### B
QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11
SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer: A #### A
QUESTION:When 2/3 of the garments in the shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 80 percent of the garments in the shipment pass?
options: A)6 B)9 C)8 D)7 E)5
SOLUTION:B = 9
2/3x= 20
x=30
for 80% approval we need 24 garments approved.
already approved = 18
we need 6 more.
Answer : A #### A
QUESTION:What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81?
options: A)1020600 B)1020593 C)56693 D)28343 E)18900
SOLUTION:14 = 2 * 7
25 = 5 * 5
36 = 2 * 2 * 3 * 3
81 = 3 * 3 * 3 * 3
So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C. #### C
QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1
SOLUTION:Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer:A #### A
QUESTION:The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840.At what rate of interest the same amount of interest can be received on the same sum after 5 years ?
options: A)6% B)8% C)9% D)10% E)None
SOLUTION:Solution
S.I. = Rs. 840,R =5%,T= 8 Years.
Principal = Rs.(800x840/5x8)= Rs. 2100.
Now,P = Rs. 2100,S.I. = Rs. 840, T = 5 years.
∴ Rate =(100x840/2100x5) = 8%.
Answer B #### B
QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h?
options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4
SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E #### E
QUESTION:In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater?
options: A)600 B)640 C)680 D)720 E)760
SOLUTION:The number of seats in the theater is
15 + (15+2) + ...+ (15+38)=
20(15) + 2(1+2+...+19)=
20(15) + 2(19)(20)/2=
20(15+19) = 20(34) = 680
The answer is C. #### C
QUESTION:If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be
options: A)2 B)5 C)6 D)7 E)14
SOLUTION:i just tried plugging in the numbers and found out that
5*8820 = 44, 100, which is a square of 210
B #### B
QUESTION:For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
options: A)Rs. 8000 B)Rs. 9000 C)Rs. 9900 D)Rs. 9990 E)Rs. 10000
SOLUTION:Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E #### E
QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these
SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 4/5
5n + 5 = 4d + 4
5n + 5 = 4(2n - 1) + 4 => n = 5/3
d = 2n - 1 => d = 3/7
Hence the fraction is : 5/7
ANSWER:B #### B
QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction?
options: A)5hours B)10hours C)8hours D)10hours E)12hours
SOLUTION:To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 20 =10 hours
Answer is B #### B
QUESTION:8 hens weigh equal to as many duck as are equal to 7 cats. All of them weigh 264kg only. Hen's weighs are?
options: A)6 B)5 C)2 D)7 E)11
SOLUTION:8h = xd = 7c
8h + xd + 7c ----- 264kg.
8h+8h+8h ----- 264kg.
24h ------ 264kgs. => 1h = 11kg
Answer: E #### E
QUESTION:The average of first 11 prime numbers is?
options: A)14.55 B)11.11 C)12.11 D)13.11 E)14.11
SOLUTION:Sum of 11 prime no. = 160
Average = 160/11 = 14.55
ANSWER: A #### A
QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between?
options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p
SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p.
2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate.
1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound.
So range is 5p to 10p.
Answer C. #### C
QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.
options: A)12sec B)20sec C)15sec D)18sec E)10sec
SOLUTION:Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec
Answer : E #### E
<<<Examples ends
QUESTION:9 - 3 ÷ 1/3 + 4 = ?
options: A)4 B)3 C)6 D)9 E)12
SOLUTION:9 - 3 1/3 + 4
=9-3÷1/3+4
=9-(3X3) +4
=9-9+4
=4
CORRECT ANSWER : A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
options: A)9 B)8 C)7 D)6 E)5
SOLUTION:0.[u]225[/u = 0.225225225.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E #### E
QUESTION:A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item
options: A)Rs. 480 B)Rs. 760 C)Rs. 860 D)Rs. 960 E)None of these
SOLUTION:Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 600
= 80/100 * 600
= 480
Option A #### A
QUESTION:A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and B leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost?
options: A)3 2/3 B)5 2/3 C)6 2/3 D)4 2/3 E)7 2/3
SOLUTION:x/10 + 2/15 + 4/20 = 1
x = 40/60*10 = 6 2/3
Answer: C #### C
QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use?
options: A)14 B)47 C)54 D)180 E)64
SOLUTION:Area = Length x Breadth
480 = 40 x Breadth
So, Breadth = 12 Units
Fencing required is -
Breadth + Breadth + Length
12 + 12 + 40 => 64 feet
Answer must be (E) 64 #### E
QUESTION:Among the answers given below, which is nearly equal to √7?
options: A)2.3 B)1.9 C)2.6 D)2.5 E)3.0
SOLUTION:2.6 is nearly equal to the square root of 7
2.6*2.6=6.76
2.5*2.5=6.25
difference
7 - 6.76=0.24
7 - 6.25=0.75
Since 0.24 is lesser of both, 2.6 is closer.
Answer is C #### C
QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase?
options: A)80% B)90% C)70% D)60% E)50%
SOLUTION:Ans. Let previous income = Rs. 100
Previous savings = 10% of Rs. 100 = Rs. 10
Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120
Increased savings = 15% of Rs. 120 = Rs. 18
Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8
Therefore, Percent increase in savings = 8/10 x 100 = 80%
Answer A #### A
QUESTION:Two water pumps, working simultaneously at their respective constant rates, took exactly six hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
options: A)8 B)10 C)12 D)14 E)16
SOLUTION:Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump.
Both pumps together can fill 1/6 of the pool each hour.
2.5x = 1/6
x = 1/15
1.5x = 1.5/15 = 1/10
The faster pump could fill the pool in 10 hours.
The answer is B. #### B
QUESTION:Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h
options: A)20 seconds B)3 C)4 D)1 E)5
SOLUTION:swim in still water at = 3
speed of river= 1.4
US = 3 - 1.4= 1.6
Distance = 8
T = 8/1.6 = 5
Answer: E #### E
QUESTION:The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
options: A)23 years B)24 years C)25 years D)None of these E)18 years
SOLUTION:Let the average age of the whole team by x years.
11x - (26 + 29) = 9(x -1)
11x - 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years.
Answer: Option A #### A
QUESTION:When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction?
options: A)5/4 B)4/7 C)5/6 D)6/7 E)None of these
SOLUTION:Let the fraction be x/y.
When the numerator decreased by 25% and the denominator decreased by 20%.
(x * 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5
ANSWER:E #### E
QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5)
SOLUTION:3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5.
Answer: D. #### D
QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
options: A)-2 B)-1 C)0 D)1 E)2
SOLUTION:P = {3,-8,Y,19,-6}
B = {k,-3,0,16,-5,9}
Y > 21
So L = Median of P = 3
M = Mode of Set B
Z = (3)^M
If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor
=> M = 0
Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.
Answer - C #### C
QUESTION:A worker earns $20 on the first day and spends $15 on the second day. The worker earns $20 on the third day and spends $15 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $100?
options: A)30 B)33 C)35 D)38 E)40
SOLUTION:Every two days, the net total is $5.
After 32 days, the worker will have $80.
On day 33, the worker will receive $20 for a net total of $100.
The answer is B. #### B
QUESTION:On a ferry, there are 27 cars and 13 trucks. The cars have an average mass of 1100 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry?
options: A)1515.5 B)1616.5 C)1717.5 D)1818.5 E)1919.5
SOLUTION:The total mass of the vehicles is 27*1100+13*3000=68700
The average mass is 68700/40=1717.5
The answer is C. #### C
QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes
options: A)18kms B)16kms C)50kms D)30kms E)40kms
SOLUTION:total eastward distance= 25kmph*1/4hr=6.25 km
total westward distance= 40kmph*1/4hr=10 km
total distn betn them= 6.25+10=16.25km
ans 16km
ANSWER:B #### B
QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction?
options: A)5hours B)40hours C)8hours D)20hours E)30hours
SOLUTION:To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 40 =20 hours
Answer is D #### D
QUESTION:If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area?
options: A)26% B)21% C)15% D)18% E)12%
SOLUTION:a =1/2 x b x h or 1/2 x 2a x a(for simplification)
New h = 220a / 100 = 22a / 10
New b =(110a x 100) ==11a/10
New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100)
increased area== (121a²/100) - a²
Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21%
answer :B #### B
QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1
SOLUTION:distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
Answer :D #### D
QUESTION:The largest 4 digit number exactly divisible by 44 is?
options: A)9988 B)9939 C)9944 D)9954 E)9960
SOLUTION:Largest 4-digit number = 9999
44) 9999 (227
9988
Largest number : 9988
Answer : A #### A
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform?
options: A)338 B)240 C)287 D)400 E)191
SOLUTION:Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m.
Answer: D #### D
QUESTION:A rectangular box of volume x has width, depth and height in the ratio of 5:1:2 (in that order). What is the width as a function of x?
options: A)(4x/12)^(1/2) B)(10x/4)^(1/2) C)(5x)^(1/2) D)(2x/5)^(1/2) E)(4x/3)^(1/2)
SOLUTION:We are given width = 5, depth = 1, height = 2
Then Volume x = Width x Depth x Height = 5*1*2 = 10
i.e. x = 10
i.e. The correct option should result in 5 (the width) on substituting the value of x=10
Checking options with x=10
A) (4x/12)^(1/2) = (4*10/12)^(1/2) = (40/12)^(1/2) INCORRECT ANSWER
B) (10x/4)^(1/2) = (10*10/4)^(1/2) = 25^(1/2) = 5 CORRECT ANSWER
C) (5x)^(1/2) = (5*10)^(1/2) = 50^(1/2) INCORRECT ANSWER
D) (2x/5)^(1/2) = (2*10/5)^(1/2) = 4^(1/2) = 2 INCORRECT ANSWER
E) (4x/3)^(1/2) = (4*10/3)^(1/2) = 40/3^(1/2) INCORRECT ANSWER
Answer: Option B #### B
QUESTION:If x, 3, 5, 7 are there and the range and median of them are the same, what is the value of x?
options: A)0 B)1 C)2 D)5 E)4
SOLUTION:Try taking the values of x as you suggested and then see if the median and the range are equal.
Once you do that, you will get the answer yourself.
Tried substituting values starting with 3, 5, 7...
only x = 5 satisfies the condition.
D #### D
QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train?
options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm
SOLUTION:In one hour, the first train travels 60 km.
The second train catches the first train with a relative speed of 20 km/h.
The second train will catch the first train at 10:00 am.
The answer is B. #### B
QUESTION:Marie has 248 $ in her account of the bank. She has to buy presents for her 7 children and wants to distribute the money fairly. How much he will once have the money shared fairly?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:(248$ / 7children) = 35.42
Took the lowest number = 35 * 7 children = $245
$248 - $245 = staying $3
Correct option: C) 3$ #### C
QUESTION:An office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
options: A)18 B)24 C)30 D)45 E)60
SOLUTION:First let's consider the small notebooks.
There are 5 ways to choose notebooks of the same color.
The number of ways to choose four notebooks with different colors is 5C4=5.
There are 10 different packages we can make with the small notebooks.
We can use the same process to find 10 different packages with medium and large notebooks.
The total number of different packages is 30.
The answer is C. #### C
QUESTION:The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Ans: E - 4 pairs
(xˆ2)(yˆ2) = 900 [square root both sides]
xy = 30
20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15
Cancel the repeats
This leaves us with exactly 4 options.
Hence, E #### E
QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen?
options: A)6 B)24 C)36 D)66 E)72
SOLUTION:Try using the formula for combinations:
n!/r!(n-r)!
12!/2!(12-2)!
12!/2!*10!
12*11/2*1
=66
ANSWER:D #### D
QUESTION:If 75 percent of 600 is 50 percent of x, then x=?
options: A)800 B)900 C)1000 D)1100 E)1200
SOLUTION:0.75 * 600 = 0.5 * x
x = 7.5/5 * 600 = 900 #### B
QUESTION:If x : y = 3 : 4, find (4x + 5y) : (5x - 2y).
options: A)32/7 B)13/7 C)2/7 D)32/17 E)2/17
SOLUTION:. X/Y=3/4 (4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2) =(4(3/4)+5)/(5(3/4)-2)
=(3+5)/(7/4)=32/7
ANSWER A 32/7 #### A
QUESTION:Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm.
options: A)227 B)299 C)300 D)161 E)212
SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (22 + 18) * (15)
= 300 cm2
Answer: C #### C
QUESTION:Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
options: A)2:5 B)5:15 C)3:5 D)4:7 E)14:5
SOLUTION:Answer = B) 5:15
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 10:30 = 5:15
B #### B
QUESTION:The true discount on a bill of Rs.1080 is Rs.180.The banker's discount is
options: A)210 B)212 C)214 D)216 E)None of these
SOLUTION:Solution
P.W = Rs.(1080 - 180)
= Rs. 900
S.I on Rs. 1080 =Rs.(180/900 x 1080)
= Rs. 216.
Answer D #### D
QUESTION:A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ?
options: A)9 B)10 C)11 D)12 E)13
SOLUTION:A
5 cartons for large boxes = 5 * 6 = 30 boxes
4 cartons for small boxes = 4 * 9 = 36 boxes
He will need 9 cartons to place 66 boxes. #### A
QUESTION:Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:here when he step down 26 steps he has 30 seconds for remaining steps.
if he step down 34 stairs he has only 18 sec.
30-18=12
12 secs for 8 steps..
18 secs for 12 steps.
12+34=46
so ans is 46..
ANSWER:B #### B
QUESTION:If 5^10 x 2^10 = 10^n what is the value of n?
options: A)16 B)14 C)12 D)10 E)18
SOLUTION:5^10*2^10 = 10^n
or 10^10 =10^n
n=10
D #### D
QUESTION:A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C
together need 3 hours to finish the same work. In how many hours B can complete the work ?
options: A)10 hours B)12 hours C)16 hours D)18 hours E)None of these
SOLUTION:ExplanaƟon:
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12
Work done by B in 1 hour = (7/12)�(1/2) = 1/12
=> B alone can complete the work in 12 hour
Answer: B #### B
QUESTION:There are between 100 and 110 marbles in a collection of cards. If they are counted out 3 at a time, there are 1 left over, but if they are counted out 4 at a time, there is 4 left over. How many marbles are in the collection?
options: A) 100 B) 103 C) 106 D) 108 E) 109
SOLUTION:Let number of cards = x
If the cards are counted 3 at a time , there are 2 left over-
x = 3p+1
x can take values 100 , 104 , 109
If the cards are counted 4 at a time , there is 1 left over
x= 4q+4
x can take values 100 , 108
Therefore , x = 100
Answer A #### A
QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
options: A)1227 B)2088 C)26788 D)8112 E)1871
SOLUTION:A = 7500(26/25)2 = 8112
Answer: D #### D
QUESTION:1.5, 2.3, 3.1, 3.9, ..?
options: A)0.6 B)0.8 C)0.4 D)0.24 E)0.15
SOLUTION:1.5+0.8=2.3
2.3+0.8=3.1
3.1+0.8=3.9
3.9+0.8=4.7
ANSWER:B #### B
QUESTION:The greatest ratio out of 2:1, 5:8, 3:2, 8:9 and 8:5 is?
options: A)2:1 B)3:2 C)5:8 D)8:5 E)8:9
SOLUTION:2/1=2
5/8=0.625
3/2=1.5
8/9=0.888
8/5=1.6
ANSWER:A #### A
QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
options: A)14355 B)15432 C)17576 D)18543 E)16878
SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C #### C
QUESTION:The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π
SOLUTION:=Square - Quarter circle
=12- pi*12/4
=12- pi*3
ANSWER:B #### B
QUESTION:In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N?
options: A)(N-M) B)MN/(M + N) C)(NM) D)(N-M)/(M+N) E)NONE OF THESE
SOLUTION:The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N).
Answer: B #### B
QUESTION:Find avrg speed if a man travels at speed of 18km/hr up and 24km/hr dawn at an altitude of 300m.
options: A)25.8 B)26.8 C)27.8 D)20.5 E)21.8
SOLUTION:avg speed=2*x*y/(x+y)
=2*18*24/(18+24)=20.5
ANSWER:D #### D
QUESTION:How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest?
options: A)2.35 years B)4.25 years C)7 years D)1.25 years E)2 years
SOLUTION:Explanation:
Time = (100 x 60)/(400 x 12) years
= 1.25 years.
Answer: D #### D
QUESTION:A is the average (arithmetic mean) of the first 7 positive multiples of 4 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?
options: A)2 B)4 C)6 D)8 E)10
SOLUTION:If A^2 - B^2 = 0, then let's assume that A = B.
A must equal the 4th positive multiple of 4, thus A = 16, which also equals B.
B is the second positive multiple of n, thus n = 16/2 = 8.
The answer is D. #### D
QUESTION:If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many C such committees are possible?
options: A)20 B)40 C)C=50 D)C=80 E)C=120
SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D. #### D
QUESTION:Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 35.1 kg of zinc has been consumed in it?
options: A)78 kg B)60 kg C)64 kg D)70 kg E)None
SOLUTION:Sol.
For 9 kg Zinc, mixture melted = (9+11) kg.
For 35.1 kg Zinc, mixture, melted = [20/9 x 35.1] kg
= 78 kg.
Answer A #### A
QUESTION:Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes.
How much time will it take Roy to consume all the five tablets?
options: A)60 min B)50 min C)70 min D)65 min E)80 min
SOLUTION:A
60 min
Roy will be able to consume all the five tablets in an hour.
Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min. #### A
QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is
options: A)22 B)21 C)24 D)20 E)19
SOLUTION:Let the mother’s present age be ’x’
Let the daughter’s age be ’y’;
10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1)
10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2)
Solving (1) & (2)
y = 20
ANSWER:D #### D
QUESTION:How many digits are in (12×10^14)(10×10^15)?
options: A)24 B)25 C)26 D)27 E)32
SOLUTION:The question simplfies to (12×10^14)(10^16)
=> 12*10^30
=> Will contain 30 zeros +2 digit 12
=>32
Ans E #### E
QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was?
options: A)23777 B)35000 C)29977 D)26777 E)19871
SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100)
(9x + 1100000 - 11x)/100 = 29000/3 = 9700
(9x + 1100000 - 11x) = 970000
x = 65000
Sum invested at 9% = Rs. 65000
Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000.
Answer: B #### B
QUESTION:A five digit number is to be formed using each of the digits 1, 2, 3, 4 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?
options: A)12 B) 36 C) 72 D) 60 E) 120
SOLUTION:Reqd ways = (Total No. of ways - cases when both 1 and 2 are together)
4 numbers can be arranged in 4 places in 4! ways. Now tie 1 and 2 together so effectively there are 4 nos. they can be arranged in 3! ways. 1 and 2 can be arranged within themselves in 2!ways.
Reqd. Answer = 4! - 3!2! = 24 - (6*2) = 12
Answer: A #### A
QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
options: A)1 B)2 C)4 D)5 E)6
SOLUTION:46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A #### A
QUESTION:Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer B admitted 15 applicants, A admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?
options: A) 8 B) 2 C) 6 D) 0 E) 12
SOLUTION:If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
Answer : D #### D
QUESTION:2+2+2²+2³ ... +2^9
options: A)2^9 B)2^10 C)2^16 D)2^35 E)2^37
SOLUTION:2+2=2^2
2^2+2^2=(2^2)*(1+1)=2^3
2^3+2^3=(2^3)*(1+1)=2^4
so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10
Answer B #### B
QUESTION:In a school 10% of the boys are same in number as 1/3th of the girls. what is the ratio of boys to the girls in the school?
options: A)5:2 B)2:3 C)10:3 D)3:7 E)2:5
SOLUTION:10% of B = 1/3 G
10B/100 = G/3
B = 10G/3
B/G = 10/3
B:G = 10:3
Answer is C #### C
QUESTION:What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5?
options: A) 94 B) 99 C) 26 D) 73 E) None of the Above
SOLUTION:Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -10
Thus 2xy +5 = x^2 + y^2 - 10
x^2 + y^2 -2xy = 15
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 94
Thus the answer is A #### A
QUESTION:What percent of 180 is 45?
options: A)0.25% B)4% C)25% D)40% E)250%
SOLUTION:Here's an algebraic approach.
Let p = the required percent.
This means p/100 = the percent as a fraction.
So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45
Or: (p/100)(180) = 45
Divide both sides by 180 to get: p/100 = 45/180
Simplify right side: p/100 = 1/4
Multiply both sides by 100 to get: p = 25
ANSWER:C #### C
QUESTION:The distance light travels in one year is approximately 5,890,000,000,000 miles. The distance light travels in 100 years is
options: A)A) 587 × 108 miles B)B) 587 × 1010 miles C)C) 587 × 10-10 miles D)D) 589 × 1012 miles E)E) 587 × 10-12 miles
SOLUTION:The distance of the light travels in 100 years is:
5,890,000,000,000 × 100 miles.
= 589,000,000,000,000 miles.
= 589 × 1012 miles.
The answer is (D) #### D
QUESTION:a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles?
options: A)0.76 B)0.86 C)0.96 D)1.16 E)1.26
SOLUTION:let the radius of circle is 'r'
area of the circle which is at corner = (22/7*r^2)/4
hence the area of all four circles are = 22/7*r^2
areaof circle which is made on center of suare is = 22/7*r^2
total area of all circles are = 2*22/7*r^2...........................(1)
if we construct the diagram we get the relation
4r = 2sqrt2
r = 1/sqrt2
put the value of r in eqn 1 and we get
2*22/7*1/2 = 22/7 = 3.14
area of suare = 2^2 = 4
area of remaining part = 4-3.14 = 0.86
ANSWER:B #### B
QUESTION:8500 + (1600 ÷ ?) of 1/5 = 8501
options: A)310 B)312 C)320 D)325 E)345
SOLUTION:Explanation:
=> 8500 + (1600/?) × 1/5 = 8501
=> 1600/? × 1/5 = 8501 - 8500 = 1
=> ? = 1600/5 = 320
Answer: Option C #### C
QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations?
options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10
SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others
C #### C
QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+79)=?
options: A)4500 B)4250 C)4350 D)4800 E)4150
SOLUTION:Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 79=1+(n-1)2
=> n=40
Use value of n in (1)
then,
Sn = (40/2)(1+79) = 1600
Ans:- 3(Sn) = 4800
Answer : D #### D
<<<Examples ends
QUESTION:What percent is 4 gm of 1 kg?
options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 %
SOLUTION:1 kg = 1000 gm
4/1000 × 100 = 400/1000
=2/5 = 0.4 %
B) #### B
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Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (p,c). If c = 2, which of the following could be the equation of line m, which is perpendicular to line L?
options: A) 2x + y = px + 7 B) 2x + y = –px C) x + 2y = px + 7 D) y – 7 = x ÷ (p – 2) E) 2x + y = 7 – px
SOLUTION:So we need m=p-2, so we should get y=mx+b form in answer choices
(A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need
(B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong
(C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong
(E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong
A #### A
QUESTION:The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday?
options: A)39oC B)44oC C)38oC D)41oC E)None
SOLUTION:Solution: Average temperature for Wednesday, Thursday and Friday = 40oC
Total temperature = 3*40 = 120oC
Average temperature for Thursday, Friday and Saturday = 41oC
Total temperature = 41*3 = 123oC
Temperature on Saturday = 42oC
Now,
(Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120;
Saturday - Wednesday = 3
Wednesday = 42-3 = 39oC.
Answer: Option A #### A
QUESTION:Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 8%. What is the approximate interest he pays annually?
options: A)1500 B)1750 C)2000 D)3500 E)2500
SOLUTION:An easy way too attempt this is by approximation:
For the first quarter, he pays 8% of 10,000 which is $800.
So for the four quarters in the year, he will approximately play 800*4=3200 over the entire year.
Because of compound interest it will be more than 3200. Approx. option D is correct.
Answer :D #### D
QUESTION:Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
options: A)7 min B)9 min C)4 min D)9 min E)1 min
SOLUTION:Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9
Answer:B #### B
QUESTION:Find the highest common factor of 36 and 84.
options: A)4 B)6 C)12 D)18 E)19
SOLUTION:36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.
Answer: Option C #### C
QUESTION:What was the day of the week on, 18th July, 1776?
options: A)Thursday B)Wednesday C)Monday D)Saturday E)SUNDAY
SOLUTION:16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days)
Total number of odd days = (0 + 4) = 4.
Required day was 'Thursday'.
Answer:A #### A
QUESTION:y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
options: A)-512 B)-257 C)-256 D)-513 E)128
SOLUTION:As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form of ax^2+bx+c=0,
The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b
512 can be expressed as product of two numbers in the following ways:
1 * 512
2 * 256
4 * 128
8 * 64
16 *32
The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513.
The least value possible for b is therefore -513.
D #### D
QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec. What is the length of the platform?
options: A)389 m B)350 m C)187.5 m D)299 m E)219.5 m
SOLUTION:Speed = 300/24 = 25/2 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 25/2
=> x = 187.5 m.
Answer:C #### C
QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph
SOLUTION:Speed downstream = 55 + 20
= 75 kmph
Speed upstream = 55 - 20
= 35 kmph
Answer: C #### C
QUESTION:A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
options: A)10.18 p.m B)10.29 p.m C)10.30 p.m D)10.38 p.m E)10.32 p.m
SOLUTION:D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C #### C
QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
options: A)19 B)19.7 C)20 D)21.1 E)23
SOLUTION:Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B) #### B
QUESTION:Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
options: A)4 B)10 C)7 D)8 E)12
SOLUTION:Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence
X + Y = 20
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 20
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve
0.25 X + 0.15 (20 - X) = 4.2
X(0.25 - 0.15) + 3 = 4.2
0.1 X = 1.2
X = 12 and Y = 20 - 12 = 8
correct answer D #### D
QUESTION:A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
options: A)$4,040 B)$4,120 C)$1,960 D)$4,920 E)$1,400
SOLUTION:In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost.
Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $5,000-$880=$4,120.
Answer: B. #### B
QUESTION:A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 1/2 days. How many more days are required to complete the remaining work if they work together?
options: A)3 (5/18) B)3 (5/16) C)3 (5/11) D)4 (21/22) E)3 (5/21)
SOLUTION:A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 1/2 days.
The number of days required to complete remaining work => 60/11 - 1/2 = 109/22 = 4 (21/22) days.
Answer:D #### D
QUESTION:a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles?
options: A)0.76 B)0.86 C)0.96 D)1.16 E)1.26
SOLUTION:let the radius of circle is 'r'
area of the circle which is at corner = (22/7*r^2)/4
hence the area of all four circles are = 22/7*r^2
areaof circle which is made on center of suare is = 22/7*r^2
total area of all circles are = 2*22/7*r^2...........................(1)
if we construct the diagram we get the relation
4r = 2sqrt2
r = 1/sqrt2
put the value of r in eqn 1 and we get
2*22/7*1/2 = 22/7 = 3.14
area of suare = 2^2 = 4
area of remaining part = 4-3.14 = 0.86
ANSWER:B #### B
QUESTION:A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is
options: A)250 B)276 C)280 D)285 E)None
SOLUTION:Solution
since the month begins with a sunday , so there will be five sundays in the month.
Required Average = (510x5+240x25 / 30)
= (8550 / 30)
= 285
Answer D #### D
QUESTION:What is the chance that a leap year selected at random contains 53 fridays?
options: A)1/7 B)2/7 C)3/7 D)4/7 E)5/7
SOLUTION:normal year =365 days
leap year = 366 days
now there are 52 weeks i.e. 364 days+2 odd days
the 2 odd may have Friday over a week has 7 days
so probability = 2/7
ANSWER:B #### B
QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?
options: A)120cc B)360cc C)450cc D)589C E)478cc
SOLUTION:Explanation:
r1 = x r2 = 3x
Π * x2 * h = 40
Π9 x2h = 40 * 9 = 360cc
Answer: B #### B
QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is
options: A)276 B)299 C)312 D)322 E)None
SOLUTION:Solution
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer D #### D
QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by:
I. 12 II. 24 III. 48
options: A)I B)I & III C)II D)II & III E)III
SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24.
So answer is III
Answer : E #### E
QUESTION:If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1?
options: A)a. 8 B)b. 9 C)c. 12 D)d. 7 E)e. 27
SOLUTION:Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30
We can write 30 as product of two numbers in following ways
1*30
2*15
3*10
5*6
4 cases = 4*2 i.e. 8 factors (including 1)
Factors greater than 1 = 7
Answer: Option D #### D
QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19?
options: A)7 B)6 C)9 D)10 E)3
SOLUTION:Explanation:
128 + 34 = 162/19 = 10 (Remainder)
Answer: D #### D
QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner?
options: A)33 B)34 C)35 D)36 E)37
SOLUTION:Nearest to 1749≈1750
175/50=35 (Caution: Collection is 1750 - 1 = 1749)
Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members
51* 34 = 1734 >> 15 remains which will be adjusted with 15 members
52 * 15 + 51 * 19 = 780 + 969 = 1749
Answer = B #### B
QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work?
options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs
SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work ..
Therefore, Y will do the remaining 1/10 th work alone..
As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job...
ans 10
E #### E
QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is?
Can someone please explain intuitively what the question is asking?
options: A)5 B)9 C)12 D)15 E)20
SOLUTION:In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3.
5! = 120 has 1 trailing zeros.
10! will have 2 trailing zeros.
15! will have 3 trailing zeros.
20! will have 5 trailing zeros.
Answer: E. #### E
QUESTION:A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/5 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?
options: A)x + 2000 = 1/3*(x - 3000) B)1/3*(x - 3000) = x C)x + 3000 = 1/3*x D)x - 7000 = 1/3*x E)x - 3000 = 1/5*x
SOLUTION:Plane's original altitude = x
Plane's new altitude after ascending 2000 ft = x+2000
Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000
So, after two changes plane is at 1/5 its original altitude => x-3000 = x/5
Answer (E) #### E
QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
options: A)4 B)8 C)16 D)17 E)None of these
SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B #### B
QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS:
options: A)15 B)16 C)18 D)25 E)NONE OF THESE
SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4
SUPPOSE TANYA TAKES X DAYS TO DO THE WORK;
5:4::20:X, X=(4x20/5), X=16 DAYS.
CORRECT OPTION: B #### B
QUESTION:The sum of the 1st and 3rd of 3consecutive odd integers is 131 less than three times the second integer. Find the three integers?
options: A)121 B)133 C)145 D)150 E)165
SOLUTION:Let x, x + 2 and x + 4 be three integers. The sum of the first x and third x + 4 is given by
x + (x + 4)
131 less than three times the second 3(x + 2) is given by
3(x + 2) - 131
"The sum of the first and third is 131 less than three times the second" gives
x + (x + 4) = 3(x + 2) - 131
Solve for x and find all three numbers
x = 129 , x + 2 = 131 , x + 4 = 133
As an exercise, check that the sum of the first and third is 131 less than three times
B #### B
QUESTION:A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
options: A)49/153 B)18/153 C)49/153 D)40/153 E)24/72
SOLUTION:Explanation:
Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles
2 marbles are drawn from 18 marbles at random. Therefore,
n(S) = 18C2 = 153 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 49/153
ANSWER:A #### A
QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit?
options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62
SOLUTION:Explanation:
We are given selling price = Rs. 580 and expected profit of 15 %
Therefore, we can easily solve this numerical, considering basic formulae of profit and loss.
Let cost price = x
Selling price = C.P. + Profit
S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price)
580 = x + (0.15 x)
580 = 1.15 x
Therefore,
x = 504.347
Cost Price = Rs. 504.35
Now, we have the cost price and hence,
Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65
The trader gets a profit of Rs. 75.65
ANSWER IS A #### A
QUESTION:Varma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8)
options: A)6/k B)8/k C)83k D)2/k E)1/k
SOLUTION:Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 8 minutes =8/k.
Answer: B #### B
QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14
SOLUTION:answer isB
Total probability=7C3=48
4C3 +4C2*4C1+4C1*4C2=4+24+24=42
therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8
B #### B
QUESTION:How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
options: A)1875 B)2000 C)2375 D)2500 E)3875
SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375
ANSWER:C #### C
QUESTION:Jaclyn buys $60 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter
options: A)1187.5 B)1234 C)1289 D)1425 E)None of these
SOLUTION:Explanation:
I=(p x r x t)/100
= 60000*9.5/100*(18/12)^1/6 = 1425
Answer: D #### D
QUESTION:40% of x is greater than 1/3rd of x by 110.what is x?
options: A)1100 B)2100 C)1300 D)1650 E)1400
SOLUTION:4x/10-x/3=110
1x/15=110
x=1650
ANSWER:D #### D
QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ?
options: A)-1 B)-5 C)-2 D)-3 E)-4
SOLUTION:Use answer options to solve this problem -
x is negative integer (-1,-2,-3......)
put x=-1
7x+3y=14
7(-1)+3y=14
-7+3y=14
3y=14+7
3y=21
y=7
Answer will be (A) #### A
QUESTION:The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average?
options: A)69 B)70 C)71 D)72 E)75
SOLUTION:Sum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled.
The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72.
ANSWER:D #### D
QUESTION:Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ?
options: A)2 B)5 C)1 D)9 E)4
SOLUTION:4-3=1. Answer is C #### C
QUESTION:The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be
options: A)12 years B)20 years C)25 years D)28 years E)None
SOLUTION:Solution
Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
= 54 - x = 5x - 30
‹=›6x = 84
‹=›x= 14.
∴Son's age after 6 years = (x + 6) = 20 years.
Answer B #### B
QUESTION:Two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
options: A)28 B)266 C)990 D)20 E)22
SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 160 + 280 = 440 m.
The time required = d/s = 440/20 = 22 sec.
Answer: E #### E
QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share?
options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164
SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) .
x + 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs.145
B #### B
QUESTION:The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?
options: A)106.75 B)213.5 C)427 D)729 E)1,156
SOLUTION:Diagonal of a square =√2*side of square
=> side =Diagonal/(√2)
Area of square =s*s
=(diagonal^2)/2
Difference of both tv's =(34^2-27^2)/2
=427
ANSWER:C #### C
QUESTION:Henry answered 4/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?
options: A)x B)(85/12)*x C)(85/24)*x D)(85/36)*x E)(85/48)*x
SOLUTION:Let Q be the number of homework questions.
Q = 4Q/5 + (5/17)(Q/5) + x
Q = 68Q/85 + 5Q/85 + x
12Q/85 = x
Q = (85/12)*x
The answer is B. #### B
QUESTION:A positive integer x has 60 divisors and 7x has 80 divisors. What is the greatest integer y such that 7y7y divides n?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Total number of factors of x = 60 = (p+1)*(q+1)*(r+1)... = 2^2 * 3 * 5
Now note that 7x has only one 7 more than x. The number of all other prime factors stays the same.
Total number of factors of 7x = 80 = (p+2)*(q+1)*(r+1)... = 2^4 * 5
Here, the 3 of previous expression has disappeared so it must have converted to 4. Does it make sense? Let's see:
Total number of factors of x = 60 = 2^2 * 3 * 5 = (3+1)*(2+1)*(4+1)
Total number of factors of 7x = 80 = 2^2 * 4 * 5 = (3+1)*(3+1)*(4+1)
The powers of other factors stay the same. Only the power of 7 increases by 1. So initially, in x, the power of 7 must have been 2. Hence the maximum value of y must be 2.
Answer (C) #### C
QUESTION:When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number?
options: A)228 B)103 C)286 D)122 E)102
SOLUTION:Explanation:
Let the number be x
x2 - 732 = 5280
x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609
= 10000 + 2(100)(3) + 32 = (100 + 3)2
x = 100 + 3 = 103.
Answer: B #### B
QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point?
options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west
SOLUTION:she is currently at 5km north east from the starting point
ANSWER:A #### A
QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?
options: A)5 B)8 C)24 D)15 E)20
SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min
Nick's rate - 10 laps per hour --> 10/60 laps/min
lets set equations:
20/60*t=4 (since Maria had to run 4 laps before Nick would start)
10/60*t=0 (Hick has just started and hasn't run any lap yet)
(20/60-10/60)*t=4-0 (since Nick was chasing Maria)
t=24 min needed Maria to run 4 laps
Answer : C #### C
QUESTION:Consider two statements
Statement 1 => If R is an integer and R=2p+1 where p is not an integer.
Statement 2 => If S is an integer and S=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of R and S respectively
options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined
SOLUTION:answer will be E
R = integer
R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even R would odd
if n odd R would be even
ANSWER IS E #### E
QUESTION:Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
options: A)18 sec B)70 sec C)21 sec D)20 sec E)19 sec
SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5
= 20 mps.
Distance covered in passing each other
= 120 + 280 = 400 m.
The time required = d/s
= 400/20
= 20 sec.
Answer: D #### D
QUESTION:A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?
options: A)15002 B)15001 C)15000 D)15007 E)15009
SOLUTION:Principal = (100 * 5400) / (12 * 3) = Rs. 15000.Answer:C #### C
QUESTION:A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:
options: A)1.8h B)3h C)4h D)5h E)None of these
SOLUTION:Explanation:
Upstream speed = B-S
Downstream speed = B + s
B - S = 15/5 = 3 km/h
Again B = 4S
Therefore B - S = 3 = 3S
=> S = 1 and B = 4 km/h
Therefore B + S = 5km/h
Therefore, Time during downstream = 15/5 = 3h
Answer: B #### B
QUESTION:The income tax in country X is 8% of any income up to $5000. For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income?
options: A)$10,500 B)$11,000 C)$13,000 D)$13,500 E)$14,000
SOLUTION:Given : For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income?
for first 5000 , 8% tax then we get 400$ as tax.
Now Perry paid 950$ tax... we need to check which option is going to yield 550$ on the remaining amount.
A. $10,500 - 5000 = 5500 , then we get 10% tax , we get 550$... ( $10,500 - 5000 - here already for 5000$ we have calculated the tax and we need to tally for the remaining amount)
550+400 = 950$...hence this is the option.
ANSWER :option A. #### A
QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by
options: A)330 B)340 C)350 D)360 E)370
SOLUTION:1 11 21 .......91
2 12 22........92
3 13 23........93
. . . .. . .. . .
. . .. .. . .. .
. . .. . . .. . ...
there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column
and diff of 6 and 9 is 3 so
3*1*10+3*10*10 = 330
ANSWER:A #### A
QUESTION:Tough and Tricky questions: Number Properties.
If (z + 3)/6 is an integer, what is remainder when z is divided by 6?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:6/6=1
Ans B #### B
QUESTION:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue?
options: A)25/153 B)28/153 C)5/17 D)E=4/9 E)E=12/17
SOLUTION:P(at least one blue) = 1 - P(0 blue) = 1 - 10/18*9/17 = 12/17.
Answer: E. #### E
QUESTION:The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 1000 years is:
options: A)587 x 10^13 miles B)999× 1238 miles C)346 × 1012 miles D)247 × 1012 miles E)587 × 1012 miles
SOLUTION:The distance of the light travels in one years is:
5,870,000,000,000 = 587 * 10 ^10
The distance of the light travels in 1000 years is:
= 587 * 10^10 x 10 ^3 = 587 x 10^13 miles
Answer :A #### A
QUESTION:Two concentric circles form a ring. The inner and outer circumferences of ring are (352/7) m and (518/7) m respectively. Find the width of the ring.
options: A)2 B)4 C)6 D)8 E)None of them
SOLUTION:Let the inner and outer radii be r and R meters.
Then 2(22/7)r = (352/7) = r =((352/7) X (7/22) X (1/2))=8m.
2(22/7)R=(528/7) = R=((528/7) X (7/22) X (1/2))= 12m.
Therefore, Width of the ring = (R - r) = (12 - 8) m = 4 m.
Answer is B. #### B
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
options: A)28% B)25% C)95% D)05% E)22%
SOLUTION:800 --- 200
100 --- ? => 25%
Answer:B #### B
QUESTION:Which of the following CAN be the least common multiple of two positive integers 5 and 25?
options: A)5 B)10 C)15 D)25 E)20
SOLUTION:LCM of 5, 25 is 25
Answer : D #### D
QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9
SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.
15 = x y and 16 = 2 x + 2 y
Solve the second equation for x
x = 8 - y
Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as
15 = (8 - y) y
Solve for y to find
y = 3 and y = 5
Use x = 8 - y to find x
when y = 3 , x = 5 and when y = 5 , x = 3.
The dimensions of the rectangle are 3 and 5.
As an exercise, check that the perimeter of this rectangle is 16 and its area is 15.
Answer A #### A
QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
options: A)230 m B)210 m C)260 m D)320 m E)330 m
SOLUTION:Relative speed = (120 + 80) km/hr
= (200 x(5/18))m/sec
= (500/9)m/sec.
Let the length of the other train be x metres.
Then, (x + 290)/9 = 500/9
x + 290 = 500
x = 210.
B #### B
QUESTION:If n is an integer, which of the following must be an even integer?
options: A)n^2-n-1 B)n^2-4n+6 C)n^2-5n+5 D)n^2+3n+8 E)n^2+2n+10
SOLUTION:Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: n^2-n-1 = -1 { If n = 1 }
B: n^2-4n+6 = 3 { If n = 1 }
C: n^2-5n+5 = 1 { If n = 1 }
D: n^2+3n+8 = 12 { If n = 1 }n^2+3n+8 = 18 { If n = 2 }
E: n^2+2n+10 = 13 { If n = 1 }
Thus the only possible answer is (D) #### D
QUESTION:Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 80 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
options: A)70 miles B)80 miles C)90 miles D)100 miles E)110 miles
SOLUTION:Every hour, Nil gets ahead of Ethan 80 - 20 =
60 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 80 × 1 = 80 miles.
correct answer B #### B
<<<Examples ends
QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed?
options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph
SOLUTION:829/7
= 118 kmph
Answer: C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
options: A)7 days B)3 days C)9 days D)8 days E)2 days
SOLUTION:C
9 days
C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C
QUESTION:12,?,68,129,220,347,516
options: A)129 B)220 C)347 D)31 E)520
SOLUTION:2*2*2 + 4 = 12
4*4*4 + 4 = 68
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
3*3*3 +4 = 31
ANSWER : D #### D
QUESTION:Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
options: A)white − wheat − wheat B)wheat − wheat − rye C)rye − white− wheat D)rye − rye − rye E)rye − rye − white
SOLUTION:In a single round Lucy drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A #### A
QUESTION:P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last?
options: A)5 days B)10 days C)14 days D)22 days E)26 days
SOLUTION:Explanation :
Work done by P in 1 day = 1/10
Work done by Q in 1 day = 1/6
Work done by P in 2 days = 2 × (1/10) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15
Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3
Total days = 2 + 3 = 5
Answer : Option A #### A
QUESTION:A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
options: A)15 B)30 C)28 D)24 E)32
SOLUTION:number of workers = 10* (25-10)/10 = 15
Answer is A #### A
QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
options: A)1 B)2 C)8 D)31 E)30
SOLUTION:Total outcome is 2^3 = 8
Favourable cases = H_ H
The second place can be occupied by either H or T
There are 2^1 =2 ways that can be done.
Hence, the correct option is B #### B
QUESTION:The 323rd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
options: A)u B)v C)w D)y E)z
SOLUTION:a is one time, b,2 times so on...
so 323=n(n+1)/2..
0r n(n+1)= 646... now 25*26=650...24*25<646 so n= 25. and 25th alphabet is Y. ans D #### D
QUESTION:The wages earned by Robin is 50% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
options: A)18.75% B)23% C)30% D)50% E)7%
SOLUTION:Let wage of Erica = 10
Wage of Robin = 1.5*10 = 15
Wage of Charles = 1.6 *10 = 16
Percentage by which wage earned by Charles is more than that earned by Robin = (16-15)/15 * 100%
= 1/15 * 100%
=7%
Answer E #### E
QUESTION:In a kilometer race, A beats B by 16 meters or 10 seconds. What time does A take to complete the race?
options: A)167 sec B)190 sec C)176 sec D)716 sec E)615 sec
SOLUTION:Time taken by B run 1000 meters
= (1000 * 10)/16 = 625 sec.
Time taken by A = 625 - 10
= 615 sec.
Answer:E #### E
QUESTION:How many integers between 4000 and 5000 that have distinct digits and increase from left to right ?
options: A)10 B)48 C)60 D)20 E)600
SOLUTION:Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
445_ --> 4
446_ --> 3
447_ --> 2
448_ --> 1
456_ --> 3
457_ --> 2
458_ --> 1
467_ --> 2
468_ --> 1
478_ --> 1
Number of integers =20
D #### D
QUESTION:Find the average of all numbers between 1 and 76 which are divisible by 5
options: A)40 B)20 C)25 D)30 E)35
SOLUTION:Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75)/15=600/15=40
Answer: Option A #### A
QUESTION:In a family, there are six members A, B, C, D, E and F.
A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died.
How many male members are there in the family ?
options: A)1 B)9 C)3 D)4 E)6
SOLUTION:Explanation:
A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A.
A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males.
Answer: C) 3 #### C
QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
options: A)109% B)160% C)100% D)600% E)108%
SOLUTION:MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C #### C
QUESTION:(112 x 54) = ?
options: A)70000 B)71000 C)72000 D)73000 E)74000
SOLUTION:(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000
2 24 16
A) #### A
QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
options: A)299 meters B)278 meters C)500 meters D)276 meters E)299 meters
SOLUTION:Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C #### C
QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
options: A)10 B)12 C)16 D)18 E)21
SOLUTION:Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B #### B
QUESTION:What is the least integer that is a sum of four different prime numbers each greater than 50?
options: A)232 B)234 C)236 D)238 E)240
SOLUTION:The sum of the four smallest primes greater than 53+59+61+67=240.
The answer is E. #### E
QUESTION:In 20 years, A will be twice as old as B was 20 years ago. If A is now 10 years older than B, the present age of B is?
options: A)35yrs B)40yrs C)50yrs D)60yrs E)70yrs
SOLUTION:Let B's present age = x years
Then A's present age = x+10 years
x+10+20 = 2(x-20)
x + 30 = 2x - 40
x = 70years
Answer is E #### E
QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 46 years, was replaced by a new person. Find the age of the new person?
options: A)18 B)56 C)16 D)17 E)14
SOLUTION:Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 46 + Q
=> Q = 16
Answer:C #### C
QUESTION:Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
options: A)7 min B)9 min C)4 min D)9 min E)1 min
SOLUTION:Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9
Answer:B #### B
QUESTION:During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
options: A)9/xz B)9zx C)9x/z D)9z/x E)xz/9
SOLUTION:Speed of Peter = x/9 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x
Option D
The values 100m and 200m have no role to play here and are just given to confuse you. #### D
QUESTION:Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
options: A)7/8 B)1/8 C)1/3 D)1/5 E)1/9
SOLUTION:Original share of 1 person =1/6
New share of 1 person =1/5
Increase =1/5 - 1/6 =1/30
Required fraction = (1/30)/(1/6)=1/5
Answer is D. #### D
QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.2200, then what is the income of P1?
options: A)s.800 B)s.2400 C)s.4000 D)s.5500 E)s.4200
SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 2200 …(i) and 4x – 2y = 2200 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 2200 -> x = 1100
P1’s income = Rs 5*1100 = Rs.5500
ANSWER:D #### D
QUESTION:A 2-year certificate of deposit is purchased for R dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?
options: A)k(1.06)^2 B)k(1.06)^8 C)k(1.015)^2 D)R(1.015)^8 E)k(1.03)^4
SOLUTION:Annual Rate of interest= 6%
Quaterly rate of interest= 6/4% = 1.5%
Now, periods of compounding in 2 years= 8 (8 quarters)
Thus R(1.015)^8
Answer: D #### D
QUESTION:A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
options: A)Rs.3178 B)Rs.3120 C)Rs.3127 D)Rs.3121 E)Rs.3122
SOLUTION:Explanation:
Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B #### B
QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is
options: A)277 B)668 C)119 D)177 E)121
SOLUTION:Number of words which can be formed
= 5! - 1 = 120 - 1 = 119.
Answer: C #### C
QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three?
options: A)14 B)16 C)18 D)24 E)25
SOLUTION:Explanation:
Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
ANSWER IS A #### A
QUESTION:The product of all the prime numbers less than 30 is closest to which of the following powers of 10?
options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^9
SOLUTION:Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19 ,23, 29
= 1*10^7 *2.3*2.9*10^9
=6.67*10^9
E #### E
QUESTION:If a < b < c , which of the following must be true?
(I) a < b^2
(II) a < c - b
(III) a^2 < b^2 < c^2
options: A)None B)I only C)II only D)III only E)II and III
SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: A. #### A
QUESTION:X is an even number and Y is a positive odd number. Which of the following expressions cannot be even?
options: A)(XY)^Y B)X^3Y^3 C)X^3 D)XY E)Y^2
SOLUTION:If x is even, let x = 0 and see what happens.
A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE)
B. 0³Y³ = 0 (EVEN - ELIMINATE)
C. 0³ = 0 (EVEN - ELIMINATE)
D. (0)Y = 0 (EVEN - ELIMINATE)
E. Y²
Answer:E #### E
QUESTION:A train 310 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
options: A)4 B)6 C)5 D)17 E)13
SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [310 * 3/55] sec = 17 sec
ANSWER:D #### D
QUESTION:24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M?
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D #### D
QUESTION:Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of
Rs. 13,800. Deepak's share is
options: A)Rs 9600 B)Rs 8500 C)Rs 8450 D)Rs 8400 E)None of these
SOLUTION:Explanation:
Ratio of their shares = 22500 : 35000
=9 : 14
Deepak's share = Rs.(13800×14/23)
= Rs. 8400
Option D #### D
QUESTION:Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest W?
options: A) 60 B) 61 C) 62 D) 63 E) 64
SOLUTION:60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=W
answer is A. #### A
QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c?
options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12
SOLUTION:6a/100 = 12
a = 200
12b/100 = 6
b = 50
c = b/a = 50 / 200 = 1/4
The answer is C. #### C
QUESTION:If log10 2 = 0.3010, the value of log10 80 is:
options: A)1.5252 B)1.903 C)3.9252 D)3.903 E)2.5252
SOLUTION:= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
ANSWER B #### B
QUESTION:A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
options: A)110 B)120 C)128 D)143 E)145
SOLUTION:First Purchased = 250 Wes= 128
C #### C
QUESTION:if log 5 = 0.69897, the number of digits in 5128 is
options: A)90 B)39 C)88 D)28 E)11
SOLUTION:Explanation:
log(5128) = 128log(5) = 128 × 0.69897 ≈ 89.46
ie, its characteristic = 89
Hence, number of digits in 2128 = 89+1 = 90
Answer: Option A #### A
QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
options: A)5 B)2 C)8 D)4 E)16
SOLUTION:1. We need to find out the time taken by 7 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 16*8 = 128 days
4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job.
5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7* total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days.
6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days.
The answer is choice E #### E
QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
options: A)11 B)408 C)2881 D)287 E)221
SOLUTION:1h ----- 5
? ------ 60
12 h
RS = 13 + 21 = 34
T = 12
D = 34 * 12 = 408
Answer:B #### B
QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2
SOLUTION:RT = W
Given:
R = 1/3 + 1/3 = 2/3
T = ?
W = 1
T = 1 / (2/3) = 3/2 = 1 1/2
Answer: E #### E
QUESTION:Positive Integer A gives the remainder of 9 when divided by another positive Integer B. If A/B = 47.45, what is the value of B?
options: A)96 B)75 C)48 D)20 E)12
SOLUTION:I think the answer should be 25.
This is how i solved.
.45 of B = Remainder
.45 of B = 9
B = (9 *100) / 45 = 20.
D #### D
QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced?
options: A)70% B)15% C)20% D)25% E)30%
SOLUTION:price of a coat in a certain store = $500
the price of the coat is to be reduced by $350
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (350)*100 / 500 = 70%
Answer: Option A #### A
QUESTION:Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
options: A)2 B)4 C)6 D)8 E)10
SOLUTION:P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
880/x = 880/1.1x + 10
1.1(880) = 880 + 11x
11x = 88
x = 8
The answer is D. #### D
QUESTION:Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket
to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
options: A)$8 B)$14 C)$5 D)$15 E)$0
SOLUTION:1/5 x $60 = $12 for sandwich
1/6 x $60 = $10 for museum
1/2 x $60 = $30 for book
$12 + $10 + $30 = $52 spent
$60 - $52 = $8 left over
correct answer A #### A
QUESTION:Convert 2/5 to a decimal
options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5
SOLUTION:Divide 2 by 5: 2 / 5 = 0.4
Answer: 2/5 = 0.4 (D) #### D
QUESTION:The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
options: A)A)17 B)B)18 C)C)19 D)D)22 E)E)24
SOLUTION:Explanation:
10 * 16 + 36 – 26=170 => 170/10 = 17
A) #### A
QUESTION:In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was:
options: A)2500 B)2520 C)3000 D)3100 E)None of these
SOLUTION:Explanation :
Number of valid votes = 70% of 9000
= 6300.
Valid votes polled by other candidates = 40% of 6300
(40/1006300)
= 2520.
Harsh Mishra a year ago
0 upvotes
Answer : B #### B
QUESTION:A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight?
options: A)20 lb B)11 lb C)10 lb D)15 lb E)5 lb
SOLUTION:Sol.
66÷6 = 11.
Answer : B #### B
QUESTION:WHEN A PERSON SELLS TWO ITEMS $1656 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURS A LOSS OR GAIN OF:
options: A)no loss no gain B)20 % profit C)4% loss D)2% profit E)2% loss.
SOLUTION:The 2 items are sold at 1656 each , one at a profit of 20% and the other at a loss of 20%
So the original rates of the items are 1380 and 2070 respectively
So the total he spend for those 2 items is 3450 but he ended up in selling them with (1656*2) 3312
So the loss is 3450 - 3312 = 138
The loss percentage is (138/3450) *100 = 4% loss - Answer C #### C
QUESTION:At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
options: A)62.5 B)62.8 C)62.1 D)62.9 E)32.5
SOLUTION:Explanation:
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A #### A
QUESTION:A certain sum amounts to Rs.1525 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
options: A)6.76% B)3.76% C)5.26% D)5.76% E)4.76%
SOLUTION:3 --- 1525
5 --- 1875
--------------
2 --- 350
N = 1 I = 75 R = ?
P = 1525 - 225 = 1300
75 = (1300*1*R)/100
R = 5.76%
ANSWER:D #### D
QUESTION:Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet?
options: A)15 B)18 C)21 D)24 E)27
SOLUTION:Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him Y: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer. #### D
QUESTION:The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 6 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
options: A)45 B)65 C)75 D)78 E)90
SOLUTION:A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 6 = 74
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 74 + 4 = 78
D #### D
QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage
options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain
SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100
= (750 ~ 1020)/1020 = 26% Loss
A #### A
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
options: A)2288 B)277 C)800 D)2878 E)211
SOLUTION:25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800.Answer: C #### C
QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2
SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2
= 62 m2.
answer :D #### D
QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
options: A)18 B)30 C)60 D)120 E)216
SOLUTION:Arrangment means permutations questions..
5P3 = 5!/3! = 60.
IMO option C is correct answer.. #### C
QUESTION:The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 32,000 locusts?
options: A)2 B)4 C)6 D)8 E)9
SOLUTION:- 4 hours: 1,000
-2 hours: 2,000
Now: 4,000
+ 2 hours: 8,000
+ 4 hours: 16,000
+ 6 hours: 32,000
Answer : C #### C
QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true?
I. h = y
II. y = 1
III. h and y are prime integers.
options: A) None B) I only C) II only D) III only E) I and II
SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2).
I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2);
II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2);
III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2).
Answer: A. #### A
QUESTION:The total of company C's assets in 1994 was 150% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
options: A)7N B)8N C)9N D)12.5N E)20
SOLUTION:Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 150% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:
$500 + 1.5x$500 = $500 + $750 =$1250
This is 12.5 times the 1992 number, so the correct answer is 12.5N.
D #### D
QUESTION:A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
options: A)5/8 B)6/13 C)5/16 D)5/13 E)5/11
SOLUTION:Two balls can be picked from thirteen balls in 13Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (9 * 4) = 36/78 = 6/13
Answer: B #### B
QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
options: A)-2 B)-1 C)0 D)1 E)2
SOLUTION:P = {3,-8,Y,19,-6}
B = {k,-3,0,16,-5,9}
Y > 21
So L = Median of P = 3
M = Mode of Set B
Z = (3)^M
If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor
=> M = 0
Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.
Answer - C #### C
QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
options: A)180 B)787 C)178 D)179 E)172
SOLUTION:Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers
= (S + T)/2 = 180.
Answer:A #### A
<<<Examples ends
QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third smallest sector?
options: A)1/72 B)1/36 C)1/18 D)1/12 E)1/9
SOLUTION:Its an AP question .... it is given clearly in the question .
Let the smallest angle be a
and the circle has 8 sectors and hence 8 angle with a common difference d
hence all the angles can be written in AP form with Cd as d ,
a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,
given that a+7d = 80 --------1
also
a + a+d + a+2d + a+3d +
a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)
which is 8a + 28d = 360 --------2
solving 1 and 2
we get a=10
We are almost done ,
now the question ask what fraction of the wheel’s area is represented by the smallest sector ?
(30/360)( pie r*r)/ (pie r*r) = 30/360= 1/12
D ans .... #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?
options: A)3/10 B)3/20 C)2/5 D)1/2 E)1/3
SOLUTION:S={1,2,3,….20}
E={3, 6,9,12,15,18}
P(E)=6/20
=3/10
Option A #### A
QUESTION:The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
options: A)A)17 B)B)18 C)C)19 D)D)22 E)E)24
SOLUTION:Explanation:
10 * 16 + 36 – 26=170 => 170/10 = 17
A) #### A
QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years?
options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 %
SOLUTION:Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11)
= 100/11 = 9.09 %
ANSWER:A #### A
QUESTION:From 2005 to 2015 the world's population grew by 11.27%, and from 2005 to 2010 the world's population grew by 6.20%. What was the percentage growth in the world's population from 2010 to 2015?
options: A) 5% B) 6% C) 2% D) 2.5% E) 5.5%
SOLUTION:Let the world's population in 2005 = x; then,
for 2005-2010, the population equation is x + 0.0620x = 1.0620x,
for 2005-2015, the population equation is x + 0.1127x = 1.1127x;
so, the growth from 2010 to 2015 = (1.1127x - 1.060x)/(1.062x) = 0.05 (rounded). Thus, the answer is 5%.
Answer is A #### A
QUESTION:If December 3rd, 1999 is a Friday, what day is January 8th, 2000?
options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday
SOLUTION:There is difference of 36 days from Dec. 3rd 1999 to Jan. 8th 2000.
36/7 has a remainder of 1.
Jan. 8th is: Friday + 1 day = Saturday
The answer is D. #### D
QUESTION:How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
options: A)3 B)4 C)5 D)6 E)7
SOLUTION:B
4
By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4. #### B
QUESTION:Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
options: A)15:8 B)15:5 C)15:9 D)15:2 E)15:3
SOLUTION:Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8
Answer:A #### A
QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
options: A)300 km B)320 km C)360 km D)390 km E)400 km
SOLUTION:Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C) #### C
QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x?
options: A)20 B)60 C)100 D)120 E)150
SOLUTION:y = 0.5*0.5*x = x/4
y%*x = 9
(y/100)*x = 9
(x/400)*x = 9
x^2 = 9*400
x = 60
The answer is B. #### B
QUESTION:Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
options: A)7 1/2 sec B)2 sec C)3 sec D)5 sec E)7 sec
SOLUTION:70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 ½ sec
ANSWER A #### A
QUESTION:Q=(429)^2 * 237 * (1243)^3 is thrice of ?
options: A)33605 * 31960 * (1243)^2 B)33654 * 538219 * (1243)^2 C)33891 * 533247 * (1243)^2 D)34122 * 532004 * (1243)^2 E)34606 * 534572 * (1243)^2
SOLUTION:Q=(429)^2*237*(1243)^3 is an odd number.
Among answer choices only C is an odd number, (so thrice C also will be an odd number).
Answer: C. #### C
QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score?
options: A)662 B)672 C)654 D)642 E)721
SOLUTION:8 * 83 = 664 – 10 = 654
ANSWER:C #### C
QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is
options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5
SOLUTION:Work done by 20 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/(14×30)
Work done by 14 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×14)
Ratio of the capacity of a man and woman =1/(15×14) : 1/(14×30) = 1/15 : 1/30
= 1/3 :1/6 = 1/1=1/2=2:1
Answer is C #### C
QUESTION:The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres?
options: A)11 B)12 C)13 D)14 E)15
SOLUTION:Speed of the boat downstream = 90 + 18 = 108 kmph
= 108 * 5/18 = 30 m/s
Hence time taken to cover 330 m = 330/30 = 11 seconds.
Answer: A #### A
QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 21,947. Approximately what was the percent increase?
options: A) 45% B) 125% C) 147% D) 150% E) 225%
SOLUTION:The percent increase is (21947-8902)/8902=13045/8902=1.47
So the approximate answer is C #### C
QUESTION:find out the probability to get 1Rs coin head, 2Rs coin Tail and 5Rs coin head??
options: A)1/2 B)1/8 C)1/16 D)1/4 E)None of these
SOLUTION:1Rs coin head=1/2
2Rs coin Tail=1/2
5Rs coin head=1/2
=(1/2)*(1/2)*(1/2)
=1/8
ANSWER:B #### B
QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches?
options: A)24 B)26 C)28 D)30 E)32
SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x
x=30
answer is D #### D
QUESTION:If 0.75: x :: 5:9, then x is equal to:
options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these
SOLUTION:Explanation:
(x * 5) = (0.75 *9)
X=6.75/5 = 1.35
Answer: D #### D
QUESTION:A man can buy a new house in 4 years with all of his earnings. But he spend the same amount in household expenses in 8 years and for savings in 12 years. How many time needed for buying the house?
options: A)12 B)20 C)30 D)15 E)24
SOLUTION:His savings in 1 year = 1/4 - (1/8+ 1/12) = 1/24
He can buy a new house in 24 years
ANSWER:E #### E
QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
options: A)299 m B)777 m C)200 m D)167 m E)128 m
SOLUTION:2(l + 100) = 600 => l
= 200 m
Answer:C #### C
QUESTION:9886 + x = 13200, then x is ?
options: A)3327 B)3237 C)3337 D)2337 E)None of these
SOLUTION:Answer
x = 13200 - 9886 = 3314
Option: E #### E
QUESTION:R and S start walking each other at 10 AM at the speeds of 3 km/h and 4 km/h respectively. They were initially 17.5 km apart. At what time do they meet?
options: A)2 : 30 PM B)11 : 30 AM C)1 : 30 PM D)12 : 30 PM E)None of these
SOLUTION:Let after t hours they meet then,
3t + 4t = 17.5 ⇒ t = 25
∴ Time = 10 am + 2.5 h = 12 : 30 am
Answer D #### D
QUESTION:If n is a natural number, then(6n^2+6n) is always divisible by?
options: A)6 only B)6 and 12 C)12 only D)by 18 only E)None of these
SOLUTION:(6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Correct Option: B #### B
QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
options: A)5040 B)2520 C)360 D)120 E)42
SOLUTION:6! = 720
720/2=360 half the time carmelo is in front, vice versa
Answer:
(C) 360 #### C
QUESTION:If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it?
options: A)22 B)38 C)60 D)88 E)90
SOLUTION:Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
\inline \fn_jvn \therefore 10:36 ::25:x \inline \fn_jvn \Leftrightarrow (10 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{10}=90
Hence, 10 men can do it in 90 hours.
Answer: E) 90 #### E
QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train?
options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm
SOLUTION:In one hour, the first train travels 60 km.
The second train catches the first train with a relative speed of 20 km/h.
The second train will catch the first train at 10:00 am.
The answer is B. #### B
QUESTION:The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is
options: A)112 B)22 C)56 D)27 E)35
SOLUTION:Explanation:
Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 16 and 28.
L.C.M. of 16 and 28 = 112.
Answer: Option A #### A
QUESTION:A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $45,000 commission, how many machines did she sell?
options: A) 140 B) 103 C) 105 D) 115 E) 120
SOLUTION:First 100 machines = 3% commission = 0.03*100*10000 = 30000
Commission from sale of next machines = 46000 - 30000 = 16000
So 40 more machines..
Total = 140 machines
IMO A.. #### A
QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there?
options: A)20 coins B)30 coins C)40 coins D)60 coins E)None of these
SOLUTION:Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 105
⇒ 1.75x = 105 ⇒ x = 60 coins
Answer D #### D
QUESTION:Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together.
options: A)10x11/10 B)10x10/11 C)11x10/11 D)12x10/11 E)None
SOLUTION:Solution
At 8 o'clock, the hour is at 8 and the minute hand is at 12,i.e. the two hands are 20 min. Spaces apart.
So, the minute hand gain = (30 - 20)minute
55 minutes will be gained in 60 min.
10 minutes spaces will be gained in (60/55 x10) min. = 10x10/11 min.
The hands will be in the same straight line but not together at 10x10/11 min.past 8.
Answer B #### B
QUESTION:How many numbers from 29 to 79 are exactly divisible by 11
options: A)5 B)7 C)8 D)9 E)11
SOLUTION:29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers
Option 'A' #### A
QUESTION:A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase?
options: A)10% B)12% C)14% D)16% E)18%
SOLUTION:Let x be the amount of money paid for the first purchase.
The second time, the customer paid 0.8(1.1x)=0.88x.
The difference is 12%.
The answer is B. #### B
QUESTION:The sale price sarees listed for Rs.390 after successive discount is 15% and 25% is?
options: A)298 B)237 C)248 D)876 E)291
SOLUTION:390*(85/100)*(75/100)
= 248
Answer: C #### C
QUESTION:If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
options: A)3⁄7 B)4⁄7 C)3⁄4 D)4⁄3 E)7⁄4
SOLUTION:Should be a sub-600 level Q..
volume= {3/7}/{4/7}=3/4
ANSWER:C #### C
QUESTION:A,B,C invested the capitals in a business. If A invested Rs. 20,000 more than B and C invested Rs.10,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000
options: A)5500, 2500, 6000 B)5200, 2800, 6000 C)4250, 2250, 7500 D)5250, 1750, 7000 E)5300, 2700, 6000
SOLUTION:A==30,000
B==10,000
C==40,000
so, ration are3:1:4
profit 14000
so,, 14000/8==1750
so,, A==5250, B==1750,, C==7000
ANSWER:D #### D
QUESTION:For an upcoming charity event, a male vocalist has agreed to sing 4 out of 6 “old songs” and 2 out of 5 “new songs.” How many ways can the singer make his selection?
options: A)25 B)50 C)150 D)480 E)600
SOLUTION:Number of ways the vocalist can sing "old songs" = C64=15
Number of ways the vocalist can sing "new songs" = C52=10
Therefore total number of ways the singer can make the selection = (Number of ways the vocalist can sing "old songs")*(Number of ways the vocalist can sing "new songs")= 15*10=150
Answer: C #### C
QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
options: A)34 B)97 C)37 D)80 E)22
SOLUTION:1/2 * d (10 + 6) = 640
d = 80
Answer: D #### D
QUESTION:A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
options: A)15 sec B)16 sec C)18 sec D)20 sec E)25 sec
SOLUTION:Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec
ANSWER: D #### D
QUESTION:In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive?
options: A)48400 B)48000 C)48100 D)48500 E)48600
SOLUTION:Assume that investment of C =x
Then, investment of A =2x
Investment of B =4x/3
A:B:C =2x:(4x)/3:x
=2:4/3:1=6:4:3
B's share =157300×4/(6+4+3)
=157300×4/13=12100×4=48400
Answer is A. #### A
QUESTION:The population of a city increases by 6% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
options: A)9% B)9.27% C)27% D)15.76% E)None of these
SOLUTION:Actual increase in population=5%
Let, earlier population=100 then the population after 3 years
=100(1+5/100)^3=115.7625
∴Required percentage=15.7625%
ANSWER:D #### D
QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is
options: A)35 B)37 C)38 D)41 E)42
SOLUTION:Explanation:
Let B's age = x years.
Then, As age = (x+ 8) years.
(x+8+10)=2(x—10)
hence x=38.
Present age of B = 38 years
Answer: Option C #### C
QUESTION:14 times a number gives 210. The number is
options: A)11 B)12 C)15 D)None E)Cannot be determined
SOLUTION:Explanation:
Let the number be 'N'
14×N=210⇒N=15
Correct Option: C #### C
QUESTION:Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
options: A)1040 B)1050 C)1055 D)1065 E)1075
SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055
C #### C
QUESTION:How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters
SOLUTION:Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x)))
2=5%*(13+x)-------->x=27
Ans B #### B
QUESTION:The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of
options: A)20% B)19% C)18% D)11% E)10%
SOLUTION:Say the original price of the TV was $p, then the final price would be (0.9p)∗0.9=0.81p. Therefore the original price was discounted by 19%.
Answer: B. #### B
QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15
options: A)8600 B)8610 C)8620 D)8630 E)8640
SOLUTION:Explanation:
LCM of 27-18-16-15 is 2160.
After dividing 9999 by 2160 we get 1359 remainder.
So answer will be 9999-1359 = 8640
Option E #### E
QUESTION:If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was
options: A)Rs 1.56 B)Rs 2.40 C)RS 3.00 D)Rs 3.80 E)Rs 4.20
SOLUTION:first 1/5 mile costs = 1.00
remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14,
hence 14*0.20=2.80
total fare = 2.80 + 1.00 =3.80
ANSWER:D #### D
QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit.
options: A)1200 B)1400 C)2660 D)1600 E)1800
SOLUTION:A is a working member and for that, he receive 5% of the profit
= 5% of 7400 = 5*7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = 6500*6 : 8400*5 : 10000*3
= 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20
= 13 : 14 : 10
Share of B in the profit = 7030 * (14/37) = 190*14 = 2660
Answer is C #### C
QUESTION:In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had?
options: A)10.7% B)20% C)25% D)33 1/3 E)58 1/3
SOLUTION:No of bank customers in 1985 = 60 x .45 = 27
No of bank customers in 1987 = 144 x .25 = 36
increase in % = 100 X 9/27 = 100/3 or 33 1/3
D is the correct answer #### D
QUESTION:A person borrows Rs. 6000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
options: A)120 rs B)150 rs C)160 rs D)180 rs E)200 rs
SOLUTION:Gain in 2 years =
[(6000*6*2)/100]-[(6000*4*2)/100]
720-480=240
Gain in 1 year =(240/2)=120 rs
ANSWER:A #### A
QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only?
options: A)24 B)27 C)30 D)33 E)36
SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only.
Since 10% of students are in both, then 70% of students are in the band which is 84 students.
The number of students in the orchestra is (30/70)*84 = 36.
The answer is E. #### E
QUESTION:(128.5 x 32) + (13.8 x 30) = ? x 25
options: A)524.48 B)556.02 C)574.36 D)181.04 E)595.46
SOLUTION:Explanation :
? = (128.5 x 32) + (13.8 x 30)/25
= 4112 + 414/25 = 181.04
Answer : Option D #### D
QUESTION:385, 462, 572, 396, 424, 671, 264
options: A)385 B)424 C)671 D)264 E)None of these
SOLUTION:Solution
In each number except 424,the middle digit is the sum of the other two. Answer B #### B
QUESTION:The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is?
options: A)126 B)156 C)190 D)300 E)260
SOLUTION:Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1950
X = 70
Required perimeter = 2(70+80) = 300
D #### D
QUESTION:Two of his favorite buildings are Chicago’s Sears (Willis) Tower and
Dubai’s Burj Khalifa. If Burj Khalifa stands at 830 meters high and
Sears stands at 527 meters high, how much higher is Burj Khalifa than Sears?
options: A)300 B)250 C)130 D)303 E)111
SOLUTION:830-527=303. Answer is D. #### D
QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
options: A)69 B)78 C)96 D)56 E)48
SOLUTION:let the digits be x,y
x + y = 15
x - y = 3
2x = 18, x = 9 so y = 6
hence the number is 96
so the correct answer is option C) 96. #### C
QUESTION:4y - 4x = xy and x ≠ 0. If x and y are integers, which of the following could equal y?
options: A)2 B)1 C)0 D)5 E)6
SOLUTION:Plug in the answer choices in the equation from the question stem.
A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE
B) y = 1 >>> 2 - x = 2x >>> Same, POE
C) y = 0 >>> -x = 0 >>> x can not equal 0
D) y = -1 >>> 8 - 4x = 4x >>> Holds true for x = 1, no need to check E. This is the answer.
Answer A #### A
QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
a.
b.
c.
d.
e.
options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5)
SOLUTION:no of different stocks for 4-letter code = 26^4
no of different stocks for 4-letter code = 26^5
total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4)
ANS:C #### C
QUESTION:What is the area of a square field whose diagonal of length 24 m?
options: A)256 B)289 C)200 D)288 E)178
SOLUTION:d2/2 = (24 * 24)/2
= 288
Answer: D #### D
QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 9 minutes earlier. How far is the office from his house?
options: A)3 2/5 Km B)3 1/5 Km C)4 1/5 Km D)5 1/5 Km E)None
SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 17/6
= 24/2 * 17/60
= 17/5 = 3 2/5 Km
A #### A
QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 190 books with me to gift her.
Can you calculate, on which day is our anniversary?
options: A)31 B)28 C)19 D)33 E)25
SOLUTION:C
19rd day
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190
Thus our anniversary falls on the 19rd day of the month.
You can apply other formulas to shorten the process but that is the simplest way to do it. #### C
QUESTION:On a ranch, a rancher can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 4 attempts?
options: A)3/4 B)5/8 C)7/8 D)11/16 E)15/16
SOLUTION:P(missing all 4)=(1/2)^4=1/16
P(success on at least one attempt)=1-1/16=15/16
The answer is E. #### E
QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters)
options: A)92 B)90 C)82 D)78 E)75
SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
O=12.5*6 = 75=E #### E
QUESTION:The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ?
options: A)20 years B)21 years C)22 years D)34 years E)24 years
SOLUTION:The average age of the 5 members is 20 years
=> The sum of the ages of the 5 members is 20*5 = 100 years
Once the new member joins, the average age becomes 24 years.
Let the age of the new member be x.
Then (110+x)/6 = 24
=> x = 34 years
Answer D #### D
<<<Examples ends
QUESTION:In an entrance exam, 3 marks is awarded for every correct answer and (-1) for every wrong answer. If a student gets 38 marks after attempting all questions, find the number of questions answered correctly if the total questions were 70.
options: A)27 B)88 C)26 D)29 E)71
SOLUTION:Explanation:
Let x be the number of questions answered correctly. Hence, number of questions whose answer were wrong = (70 – x)
3*x + (70 – x)*(-1) = 38
4x = 38 + 70 = 108
x = 27
ANSWER:A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period?
options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3
SOLUTION:600 dollars in 2 years means 300 dollars in 1 year.
To get 2400 dollars' it will take 8 years.
To get 2400 in 3 years, we need 8/3 times money.
Answer is E. #### E
QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
options: A)21 B)36 C)39 D)60 E)65
SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room.
Therefore there are 3/8*96=36 people in the room under the age of 21.
Answer: B. #### B
QUESTION:If x:y=9:4 then (7x-3y) : (7x+3y)=?
options: A)51:76 B)6:13 C)51:75 D)51:76 E)None of these
SOLUTION:Explanation:
x/y = 9/4 (Given)
(7x − 3y)/(7x + 3y)
7(x/y) − 3/7(x/y)+3
( on dividing Nr and Dr by y)
(7(9/4) − 3)/(7(9/4) + 3)
(63/4 − 3/1)/(63/4 + 3/1)
[(63 − 12)/4]/[(63 + 12)/4] = 51/75
(7x-3y) : (7x+3y) = 51:75
Answer: Option C #### C
QUESTION:Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
options: A)8 B)6 C)4 D)10 E)12
SOLUTION:Together they make 5/4 w widgets in 3 days. So they make w widgets in 3*4/5 = 12/5 days.
1/(t+2) + 1/t = 5/12
Now, calculating this is really cumbersome so try to plug in options to get to the answer.
If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4.
1/6 + 1/4 = 5/12
It works so t = 4.
Answer : A #### A
QUESTION:A tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?
options: A)20 B)22 C)24 D)26 E)28
SOLUTION:Let the original side of the square be x.
(x-12)*(x-10) = 120 = 10*12
x = 22
The answer is B. #### B
QUESTION:Can you deduce the pattern and find the next number in the series?
7, 15, 27, 99, __?
options: A)276 B)277 C)278 D)279 E)None of these
SOLUTION:Solution:
277
Explanation:
7 = (1^1 + 2^1 + 3^1) +1
15 = (1^2 + 2^2 + 3^2) +1
37 = (1^3 + 2^3 + 3^3) +1
99 = (1^4 + 2^4 + 3^4) +1
Thus the next number will be
(1^5 + 2^5 + 3^5) +1 = 277
Answer B #### B
QUESTION:1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
options: A)$140 B)$125 C)$145 D)$135 E)$155
SOLUTION:Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
ANSWER : OPTION C =$145 #### C
QUESTION:Two whole numbers whose sum is 72 cannot be in the ratio
options: A)3 : 4 B)3 : 5 C)4 : 5 D)5 : 7 E)None
SOLUTION:Sol.
The sum of the ratio terms must divide 72. So, the ratio
cannot be 3 : 4.
Answer A #### A
QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum Q of even integers from 102 to 200 inclusive?
options: A)5100 B)7550 C)10100 D)15500 E)20100
SOLUTION:My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
Q=2550+(100*50)=7550.B #### B
QUESTION:If xy > 0, which of the following must be negative?
options: A)-x/y B)xy C)x/y D)2xy E)2x/y
SOLUTION:- / + = -
Answer : A #### A
QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 9000 interest. The principal amount borrowed by him was.
options: A)Rs 14000 B)Rs 25000 C)Rs 16000 D)Rs 17000 E)None of these
SOLUTION:Explanation:
S.I.=P∗R∗T/100
=>P=S.I.∗100/R∗T
=>P=9000∗100/12∗3=Rs25000
Option B #### B
QUESTION:By investing in 1623% stock at 64, one earns Rs. 1600. The investment made is
options: A)s. 9600 B)s. 7500 C)s. 5640 D)s. 6144 E)s. 6760
SOLUTION:Explanation :
Market Value = Rs.64
Face Value is not given and hence take it as Rs.100
16 2/3% of the face value = 50/3
ie, to earn 50/3, investment = Rs.64
Hence, to earn Rs.1600, investment needed = 64×3×1600/50=6144
Answer : Option D #### D
QUESTION:3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
options: A)8 B)10 C)12 D)18 E)20
SOLUTION:Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D #### D
QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
options: A)18% B)19% C)28% D)68% E)48%
SOLUTION:1500 ---- 270
100 ---- ? => 18%
Answer: A #### A
QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true?
options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11
SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E
QUESTION:A team consists of 4 boys and 3 girls. If you pick two persons at the same time, what's the probability that one person is boy and other one is girl ?
options: A)2/7 B)5/7 C)4/7 D)3/7 E)1/2
SOLUTION:P(1st b, 2nd g) = 4/7*3/6 = 4/14;
P(1st g, 2nd b) = 3/7*4/6 = 4/14.
P = 4/14 + 4/14 = 4/7.
Answer: C. #### C
QUESTION:There are 22 students in a class. In how many different ways can a committee of 3 students be formed?
options: A)1180 B)1320 C)1540 D)1760 E)1920
SOLUTION:22C3 = 22*21*20 / 6 = 1540
The answer is C. #### C
QUESTION:A palindrome is a number that reads the same forward and backward, such as 242. How many even thirteen-digit numbers are palindromes?
options: A)40 B)400 C)500 D)5,000 E)40,000,000
SOLUTION:if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144.
The middle number in the thirteen-digit could be 0-9 ( 10 ways), e.g 2222225222222, 2864228224682
The 2nd and fourth numbers , the 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways)
we thus have, 4 *10*10*10*10 *10*10= 4000000.E #### E
QUESTION:The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result?
options: A)600 B)480 C)538 D)650 E)560
SOLUTION:23th result = sum of 45results - sum of 44 results
10*45-16*22+20*22 = 450-352+440 = 538
Answer is C #### C
QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?
options: A)10.5 B)15 C)15.5 D)30 E)60
SOLUTION:The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes
It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10
x=15.5 minutes
Answer: C #### C
QUESTION:From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn
options: A)4/13 B)1/52 C)1/4 D)1/5 E)None of above
SOLUTION:Explanation:
Total number of cases = 52
Total face cards = 16 [favourable cases]
So probability = 16/52 = 4/13
Answer: A #### A
QUESTION:If 9^y = 3^12, what is y?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:3^2y = 3^12
2y=12, therefore y=6
E #### E
QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is
options: A)2970 B)297 C)2997 D)300 E)30
SOLUTION:(1/10)*3000 - (1/10)%*3000 =
300 - (1/1000)*3000 =
300 - 3 = 297
The answer is B. #### B
QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder?
options: A)7 B)10 C)8 D)12 E)15
SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C
QUESTION:Two thirds of the roads from A to B are at least 5 miles long, and 3/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
options: A)1/6 B)1/4 C)2/3 D)3/4 E)11/12
SOLUTION:So please:
Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-1/3*1/4=11/12.
Answer: E. #### E
QUESTION:How many of the positive factors of 19 are not factors of 29?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Factors of 19 - 1, 19
factors of 29- 1, 29
Comparing both, we have three factors of 19 which are not factors of 29- 19,
The answer is B #### B
QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race?
options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m
SOLUTION:C
111.12 m
X runs 1000 m while Y runs 900 m and Z runs 800 m.
The number of meters that Z runs when Y runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
Y can give Z = 1000 - 888.88 = 111.12 m. #### C
QUESTION:The fourth proportional to 14, 22 and 28 is?
options: A)21 B)66 C)88 D)99 E)44
SOLUTION:(22*28)/14 = 44
Answer: E #### E
QUESTION:a, b, c, and d are positive consecutive even integers and a < b < c < d.
If the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers?
options: A)2 B)4 C)8 D)12 E)20
SOLUTION:We know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on.
The product ad is 6 more than the sum bc. By testing some possible ad products (even numbers separated by two other even numbers), we can quickly see that the numbers have to be quite small: 6x12 is 72, much higher than any of the possible sums, and the products will go up much faster than the sums will.
However, the lowest possible sequence gives an ad product of 2x8, or 16. And summing the middle numbers gives 10, exactly six less than the product. We have found the sequence: 2-4-6-8.
The answer, then, is the product of the smallest two numbers, or 2x4, which is 8 (option C). #### C
QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.756 find the share of A.
options: A)240 B)388 C)288 D)277 E)122
SOLUTION:Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 756 = 288
Answer: C #### C
QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job?
options: A)4 days B)6 days C)8 days D)2 days E)9 days
SOLUTION:Sandy can do 1/6 of the job each day.
Molly can do 1/12 of the job each day.
The combined rate is 1/6 + 1/12 = 1/4 of the job each day.
The job will take 4 days.
The answer is A. #### A
QUESTION:The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is?
options: A)126 B)156 C)190 D)300 E)260
SOLUTION:Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1950
X = 70
Required perimeter = 2(70+80) = 300
D #### D
QUESTION:In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥60. The smallest n which fulfills this condition is n = 8.
Answer C #### C
QUESTION:A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
options: A)5520 B)2789 C)5550 D)2889 E)2788
SOLUTION:Total production of salt by the company in that year = 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year = 66600/12 = 5550.
Answer: C #### C
QUESTION:If Jenee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased?
options: A)1/4 B)1/5 C)1/10 D)3/50 E)1/20
SOLUTION:Perhaps it is also easy to just translate the % into fractions:
6%: 6/100 = 3/50
7%: 7/100
8%: 8/100 = 4/50 =2/25
9%: 9/100
Only 3/50 exists in the answer choices, so ANS D #### D
QUESTION:If four coins are tossed, the probability of getting two heads and two tails is ?
options: A)3/8 B)3/6 C)3/1 D)3/2 E)3/4
SOLUTION:Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A #### A
QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
options: A)12 B)15 C)16 D)18 E)19
SOLUTION:one day work done by A=1/20
work done by A in 2 days=1/10
work done by A,B,C on 3rd day=1/10+1/10=1/5
1/5th of the work will be completed at the end of 3 days
the remaining work =1-1/5=4/5
1/5 of work is completed in 3 days
total work wiil be done in 3*5=15 days
ANSWER:B #### B
QUESTION:How many different eight letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
options: A)59 B)11!/(2!*2!*2!) C)56 D)76 E)11!/(3!*2!*2!*2!)
SOLUTION:E- -R
We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.
We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.
2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.
Total = 56 + 3 = 76.
Answer: D. #### D
QUESTION:The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
options: A)70 B)72 C)75 D)78 E)80
SOLUTION:Income of 6 months = (6 × 85) – debt
= 510 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 780
Average monthly income = 780 ÷ 10 = 78
Answer D #### D
QUESTION:A,B,C invested the capitals in a business. If A invested Rs. 20,000 more than B and C invested Rs.10,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000
options: A)5500, 2500, 6000 B)5200, 2800, 6000 C)4250, 2250, 7500 D)5250, 1750, 7000 E)5300, 2700, 6000
SOLUTION:A==30,000
B==10,000
C==40,000
so, ration are3:1:4
profit 14000
so,, 14000/8==1750
so,, A==5250, B==1750,, C==7000
ANSWER:D #### D
QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?
options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2)
SOLUTION:5 LINES IN 20 SECONDS
SO FOR 1 MINUTE ( 5 X 3 = 15 LINES )
I HOUR = 60 MINUTES
15 X 60 = 900 LINES IN AN HOUR
11 HOURS = 900 X 11 = 99(10^2)
ANSWER E #### E
QUESTION:Which of the following is(are) true for a@b=b@a?
I. a@b=b+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ
SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A
QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages.
options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these
SOLUTION:Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 136
20x = 160 => x = 8
Their present ages are 32, 56 and 72 years respectively.
ANSWER:D #### D
QUESTION:he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
options: A)0 B)1 C)10 D)19 E)8
SOLUTION:Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a).
Answer: Option D #### D
QUESTION:Lisa plays a dice game in which she rolls two, fair, six-sided dice two times. If her second roll matches her first roll, she wins. What is the probability that she wins if her first roll was 10?
options: A)1/6 B)5/36 C)1/9 D)1/12 E)1/18
SOLUTION:There are 3 ways to roll a 10 with two six-sided dice: 4 and 6, 6 and 4, 5 and 5. You only count 5 and 5 once.
There are 6*6=36 ways to roll two six-sided dice. Thus the probability of rolling a 10 is 3/36 = 1/12.
D #### D
QUESTION:A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent?
options: A)25% B)5% C)10% D)15% E)20%
SOLUTION:3000 --- 600
100 --- ? => 20%
Answer: E #### E
QUESTION:A person spent Rs. 5,040 from his salary on food and 5,000 on house rent. After that he was left with 20% of his monthly salary. What is his monthly salary ?
options: A)22,550 B)32,550 C)52,550 D)62,550 E)12,550
SOLUTION:Total money spent on food and house rent = 5,040+5,000 = 10,040
Which is 100 - 20 = 80% of his monthly salary
∴ His salary = 10040x100/80 = 12550
Answer : E #### E
QUESTION:In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ?
options: A)100 B)72 C)110 D)135 E)145
SOLUTION:Explanation :
Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x.
.'. 60% of x = 36 +5/6 *36
=>60/100 * x = 66
=>x = 110
Answer : C #### C
QUESTION:A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is?
options: A)200 B)150 C)455 D)300 E)600
SOLUTION:Amount = (15000)* (1 + (3/4*100))^4
Amount = 15000 * (1+ 0.0075)^4 = 15455 ------(for investment in 1st month)
Interest = 15455-15000 = 455..............
Ans -C #### C
QUESTION:Mary works in a restaurant a maximum of 60 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
options: A)300 B)420 C)560 D)320 E)400
SOLUTION:Mary receives $8(20)=$160 for the first 20 hours.
For the 40 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(40)=$400.
The total amount is $160+$400 = $560
Answer C 560. #### C
QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor?
options: A)163 B)785 C)852 D)456 E)852
SOLUTION:Divisor *quotient+remainder=dividend
divisor=(dividend)-(remainder)/quotient
(12401-13)/76=163
Answer(A) #### A
QUESTION:For which of the following functions f is f(c) = f(1-c) for all c?
options: A)f (c) = 1 - c B)f (c) = 1 - c^2 C)f (c) = c^2 - (1 - c)^2 D)f (c) = c^2*(1 - c)^2 E)f (x) = x/(1 - x)
SOLUTION:I remember seeing this problem in a GMATprep test. I think choice D should be F(c)=(c^2) (1-c)^2. If that is true then substituting (1-c) for will give us the same function back and the answer choice is D, where the function is multiplicative #### D
QUESTION:In Bangalore there is a well known Science Institute. During a visit I asked two of the men to tell me their ages. One replied, 'One of our ages subtracted from the other's equal 30.'
Then the other man spoke . 'Our ages multiplied together equal 1624.'
What were their ages?
options: A)60 and 23 B)66 and 25 C)29 and 56 D)71 and 43 E)58 and 28
SOLUTION:E
Their ages were respectively 58 and 28 #### E
QUESTION:Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
options: A)2 : 3 : 4 B)6 : 7 : 8 C)6 : 8 : 9 D)4 : 6 : 8 E)None of these
SOLUTION:Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
(140/100 * 5x), (150/100 * 7x) and (175/100* 8x)
7x, 21x/2 and 14x
The required ratio = 7x : 21x/2 : 14x
14x : 21x : 28x
2 : 3 : 4
Answer = A #### A
QUESTION:There are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?
options: A)980 B)1150 C)1360 D)1540 E)1720
SOLUTION:The number of ways to choose two teams is 17C2 = 17*16/2 = 136
The total number of games in the season is 10*136 = 1360.
The answer is C. #### C
QUESTION:A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
options: A)1:3 B)1:2 C)2:3 D)2:1 E)3:1
SOLUTION:From the wording in the prompt, we're essentially mixing two liquids:
Liquid X is 40% concentrate
Liquid Y is 25% concentrate
We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra:
X = # of ounces of liquid X
Y = # of ounces of liquid Y
(.4X + .25Y) / (X + Y) = .35
.4X + .25Y = .35X + .35Y
.05X = .1Y
5X = 10Y
From here, you have to be CAREFUL to answer the question that is ASKED.
5X = 10Y
Y/X = 5/10 = 1/2
ANSWER:B #### B
QUESTION:The wages earned by Robin is 44% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?
options: A)23% B)18.75% C)30% D)30.55% E)100%
SOLUTION:Explanatory Answer
Let the wages earned by Erica be $100
Then, wages earned by Robin and Charles will be $144 and $160 respectively.
Charles earns $44 more than Robin who earns $144.
Therefore, Charles' wage is 44/144*100 = 30.55%.
The correct choice is (D) #### D
QUESTION:A shopkeeper purchased 85 kg of potatoes for Rs. 595 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent?
options: A)18 1/9 % B)18 9/3 % C)18 1/3 % D)14 2/7 % E)18 7/3 %
SOLUTION:C.P. of 1 kg = 595/85 = Rs. 7
S.P. of 1 kg = Rs. 8
Gain % = 1/7 * 100 = 100/7 = 14 2/7 %
Answer: D #### D
QUESTION:3,8,18,38,78,__
options: A)158 B)156 C)154 D)150 E)148
SOLUTION:8=3*2+2
18=8*2+2
38=18*2+2
78=38*2+2
158=78*2+2
ANSWER:A #### A
QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years
options: A)27 B)24 C)40 D)32 E)35
SOLUTION:sameer and anand be 5x years and 4x years respectively
(5x+3)/(4x+3)=11/9
9(5x+3)= 11(4x+3), 45x+27=44x+33
45x-44x=33-27
x=6, therefore anand's present age : 4x=24 years
correct answer(B) #### B
QUESTION:If a number p is prime, and 2p+4 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?
options: A)1 B)3 C)5 D)7 E)9
SOLUTION:1/6 = 0.1666666... (a repeating pattern one digit long)
A #### A
QUESTION:9 - 3 ÷ 1/3 + 4 = ?
options: A)4 B)3 C)6 D)9 E)12
SOLUTION:9 - 3 1/3 + 4
=9-3÷1/3+4
=9-(3X3) +4
=9-9+4
=4
CORRECT ANSWER : A #### A
QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10 is?
Can someone please explain intuitively what the question is asking?
options: A)5 B)9 C)12 D)15 E)30
SOLUTION:In order x! to be divisible by 1,0, it should have at least 1 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 1.
5! = 120 has 1 trailing zeros.
Answer: A #### A
QUESTION:If two letters are chosen at random (without replacement) from the word COMPUTER, what is the probability that none of the letters are vowels?
options: A)2/7 B)3/7 C)3/14 D)5/14 E)11/28
SOLUTION:The number of ways to choose two letters is 8C2 = 28
The number of ways to choose two consonants is 5C2 = 10.
P(no vowels) = 10/28 = 5/14
The answer is D. #### D
<<<Examples ends
QUESTION:Find the simple interest on Rs. 73,000 at 16 2/3% per year for 9 months.
options: A)7500 B)6500 C)8125 D)9125 E)None of them
SOLUTION:P = Rs.73000,R = 50/3% p.a and T = 9/12 years = 3/4years.
Simple Interest = (P*R*T)/100 = Rs.(73,000*(50/3)*(3/4)*(1/100))= Rs.9125
Answer is D. #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
options: A)8*9! B)8*8! C)7*9! D)9*8! E)None
SOLUTION:Solution: No. of ways in which 10 paper can arranged is 10! Ways.
When the best and the worst papers come together, regarding the two as one paper, we have only 9 papers.
These 9 papers can be arranged in 9! Ways.
And two papers can be arranged themselves in 2! Ways.
No. of arrangement when best and worst paper do not come together,
= 10!- 9!.2! = 9!(10-2) = 8.9!.
Answer A #### A
QUESTION:A bag contains 6 green jacks and 24 white jacks. One jack is drawn at random. What is the probability that the jack is white?
options: A)3/4 B)4/5 C)7/8 D)1 E)None of these
SOLUTION:Explanation:
Total cases = 6 + 24 = 30
Favourable cases = 24
So probability = 24/30 = 4/5
Answer: A #### A
QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities?
options: A)48 B)72 C)96 D)120 E)192
SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance Q to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E #### E
QUESTION:How many words can be formed by using all letters of the word “BIHAR”
options: A)452 B)320 C)365 D)456 E)120
SOLUTION:The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
Ans: E #### E
QUESTION:9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day?
options: A)18 B)9 C)10 D)8 E)11
SOLUTION:We have, M1D1H1 = M2D2H2
So, 9*12*4= 6*D2*8
D2 = 9*12*4/6*8 = 9
ANSWER:B #### B
QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week?
options: A)40 B)30 C)35 D)25 E)45
SOLUTION:For 30 hrs = 30*16=480
Excess = 760-480=280
For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28
Number of extra hrs =280/28=10
Total hrs =30+10=40
Answer A 40 #### A
QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
options: A)1200 B)1723 C)1129 D)2613 E)1372
SOLUTION:A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 150= 3k + 150 => 2k = 300 => k = 150
The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A
QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 65% increase on the price he bought it. What percent of profit did he make on the original price?
options: A)A)2% B)B)12% C)C)14% D)D)20% E)E)32%
SOLUTION:Original price = 100
CP = 80
S = 80*(165/100) = 132
100 - 132= 32%
E) #### E
QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had?
options: A)23 B)24 C)25 D)26 E)27
SOLUTION:Explanation :
If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible
number of books = 15,17,19,21,23,25,27,29
If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible
number of books = 17,20,23,26,29
If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible
number of books = 15,19,23,27
Hence ,the common number is only 23 so it will be answer.
Answer : A #### A
QUESTION:Which of the following equations has a root in common with x^2−4x+3=0 ?
options: A)x^2-4x-4=0 B)x^2-2x+1=0 C)x^2-x-1=0 D)x^2-10x-1=0 E)x^2+1=0
SOLUTION:If we carefully look at the given equation we can arrange it in the following manner:
(x-1)(x-3) = 0
so the two roots are 1 and 3.
Now put 1 and 3 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 1: we get -7; Putting 3 we get -7. Reject this option.
(B) putting 1: we get 0. This is the equation.
We are lucky. No need to check other options.
B is the answer. #### B
QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price
options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/-
SOLUTION:100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
A #### A
QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
.
options: A)Rs. 650 B)Rs. 690 C)Rs. 698 D)Rs. 700 E)Rs. 720
SOLUTION:S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698. Answer: Option C #### C
QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
options: A)29 B)29 C)60 D)19 E)12
SOLUTION:Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5
= 60 km/hr.
Answer:C #### C
QUESTION:The current of a stream runs at the rate of 3 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
options: A)A)7.24 B)B)2 C)C)8.5 D)D)6.67 E)E)3
SOLUTION:S = 3
M = x
DS = x + 3
US = x - 3
6/(x + 3) + 6/(x - 3) = 2
x = 7.24
Answer:A #### A
QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
options: A)10 B)12 C)15 D)20 E)25
SOLUTION:Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
ANSWER:B #### B
QUESTION:The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago?
options: A)1: 3 B)2: 3 C)3:3 D)4: 3 E)5: 4
SOLUTION:3x-25/2x-25 = 4/3
Therefore x=-25
Age cannot be negative.
Answer: D #### D
QUESTION:How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?
options: A)56 B)72 C)48 D)60 E)59
SOLUTION:The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged amongst themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48 ways.
Total number of words formed by using all the letters of the given words
= 5! = (5x4x3x2x1) = 120.
Number of words, each having vowels never together = (120-48) = 72.
Ans: B #### B
QUESTION:Find the unit's digit in the product 2467 153 * 34172?
options: A)1 B)3 C)2 D)5 E)7
SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172
Now 7 4 gives unit digit 1
7 152 gives unit digit 1
7 153 gives 1*7=7.Also 172 gives 1
Hence unit's digit in the product =7*1=7.
Option A #### A
QUESTION:What is the probability of drawing a queen from a deck of 52 cards?
options: A)4/13 B)1/13 C)4 D)1 E)2/13
SOLUTION:Total number of cards,n(s)=52
Total number of queen cards,n(e)=4
p(e)=n(e)/n(s)=4/52=1/13
Option B is answer #### B
QUESTION:If x is a sum of all even integers on the interval 13...63 and y is their number, what is the GCD (x, y)?
options: A) 1 B) 13 C) 26 D)25 E) 1014
SOLUTION:x = 14 + 16 + ... + 62 = (largest + smallest)/2 *(# of terms) = (14 + 62)/2*25 = 38*25.
GCD of 25 and 39*25 is 25.
Answer: D. #### D
QUESTION:A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is?
options: A)200 B)150 C)455 D)300 E)600
SOLUTION:Amount = (15000)* (1 + (3/4*100))^4
Amount = 15000 * (1+ 0.0075)^4 = 15455 ------(for investment in 1st month)
Interest = 15455-15000 = 455..............
Ans -C #### C
QUESTION:What is the remainder when 25472 is divided by 2?
options: A)3 B)1 C)8 D)7 E)0
SOLUTION:If the digit in unit place is even, the number will be divisible by 2.
2 is an even number,so the number is divisible by 2
ANSWER:0 #### E
QUESTION:In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old?
options: A)231/260 B)117/130 C)51/65 D)23/32 E)11/16
SOLUTION:The number of people younger than 70 years old is 2600-800 = 1800
The number of females older than 70 years old is 0.6*850 = 510
The number of people who are either female or younger than 70 is 1800+510 = 2310.
P(a person is younger than 70 or male) = 2310/2600 = 231/260
The answer is A. #### A
QUESTION:How many seconds does a train 110 meters long, traveling at 54 km/h, take to completely cross a bridge of 160 meters in length?
options: A)18 B)20 C)22 D)24 E)26
SOLUTION:54 km/h = 54000/3600 = 15 m/s
Time = 270 / 15 = 18 seconds
The answer is A. #### A
QUESTION:What is the HCF of 2/3, 4/15 and 6/5
options: A)7/45 B)2/45 C)4/15 D)8/45 E)2/15
SOLUTION:Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 15, 5) = 2/15
Answer: Option E #### E
QUESTION:In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N?
options: A)(N-M) B)MN/(M + N) C)(NM) D)(N-M)/(M+N) E)NONE OF THESE
SOLUTION:The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N).
Answer: B #### B
QUESTION:The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?
options: A)(P-7)*6 B)(P-7)*5 C)(P-7)*2 D)(P-7)*3 E)(P-7)*4
SOLUTION:M/84 =(P-7)/21
M = (P-7)*84/21
=(P-7)*4
E #### E
QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24?
options: A)101 B)187 C)191 D)201 E)287
SOLUTION:here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 24 = t 3 + 3 + 4 + 5 + 6....+ 23
the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 23 sequence is equal to n*(n+1)/2 with n being 23, so equal to 23 * 24 / 2 = 276
so :
t 20 = t 3 + 276 - 3
t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E
QUESTION:Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
options: A)35 years B)77 years C)55 years D)44 years E)33 years
SOLUTION:Let the present ages of X and Y be 5x and 6x years respectively.
Then, (5x + 7)/(6x + 7) = 6/7
7(5x + 7) = 6(6x + 7) => x = 7
X's present age = 5x = 35 years.Answer: A #### A
QUESTION:In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y?
options: A)6 B)3 C)4 D)5 E)7
SOLUTION:lets start from z, as per the question stem
z + 5 + 7 = 16
-->> z= 4
similarly, y + 4 + 5 = 7
--> y = -2
similarly,, x + -2 + 4 = 5
--> x = 3
hence , x-y = 3+2 = 5
ANSWER:D #### D
QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
options: A)5 B)2 C)8 D)4 E)16
SOLUTION:1. We need to find out the time taken by 7 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 16*8 = 128 days
4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job.
5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7* total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days.
6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days.
The answer is choice E #### E
QUESTION:A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 80 km downstream?
options: A)2 hours B)3 hours C)4 hours D)5 hours E)None
SOLUTION:Solution
Speed Downstream = (13 + 4) km/hr
= 17 km/hr.
Time taken to travel 80 km downstream =(80 / 17)hrs
= 4 hrs 42 minutes.
Answer E #### E
QUESTION:A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible?
options: A)3 B)Z=4 C)Z=5 D)Z=6 E)Z=8
SOLUTION:The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8.E #### E
QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is
options: A)70 B)71 C)72 D)73 E)74
SOLUTION:Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=264
<=>11x/3=264
=>x=72
Answer: Option C #### C
QUESTION:The age of teacher is the same as the digit in the student's age, but in reverse order. In five years teacher will be twice as old as student will be then. what is the difference in their current age ?
options: A)18 B)12 C)25 D)13 E)7
SOLUTION:Teacher's age= 10x+y so student's age= 10y+x..
after 5 years , 10x+y+5=2*(10y+x+5)....
so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is A..18 #### A
QUESTION:Two friends run the New York City marathon, one friend finishes the marathon in 400 minutes while the second friend finishes the marathon in 625 minutes. What is the ratio of their speed?
options: A)10 : 12 B)1 : 2 C)5 :10 D)20 : 25 E)None
SOLUTION:Solution
Let us name the friends
as A and B. = ( Friend A'S speed) : (Friend B's speed)
=√b : √a
= √400 : √625
= 20 : 25
Answer D #### D
QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 6 years older than B the present age of B is
options: A)37 B)36 C)39 D)40 E)41
SOLUTION:let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+6
=>2b-b-6 = 30
b=36
so the present age of b is 36 years
ANSWER:B #### B
QUESTION:A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
options: A)240 B)250 C)260 D)230 E)220
SOLUTION:Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 36
=> 300+L = 15×36 = 540
=> L = 540-300 = 240 meter
Answer is A. #### A
QUESTION:Which of the following number will completely divide (49^15)-1?
options: A)8 is the number B)6 C)22 D)12 E)14
SOLUTION:x^n - 1 will be divisible by x+1 only when n is even.
49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8
Answer is A #### A
QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
options: A)6 hrs 21 min B)6 hrs 71 min C)6 hrs 32 min D)6 hrs 27 min E)6 hrs 23 min
SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer:A #### A
QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet?
options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m
SOLUTION:D = 50 * 1 ½ = 75 km
RS = 75 – 50 = 25
T = 75/25 = 3 h
3.30 + 3 h = 6.30 p.m.
Answer: C #### C
QUESTION:In how many ways can 5 people, A, B, C, D, E, be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
options: A)384 B)396 C)576 D)24 E)696
SOLUTION:Number of total arrangements = 5!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
5! - (4!*2*2) = 120 - (24*2*2) = 24
Answer D #### D
QUESTION:A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform?
options: A)45 B)47 C)49 D)51 E)53
SOLUTION:Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 14 * 10 = 140 m.
The time taken to pass the platform = (140 +370)/ 10 = 51 seconds
The answer is D. #### D
QUESTION:How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
options: A)5040 B)40 C)400 D)5000 E)6000
SOLUTION:LOGARITHM => 10 diff letters
req no of words = No of arrangements of 10 letters taking 4 at a time
=> 10P4 = (10*9*8*7)
==> 5040
ANSWER A #### A
QUESTION:The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)
options: A)200π B)240π C)300π D)480π E)1,200π
SOLUTION:Distance traveled in 1 revolution = 2πr= 2π10/5280
Revolutions in one second= 1320
Revolutions in 60 seconds (one minute)= 1320*60
Total distance traveled= total revolutions *distance traveled in one revolution
1320*60 *2π10/5280= 300π
C is the answer #### C
QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3?
options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10
SOLUTION:arrangement = 5!/3!=20
Probability of getting all 3 balls=
3 from 5=5c3
1 from 3 red ball,1 green,1 yellow
(3c1*1c1*1c1)/5c3 =3/10
ANSWER:A #### A
QUESTION:The largest 4 digit number exactly divisible by 88 is?
options: A)9930 B)9936 C)9944 D)9952 E)9960
SOLUTION:Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
C) #### C
QUESTION:A certain sum of money at simple interest amounted Rs.640 in 10 years at 3% per annum, find the sum?
options: A)442.3 B)492.3 C)592.3 D)402.3 E)472.3
SOLUTION:640 = P [1 + (10*3)/100]
P = 492.30
ANSWER:B #### B
QUESTION:A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
options: A)24 B)72 C)720 D)336 E)420
SOLUTION:The left window will have permutations of the 5 fiction books, so the number of possibilities for that window is
permutations = 5! = (5)(4)(3)(2)(1) = 120
The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is
permutations = 3! = (3)(2)(1) = 6
Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 120*6 = 720
Answer: C. #### C
QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years?
options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11
SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320
C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5
Difference = (360.5 - 320) = Rs. 40.5
Answer: C #### C
QUESTION:A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 680 dollars, and, in a third, loses 80. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ?
options: A)-280 B)300 C)-350 D)-380 E)None
SOLUTION:In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 680 - 80 = 250
And x = -350.
Answer C #### C
QUESTION:If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b?
options: A)35 B)42 C)45 D)49 E)54
SOLUTION:First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
35 = 7 * 5
45 = 3 * 3 * 5
so, (105)^3 = 3 * 7 * 7 * 5 * 3 *3 *5 *b
Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2
b = 5*7 = 35
Correct answer A. #### A
QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C?
options: A)2250 B)3000 C)3018 D)3019 E)3012
SOLUTION:60*5:36*6:75*3
100: 72: 75
75/247 * 7410 = 2250
Answer: A #### A
QUESTION:If 5a + 7b = n, where a and b are positive integers, what is the largest possible value of n for which exactly one pair of integers (a, b) makes the equation true?
options: A)35 B)48 C)69 D)70 E)74
SOLUTION:5*a1 + 7*b1 = n
5*a2 + 7*b2 = n
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.
Lets check how it works for our numbers, starting from the largest:
E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad
D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 to a we will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 from a, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus
D is the answer #### D
QUESTION:An old priest fell on a bottom of the well of a church.
The well is 16 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
options: A)12-days B)14-days C)11-days D)19-days E)10-days
SOLUTION:A
12-days
In 11-days, he will climb 11-inch and when he climbs 5 inch more, he will be out of the well :-) #### A
QUESTION:How many factors does 35^2 have?
options: A)2 B)8 C)24 D)25 E)26
SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 6*4 = 24
Answer C. #### C
QUESTION:At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 10'o clock.
options: A)60sec B)62sec C)66sec D)64sec E)54sec
SOLUTION:At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
.
.
9'o clock 8 *6=48sec
10'o clock 9 *6=54sec
So, 54sec at 10'o clock.
ANSWER:E #### E
QUESTION:Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in?
options: A)6 B)12 C)28 D)42 E)21
SOLUTION:The part of the tank filled by three pipes in one hour
= 1/14
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/14= 1/21.
The tank can be filled in 21 hours.
Answer:E #### E
QUESTION:If q and r are even integers, which of the following is an odd integer?
options: A)qr + 2 B)q(r − 1) C)q(q + 5) D)3q + 4r E)(q + 3)(r − 1)
SOLUTION:If q and r are even integers, then:
A. qr + 2: even + even = even
B. q(r − 1): even(odd) = even
C. q(q + 5): even(odd) = even
D. 3q + 4r: even + even = even
E. (q + 3)(r − 1): (odd)(odd) = odd.
Answer is E. #### E
QUESTION:What approximate value should come in place of the question mark (?) in the following equation?
1.542 × 2408.69 + 5134.632 = ?
options: A)4600 B)4800 C)5200 D)6400 E)8800
SOLUTION:Explanation 3700 + 5100 = 8800
Answer E #### E
QUESTION:A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is
options: A)2 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None
SOLUTION:Sol.
Speed of stream = 1/2(28-10) kmph = 4 kmph.
Answer B #### B
QUESTION:The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?
options: A)1000 B)1500 C)2000 D)3000 E)4000
SOLUTION:Let monthly income of A = a
monthly income of B = b
monthly income of C = c
a + b = 2 × 5050 .... (Equation 1)
b + c = 2 × 6250 .... (Equation 2)
a + c = 2 × 5200 .... (Equation 3)
(Equation 1) + (Equation 3) - (Equation 2)
=> a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250)
=> 2a = 2(5050 + 5200 - 6250)
=> a = 4000
i.e., Monthly income of A = 4000
Answer is E. #### E
QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water?
options: A) 16 B) 72 C) 112 D) 128 E) 144
SOLUTION:Solution:
We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water.
2x + 16x = 162
18x = 162
x = 9
Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water.
Answer E. #### E
QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
options: A)17% B)22.4% C)18% D)14% E)16%
SOLUTION:Total CP = Rs. 40000 + Rs. 13000
= Rs. 53000 and SP
= Rs. 64900
Profit(%) = (64900 - 53000)/53000 * 100
= 22.4%
Answer: B #### B
<<<Examples ends
QUESTION:If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
options: A)35 B)45 C)55 D)65 E)75
SOLUTION:(a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)
Therefore, the product should have factors with a difference of 2.
35 = 5*7, so this is a possible value for the original expression.
The answer is A. #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24?
options: A)101 B)187 C)191 D)201 E)287
SOLUTION:here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 24 = t 3 + 3 + 4 + 5 + 6....+ 23
the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 23 sequence is equal to n*(n+1)/2 with n being 23, so equal to 23 * 24 / 2 = 276
so :
t 20 = t 3 + 276 - 3
t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E
QUESTION:A man had to make 3 trips to the store because he kept forgetting items his wife had requested. The store was 500 meters from his home. It took the man 45 minutes to complete the store run. What was the man's speed in kilometers per hour.
options: A)2 B)1.5 C)2.25 D)3 E)1.75
SOLUTION:The distance between the man's home and the store is 500 meters.
3 times means that the man made the 500 meter trip 6 times in total.
6 * 500 = 3000 meters or 3 km.
Since the man's total time was 45 min, we need to multiply 3000 by 3/4 or .075.
Correct answer is 2.25 km per hour #### C
QUESTION:If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ?
options: A)16 B)1.6 C)0.16 D)0.016 E)None of these
SOLUTION:Explanation :
(204/12.75) = 16
⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10)
⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B #### B
QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
options: A)299 B)277 C)266 D)992 E)188
SOLUTION:(800*3*3)/100 = 72
920 + 72 = 992
Answer:D #### D
QUESTION:A worker's daily wage is increased by 40% and the new wage is $28 per day. What was the worker's daily wage before the increase?
options: A)$18 B)$20 C)$22 D)$24 E)$25
SOLUTION:Let x be the daily wage before the increase.
1.4x = $28
x = $20
The answer is B. #### B
QUESTION:In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
options: A)65 B)44 C)86 D)29 E)26
SOLUTION:Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: B #### B
QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00?
options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00
SOLUTION:For retail price = $25
First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5
Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14
Answer: Option A #### A
QUESTION:The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?
options: A)33 B)37 C)27 D)28 E)23
SOLUTION:Explanation:
Other side = = = = 6 ft
Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.
Answer: C) 27 #### C
QUESTION:Which of the following numbers is a perfect square?
options: A)1266 B)1444 C)2022 D)4034 E)8122
SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022.
38*38 = 1444
ANSWER:B #### B
QUESTION:If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
options: A)2 days B)1 day C)3 days D)5 days E)7 days
SOLUTION:The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
B) #### B
QUESTION:In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is
options: A)50 liters B)55 liters C)60 liters D)70 liters E)75 liters
SOLUTION:Quantity of milk = 60 x 2 litres = 40 litres.
3
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = 40 .
20 + x
Now, 40 = 1
20 + x 2
20 + x = 80
x = 60.
Quantity of water to be added = 60 liters.
C #### C
QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
options: A)1 B)3 C)4 D)5 E)6
SOLUTION:The distance between the nest and the ditch is 250 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 250 = 7500.
D = ST
7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km)
D) #### D
QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ?
options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these
SOLUTION:solution:
Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)]
=23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4.
∴ Required average =8.4/2 = 4.2 Answer B #### B
QUESTION:Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
options: A)2500 m^2 B)2510 m^2 C)2520 m^2 D)2540 m^2 E)2590 m^2
SOLUTION:Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C #### C
QUESTION:What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7?
options: A)397 B)401 C)403 D)405 E)364
SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=364.
Answer: E. #### E
QUESTION:11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
options: A)84 m B)88 m C)14 m D)137 m E)None
SOLUTION:Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22] = 1400cm = 14 m.
Answer C #### C
QUESTION:The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be
options: A)37:20 B)47:20 C)47:25 D)22:25 E)97:50
SOLUTION:Sailor = 1.85 * Officer
Sailor/Officer = 1.85/1 = 185/100 = 37/20
Answer will be A #### A
QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y?
options: A)x B)y C)3y + 2x D)y - x E)yx
SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take x = 1 and y = 2 and work with the options
xy = 2
A) x take x =2, y = 1
B) y take x = 1 y = 2
C) 3y + 2x Seems tricky, lets see other options and then come back to it.
D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E) yx Always true
You don't even have to worry what C is !
ans D #### D
QUESTION:If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10?
options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5
SOLUTION:92p × 5p+r + 11r × 6pr--1=B #### B
QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show?
options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30
SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour.
The two clocks show 2:00 at 2 0'clock
At 3:00 -
Clock B is at 3:00
Clock A is at 3:20 (1 hour + gains 20 minutes)
AT 4:00 -
Clock B is at 4:00
Clock A is at 4:40 (2 hours + gains 40 minutes)
In 4 hours the clock A gains 4*20=80 minutes or 1 hour 20 minutes
If clock A is at 7:20 the clock B is at 6:00
Answer is B #### B
QUESTION:A boy has thirteen trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?
options: A)186 ways B)177 ways C)188 ways D)195 ways E)189 ways
SOLUTION:The boy can select one trouser in thirteen ways.
The boy can select one shirt in 15 ways.
The number of ways in which he can select one trouser and one shirt is 13 * 15 = 195 ways.
Answer:D #### D
QUESTION:If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
options: A)16 1⁄6% B)25% C)33 1⁄3% D)50% E)66 2⁄3%
SOLUTION:This question can be dealt with conceptually or by TESTing VALUES.
We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.
Let's TEST 2/1
If we triple the numerator and double the denominator, we end up with....
(2x3)/(1x2) = 6/2 = 3
Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50%
D #### D
QUESTION:W is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in W?
I. 9
II. 15
III. 27
options: A)I only B)II only C)I and II only D)I and III only E)I, II, and III
SOLUTION:Ans: C
W->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C #### C
QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
options: A)26 B)39 C)42 D)65 E)156
SOLUTION:Here 156 has three two's
two three's
and one 13
rest of them must be in w
so w= 13*3*4 = 156
Answer: E #### E
QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x))
is equal to :
options: A)0 B)1/12 C)1/7 D)1/4 E)1/3
SOLUTION:Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7.
ANSWER:C #### C
QUESTION:If A,B,C are three integers and AB+C is even ; which of the following must be true?
A)C is even
B)B is even
C)AB is even
options: A)I only B)II only C)III only D)II,III only E)None of the above
SOLUTION:If AB is Odd then C will not even. O+E = O
If B is even AB is even always. But If C is Odd E+O = O
None of the above are true #### E
QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true?
options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9
SOLUTION:x^2−x=k
=> x^2−x - k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 1- 4*1*(-k) ≥0
=>1 + 4k ≥0
=> k ≥ -14
Answer A #### A
QUESTION:The first three terms of a proportion are 3, 9 and 12. The fourth term is?
options: A)22 B)28 C)27 D)36 E)88
SOLUTION:(9*12)/3 = 36
Answer:D #### D
QUESTION:A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
options: A)229 B)108 C)278 D)72 E)112
SOLUTION:S = 120/6 * 18/5 = 72 kmph
Answer: D #### D
QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic?
options: A)240 B)65 C)110 D)130 E)200
SOLUTION:Adult + Children = 200
Let, Children = y
then, Adult = y+20
i.e. y+(y+20) = 200
i.e. y = 900
i.e. Adult = 90+20 = 110
Adults include only Men and Women
i.e. Men + Women = 110
Let women, W = x
then Men, M = x+20
i.e. x+(x+20) = 2x+20 = 110
i.e. x = 45
i.e. Men, M = 45+20 = 65
Answer: Option B #### B
QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
options: A)1 B)2 C)4 D)5 E)6
SOLUTION:46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A #### A
QUESTION:A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
options: A)4 min B)8 min C)9 min D)6 min E)1 min
SOLUTION:S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer:A #### A
QUESTION:Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $4,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
options: A) 11,500 B) 24,500 C) 25,500 D) 26,500 E) 27,500
SOLUTION:OFFICIAL SOLUTION:
The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 4,000), and Isabella’s are 0.10x. Set up the equation and solve:
550 + (0.08)(x – 4,000) = 0.10x
Distribute the 0.08:
550 + 0.08x – 320 = 0.10x
Combine terms and subtract 0.08x from both sides:
230 = 0.02x
Divide both sides by 0.02:
11,500 = x
Your answer is A. #### A
QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19?
options: A)7 B)6 C)9 D)10 E)3
SOLUTION:Explanation:
128 + 34 = 162/19 = 10 (Remainder)
Answer: D #### D
QUESTION:What is the decimal equivalent of (1/2)^2?
options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5
SOLUTION:(1/2)² = (1/2)(1/2)= 1/4
APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25
D #### D
QUESTION:factor: 3y (x-3)-2(x-3)
options: A)(x-3)-2(x-3) B)(x-3)power2 C)(x-3)(3y-2) D)3y(x-3) E)x-3
SOLUTION:3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C) #### C
QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ?
options: A)–4 B)–3 C)–2 D)–1 E)0
SOLUTION:Just putting values, the LHS becomes
n=0 --> 11
n=-1 --> 11/10
n=-2 --> 11/100
n=-3 --> 11/1000
Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3.
Answer is B. #### B
QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies
options: A)231 B)150 C)200 D)450 E)451
SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
Ans: C #### C
QUESTION:The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 13 percent, what was the annual interest rate last year?
options: A)1% B)1.1% C)9.1% D)11.81% E)11.50%
SOLUTION:13=1.1*x
X=11.81%
Answer D) #### D
QUESTION:A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
options: A)16 km B)87 km C)89 km D)67 km E)20 km
SOLUTION:Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 3.5
=> x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x
= 16 km.
Answer:A #### A
QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92?
options: A)60 B)70 C)80 D)90 E)100
SOLUTION:(4*90+x)/5=92
x=(5*92)-(4*90)
x= 460 - 360
total score required 460 - 360=100
Correct answer is E #### E
QUESTION:40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6?
options: A)5 B)8 C)10 D)12 E)15
SOLUTION:Let x be the amount of liquid Q to be added.
(3/8)*40 + x = (6/11)*(40+x)
1320 + 88x = 1920 + 48x
40x = 600
x = 15
The answer is E. #### E
QUESTION:Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
options: A)228gallons B)267gallons C)120gallons D)767gallons E)167gallons
SOLUTION:Explanation:
Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying]
Volume of {\color{Black} \frac{1}{40}} part = 3 gallons
Volume of whole = (3 x 40) gallons = 120 gallons.
Answer: C #### C
QUESTION:The sum of two numbers is 18. Their difference is 4. What are the numbers?
options: A)8,6 B)9,9 C)11,7 D)15,3 E)13,9
SOLUTION:Let two numbers be x and y.
Equation (i): x + y = 18
Equation (ii): x - y = 4
Solve system of equations:
2x=22
x=11
y=7
Answer C is correct. #### C
QUESTION:If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?
options: A)41 B)42 C)43 D)44 E)45
SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d.
The sum of A + B = (10c+d)+(10d+c)=11(c+d).
The only answer that is a multiple of 11 is 44.
The answer is D. #### D
QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159
SOLUTION:46 + 28 + 10 = 84%
100 – 84 = 16%
850 * 16/100 = 136
Answer:A #### A
QUESTION:Set R has a mean of 12 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
options: A){15, 16} B){3, 4} C){6, 7} D){5, 6} E){11, 13}
SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 12,the values (11,13) are closer than others.
Hence Answer : E #### E
QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
options: A)1200 B)1723 C)1129 D)2613 E)1372
SOLUTION:A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 150= 3k + 150 => 2k = 300 => k = 150
The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A
QUESTION:Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:here when he step down 26 steps he has 30 seconds for remaining steps.
if he step down 34 stairs he has only 18 sec.
30-18=12
12 secs for 8 steps..
18 secs for 12 steps.
12+34=46
so ans is 46..
ANSWER:B #### B
QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
options: A)15 bukets B)17 bukets C)18 bukets D)19 bukets E)None of these
SOLUTION:Explanation:
Capacity of the tank = (12*13.5) litres
= 162 litres
Capacity of each bucket = 9 litres.
So we can get answer by dividing total capacity of tank by total capacity of bucket.
Number of buckets needed = (162/9) = 18 buckets
Option C #### C
QUESTION:a man spends $2.6 for parking and $34.4 for petrol to travel in car from monday to friday.if he travel by public transport it costs $1.06,find the percentage of savings?
options: A)75.6 B)85.6 C)85.7 D)95.7 E)105.7
SOLUTION:2.6+34.4=37
for 5 days 1.06*5=5.3
37-5.3=31.7
now the required saving percentage is (31.7/37)*100=85.6
ANSWER:B #### B
QUESTION:A rectangular garden is to be twice as long as it is wide. If 150 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?
options: A)40 B)50 C)60 D)70 E)80
SOLUTION:ALTERNATE APPROACH
Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.
Given Perimeter is 150
So, 2 ( L + B ) = 150
Or, L + B = 75
Now use the answer options ( Given Length ; Breath will be half the length)
(A) 40
L = 40 ; B = 20
L + b = 60
(B) 50
L = 50 ; B = 25
L + b = 75
(C) 60
L = 60; B = 30
L + b = 90
(D) 70
L = 70; B = 35
L + b = 105
(E) 80
L = 80; B = 40
L + b = 120
Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (B) #### B
QUESTION:Find the average of all numbers between 2 and 63 which are divisible by 5
options: A)15 B)20 C)25 D)32.5 E)35
SOLUTION:Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60)/12=390/12=32.5
Answer: Option D #### D
QUESTION:Sara works 5 days a week at d dollars per day for m weeks out of the month. Which of the following represents her monthly pay?
options: A)m/(5d) B)20d C)5d D)5dm E)20d/m
SOLUTION:Total income of Sara in a month = d*5*m dollars. = d*5*m = 5dm Answer is D #### D
QUESTION:In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 93% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
options: A)3% B)5% C)2.5% D)4% E)3.6%
SOLUTION:Explanation :
Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.
Products from M1 = 40, from M2 = 30 and from M3 = 30.
Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.07 x 30 = 2.1
Therefore, total number of defective products = 3.6
Answer : E #### E
QUESTION:The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is?
options: A)10 years B)11 years C)12 years D)13 years E)14 years
SOLUTION:Total age of 3 boys = 24*3 =72
ratio of their ages = 1:2:3
Age of the youngest = 72*1/6 = 12 years
Answer is C #### C
QUESTION:The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
options: A)Rs. 113.5 B)Rs. 119.7 C)Rs. 124.75 D)Rs. 130.75 E)Rs. 134.45
SOLUTION:For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C #### C
QUESTION:John can complete a given task in 10 days. Jane will take only 20 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
options: A)8 B)9 C)8.5 D)9.5 E)10.5
SOLUTION:In such questions, you need to start from the end. Last 4 days John works alone and completes 4 * (1/10) = 2/5 of the work.
So 3/5 of the work should have been completed by the two of them together before Jane left.
Their combined rate of work is 1/20 + 1/12 = 8/60
Time taken to complete 4/5 of the work = (3/5)/(8/60) = 9/2 days.
So total number of days taken to complete the work =9/2 + 4 = 8.5 days.
C #### C
QUESTION:There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need
to remove so that only 96% of the apples are green?
options: A)40 B)8 C)15 D)25 E)50
SOLUTION:98−x/100−x=96100
Or, 9800−100x=9600−96x
Or, 200=4x
Or, x=50
ANSWER:E #### E
QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 2x+ 2y > 2z
III. yz > xz
IV. xy > y + z
options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only
SOLUTION:we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 2x+ 2y > 2z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B #### B
QUESTION:If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates?
options: A) 4 B) 8 C) 12 D) 15 E) 20
SOLUTION:I understand this might not be required but I used the equation of a circle.
Since the origin is at 0, x^2+y^2=5^2.
X,Y could be +/- (0,5 or 5,0) - 4 possibilities.
X,Y could be +/- (3,4 or 4,3) - 8 possibilities.
Ans: J=C #### C
QUESTION:A number is missing from the number series below.
Can you find it ?
84, 155, ?, 399 , 584, 819.
options: A)275 B)350 C)399 D)258 E)449
SOLUTION:D
The missing number is 258.
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
399 = 7^3 + 7^2 + 7
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9
Thus,
258 = 6^3 + 6^2 + 6 #### D
QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4?
options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13
SOLUTION:n(S) = 6*6 = 36
E = {(1,3),(2,2),(3,1)}
Probability = 3/36 = 1/12
Answer is D #### D
QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3%
SOLUTION:675 ---- 225
100 ---- ? => 33 1/3%
Answer:C #### C
<<<Examples ends
QUESTION:The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be
options: A)37:20 B)47:20 C)47:25 D)22:25 E)97:50
SOLUTION:Sailor = 1.85 * Officer
Sailor/Officer = 1.85/1 = 185/100 = 37/20
Answer will be A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:if 8^25 divided by 7 then what is reminder
options: A)25 B)1 C)0 D)2 E)3
SOLUTION:8^25/7
8 can be written as 7*1+1
(7*1+1)^25/7
(ax+1)^n/a always gives the remainder 1
here a=7,x=1,n=25
Hence remainder is 1
ANSWER:B #### B
QUESTION:How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height.
options: A)106 B)109 C)108 D)101 E)104
SOLUTION:(18 × 15 × 12)/(5 × 3 × 2) = 108
Answer is C. #### C
QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
options: A)20 1/2 hours B)20 1/7 hours C)20 1/3 hours D)20 3/2 hours E)20 1/4 hours
SOLUTION:1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours
Answer: A #### A
QUESTION:A certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
options: A)42 B)70 C)140 D)135 E)315
SOLUTION:1 of 3 will be chosen for the math
2 of 10 will be chosen for the computer
None of the 3 chosen people can be in more than one departments.
We can choose any of the 3 candidates for the math dep., which gives as 3 selections.
We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections.
So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:
10! /2!*8!= (9*10) / 2 = 90 / 2 = 45.
We are multiplying our individual selections: 3*45 = 135
In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.
Ans D #### D
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)246 m B)240 m C)257 m D)577 m E)567 m
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36
= 15 ==> x + 300 = 540
==> x = 240 m.
Answer: B #### B
QUESTION:Kira's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ?
options: A)7cdx/100 B)d + 7cx/100 C)7d + xc/100 D)7d + 7xc/100 E)7cdx
SOLUTION:Answer is D. #### D
QUESTION:A and B invests Rs.3000 and Rs.6500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
options: A)8:8 B)9:8 C)9:6 D)9:5 E)9:13
SOLUTION:(3*6 + 6*6): (6.5*12)
54:78 => 9:13
Answer: E #### E
QUESTION:If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ?
options: A) Two B) Three C) Four D) Six E) Eight
SOLUTION:t=4p
since t = 4p thenevendivisors are:
4p/4p= 1
4p/2p= 2
4p/4= p
4p/2= 2p
so the answer is (C) #### C
QUESTION:A pharmaceutical company received $3 million in royalties on the first $25 million in sales of and then $9 million in royalties on the next $130 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $25 million in sales to the next $130 million in sales?
options: A)8% B)15% C)35% D)42% E)56%
SOLUTION:(9/130)/(3/25) = 15/26 = 57.7% it means that 9/130 represents only 57.7%. Therefore a decrease of 42%.
Answer D #### D
QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is
options: A)3 months B)4 months C)6 months D)8 months E)10 months
SOLUTION:Solution
S.I on Rs. 1600 = T.D on Rs. 1680.
Rs.1600 is the P.W of Rs.1680.
Rs.80 is S.I on Rs.1600 at 15%.
Time = (100x80 / 600x15)
= 1/3 year
= 4 months.
Answer B #### B
QUESTION:If an average hard drive had a capacity of 0.7 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
options: A)256 B)512 C)768 D)1024 E)7168
SOLUTION:0.7*2^10=0.7*1024=716.8
The answer is E. #### E
QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm?
options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km
SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM.
It travels at 500 kmph.
Hence, the plane flying north would have covered 1000 kms from the city at 2 PM.
The plane flying east would have traveled for 1.5 hours at 2 PM.
It travels at 400 kmph.
Hence, the plane flying east would have covered 1.5*400 = 600 kms from the city at 2 PM.
The two planes are flying at right angles to each other.
The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes.
Hence, distance = 1000square + 200 square = 1166 km
The nearest 100 km distance between the two planes = 1200 kms.
Answer D #### D
QUESTION:If A got 80 marks and B got 60 marks, then what percent of A's mark is B's mark?
options: A)60% B)80% C)65% D)75% E)None of these
SOLUTION:A's marks = 80 ; B's marks = 60.
Let x% of A = B => x/100 * 80 = 60
=> x = (60 * 100)/80 = 75
B's marks is 75% of A's marks.
ANSWER:D #### D
QUESTION:Let's play a game. I have all the ten digits of numbers available. I use all the digits just once to create a number of ten digits. Can you find out what number I have in mind using the following clues?
One digit is divisible by 1.
Two digits are divisible by 2.
Three digits are divisible by 3.
Four digits are divisible by 4.
Five digits are divisible by 5.
Six digits are divisible by 6.
Seven digits are divisible by 7.
Eight digits are divisible by 8.
Nine digits are divisible by 9.
Ten digits are divisible by 10.
options: A)3816547290 B)3816557290 C)3816547280 D)3813547290 E)3816147290
SOLUTION:A
3816547290 #### A
QUESTION:A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village?
options: A)10km B)50km C)30km D)25km E)20km
SOLUTION:Average speed = 2xy/x+y = 2*25*4/25+4 = 200/29km/hr
Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km
Distance of the post office from the village = 40/2 = 20km
Answer is E #### E
QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing?
options: A)191 B)400 C)737 D)840 E)1,560
SOLUTION:Let weight of side of beef before processing = x
(60/100)*x = 240
=> x = (240 * 100)/60 = 400
Answer B #### B
QUESTION:A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
options: A)3:3 B)3:4 C)3:8 D)3:1 E)3:2
SOLUTION:They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4.Answer: B #### B
QUESTION:The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is :
options: A)15 cm B)25 cm C)35 cm D)42 cm E)62 cm
SOLUTION:Solution
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C #### C
QUESTION:A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
options: A)5/7 B)9/14 C)13/21 D)17/28 E)23/35
SOLUTION:P(no red balls) = 6/8*5/7*4/6 = 5/14
P(at least one red ball) = 1 - 5/14 = 9/14
The answer is B. #### B
QUESTION:Set R has a mean of 15 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
options: A){11,26} B){18,19} C){16,18} D){16,16} E){14,16}
SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 15,the values (14,16) are closer than others.
Hence Answer : E #### E
QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/4 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
options: A)7/12 B)29/60 C)17/30 D)19/30 E)11/15
SOLUTION:Let s assume the platinum card spending limit =x
Gold card spending limit will be =x/2
balance on gold card is =x/2*1/3=x/6
Platinum card unspent limit is= x-1/4x=3/4x
So if gold card balance is transferred then the rest unspent will be
3/4x-x/6=7/12x
So the ans is A #### A
QUESTION:Two pipes can fill a tank in 14 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
options: A)5.5 Hours B)7.5 Hours C)8.5 Hours D)9.5 Hours E)6.5 Hours
SOLUTION:In 1 hour it fill 1/14 + 1/12 - 1/20 = 2/19
So fill tank fill up in 19/2= 9.5 Hours
ANSWER:D #### D
QUESTION:The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
options: A)1008 B)1015 C)1022 D)1032 E)1043
SOLUTION:Required Number = (L.C.M of 12, 16, 18,21,28)+7
= 1008 + 7
= 1015
Answer: B #### B
QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)
options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87
SOLUTION:Explanation:
Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer: A #### A
QUESTION:When x is multiplied by 3, the result is 4 more than the result of subtracting x from 16. What is the value of x?
options: A)-4 B)-2 C)5 D)13 E)22
SOLUTION:The equation that can be formed is:
3x-4=16-x
or, 4x=20
or, x=5.
Answer : C #### C
QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
options: A)16 B)18 C)24 D)22 E)26
SOLUTION:C
24
Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x <-> 27 x x = 36 x 18
x = (36 x 18)/27
x = 24 #### C
QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age?
options: A)22 B)15 C)77 D)21 E)182
SOLUTION:Present age is 4x and 3x,
=> 4x + 6 = 34 => x = 7
So Deepak age is = 3(7) = 21
Answer: D #### D
QUESTION:Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?
options: A)5 B)8 C)11 D)15 E)17
SOLUTION:Explanation :
Let a, b, c be the Englishmen and d, e, f be the Frenchmen.
Let a be the Englishman who knows French. 'a' calls 'b & c' and now knows the secret of both of them. So now 'a' knows 'abc' secrets. 'd' calls 'e & f' and now knows the secret of both of them. So now 'd' knows 'def' secrets. 'a' now calls 'd', and exchange all secrets in French, so now 'a' and 'd' know all the 6 secrets. Now 'a' calls 'b & c' again, and 'd' calls 'e & f' again and tell all the secrets. So, totally 9 calls.
Answer : B #### B
QUESTION:A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):
m------M---------------W
w
In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 3*15/60 =15/20 miles and the man walks the distance mM, which is 3*9/60 = 9/20 mile.
The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes.
Answer B. #### B
QUESTION:The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between
Bunuel, can you please explain this one?
options: A)0 and 0.5 B)0.5 and 1 C)1 and 1.5 D)1.5 and 2 E)2 and 2.5
SOLUTION:Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).
Try x=1 --> LHS=3^5=81*3=243 and RHS=4^4=64*4=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1.
Answer: E. #### E
QUESTION:According to a recent survey report issued by the Commerce Ministry, Government of India, 30% of the total FDI goes to Gujarat and 20% of this goes to rural areas. If the FDI in Gujarat, which goes to urban areas, is $72 m, then find the size of FDI in rural Andhra Pradesh, which attracts 50% of the FDI that comes to Andhra Pradesh, which accounts For 20% of the total FDI?
options: A)30m B)40m C)35m D)38m E)50m
SOLUTION:30% of total FDI given to Gujarat is $90m.
so,100% is $300m.
20%of 300m=60m.
50%of 60m=30m.
ANSWER:A #### A
QUESTION:A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
options: A)8 B)9 C)4 D)18 E)None
SOLUTION:Ratio of rates of working of A and B = 2 : 1
So, ratio of times taken = 1 : 2
B's 1 day's work = 1/12
Therefore A's 1 day's work = 1/6
(A + B)'s 1 day's work = (1/6 + 1/12)= 1/4
So, A and B together can finish the work in 4 days.
Answer: C #### C
QUESTION:Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
options: A)33% less than N B)25% less than N C)equal to N D)20% greater than N E)25% greater than
SOLUTION:Correct answer is (A).
This year, the price of a tree is price1=P/N.
If this price increases by 50% it becomes price2=P/N*1.50
Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.50) i.e. N/1.5 i.e. .67% less*
A #### A
QUESTION:Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ?
options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1
SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4.
Actually B is the right answer. #### B
QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
6 – 9 + 8 × 3 ÷ 15 =
options: A)6 B)10 C)12 D)-2 E)15
SOLUTION:E 15 #### E
QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?
options: A)25% B)33 1/3% C)50% D)66 2/3% E)75%
SOLUTION:General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the time between maintenance checks increased by 25−20/20∗100=25
Answer: A. #### A
QUESTION:if log 7 = 0.845098, the number of digits in 7128 is
options: A)100 B)120 C)109 D)280 E)110
SOLUTION:Explanation:
log(7128) = 128log(7) = 128 × 0.845098 ≈ 108.17
ie, its characteristic = 108
Hence, number of digits in 2128 = 108+1 = 109
Answer: Option D #### D
QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 5400 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
options: A)9000 B)98000 C)30000 D)11000 E)12000
SOLUTION:100 % - 10 % = 90 %
54%-36%=18%
18% ------> 5400 ( 18 × 300 = 5400)
100% -------> 30000 votes (100 × 300 = 30000)
C #### C
QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is
options: A)0.092 B)0.92 C)9.2 D)92 E)920
SOLUTION:F(69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33
Now,
7 × 2 = 14
7 × 1 = 7
or better:
6.9 × 1 = 6.9
6.9 × 2 = 13.8
hence,
6.9 <6.928 × 1.33 < 13.8
9.2 is the only answer that satisfies this condition.C #### C
QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11
SOLUTION:Sum = (50 * 100) / (2 * 5)
= Rs. 500
Amount = [500 * (1 + 5/100)2]
= Rs. 551.25
C.I. = (551.25 - 500)
= Rs. 51.25.
Answer: A #### A
QUESTION:The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
options: A)72 B)83 C)45 D)53 E)64
SOLUTION:Sum of all the 13 numbers = 13 * 58 = 754
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 754 = 72.
Answer:A #### A
QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true?
options: A)35 B)48 C)69 D)70 E)74
SOLUTION:5*a1 + 7*b1 = t
5*a2 + 7*b2 = t
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.
Lets check how it works for our numbers, starting from the largest:
E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad
D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus
D is the answer #### D
QUESTION:Shreyas bought an article and sold it for 112% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42750/-?
options: A)Rs.24600 B)Rs.38169 C)Rs.38989 D)Rs.23200 E)None of these
SOLUTION:Explanation:
112% of CP = Rs.42750
:. CP = Rs.42750x100/112 = Rs.38169.
Answer: Option B #### B
QUESTION:For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z?
options: A)(n/m)% B)(m × n)% C)(100 / [m × n]) % D)(100 × m/n)% E)(100 × n/m)%
SOLUTION:x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer E is 100n/m %.E #### E
QUESTION:If (x + 1)^2 = 144, which of the following could be the value of 2x?
options: A)–26 B)–13 C)–10 D)12 E)-21
SOLUTION:You can also get to the answer by backsolving using answer choices
Starting with choice B = -13
(x + 1)^2 = 144
(-13 + 1)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -13 will result in 144 in the equation so x must be -11,
Then 2x = 2 * -13 = -26
Answer: A #### A
QUESTION:When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction?
options: A)5/4 B)4/7 C)5/6 D)6/7 E)None of these
SOLUTION:Let the fraction be x/y.
When the numerator decreased by 25% and the denominator decreased by 20%.
(x * 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5
ANSWER:E #### E
QUESTION:A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $45,000 commission, how many machines did she sell?
options: A) 140 B) 103 C) 105 D) 115 E) 120
SOLUTION:First 100 machines = 3% commission = 0.03*100*10000 = 30000
Commission from sale of next machines = 46000 - 30000 = 16000
So 40 more machines..
Total = 140 machines
IMO A.. #### A
QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water?
options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1
SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q
2P=4Q
P/Q = 2/1
The answer is D. #### D
QUESTION:A man buys an item at Rs. 750 and sells it at the loss of 20 percent. Then what is the selling price of that item
options: A)Rs. 660 B)Rs. 760 C)Rs. 600 D)Rs. 960 E)None of these
SOLUTION:Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 750
= 80/100 * 750
= 600
Option C #### C
QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments.
options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3
SOLUTION:The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:21.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6.
ANSWER:A #### A
QUESTION:The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog?
options: A)12 B)24 C)30 D)48 E)120
SOLUTION:We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together.
Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!*2=48.
Answer: D #### D
QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent?
options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3%
SOLUTION:750 ---- 50
50 ---- ? => 6 2/3%
Answer: E #### E
QUESTION:A work can be finished in 30 days by 30 women. The same work can be finished in fifteen days by 15 men. The ratio between the capacity of a man and a woman is
options: A)1:3 B)4:3 C)2:3 D)4:1 E)2:4
SOLUTION:Work done by 30 women in 1 day = 1/30
Work done by 1 woman in 1 day = 1/(30×30)
Work done by 15 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×15)
Ratio of the capacity of a man and woman =1/(15×15) : 1/(30×30)) = 1/225 : 1/900
= 1/1 :1/4 = 4:1
Option D #### D
QUESTION:If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area?
options: A)26% B)21% C)15% D)18% E)12%
SOLUTION:a =1/2 x b x h or 1/2 x 2a x a(for simplification)
New h = 220a / 100 = 22a / 10
New b =(110a x 100) ==11a/10
New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100)
increased area== (121a²/100) - a²
Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21%
answer :B #### B
QUESTION:A circular well with a diameter of 6 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out?
options: A)678.6 m3 B)36 m3 C)40 m3 D)44 m3 E)None
SOLUTION:Solution
Volume = πr2h
‹=› (22 /7 ×3×3×24)m3
‹=›678.6 m3.
Answer A #### A
QUESTION:A tank is filled in SIX hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
options: A)56 hours B)28 hours C)55 hours D)66 hours E)21 hours
SOLUTION:1/A + 1/B + 1/C = 1/6 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/6
=> (1 + 2 + 4)/2B = 1/6
=> 2B/7 = 6
=> B = 21 hours.
Answer: E #### E
QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min
SOLUTION:A
20 hours 30 min
1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours #### A
QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
options: A)26 B)22 C)12 D)24 E)20
SOLUTION:Explanation:
Let the required number of days be x
More men, less days (indirect proportion)
Hence we can write as
(men) 36 : 27 :: x : 18
⇒36×18=27 × x
⇒12×18=9 × x
⇒12×2=x
⇒x=24
Answer: Option D #### D
QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900
SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/9 = 19
P = 19/900
Ans:D #### D
QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?
options: A)3 B)16 C)75 D)24 E)26
SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.
2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).
3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.
4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!
6) Answer choice E. #### E
QUESTION:A train is 360 meter long is running at a speed of 75 km/hour. In what time will it pass a bridge of 140 meter length?
options: A)87 B)69 C)40 D)72 E)24
SOLUTION:Speed = 75 Km/hr = 75*(5/18) m/sec = 125/6 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (6/125) = 24 seconds
Answer: E #### E
QUESTION:A group of men decided to do a work in 20 days, but 8 of them became absent. If the rest of the group did the work in 28 days, Find the original number of men?
options: A)60 B)28 C)40 D)50 E)25
SOLUTION:Original number of men = 8*28 / (28-20) = 28
Answer is B #### B
QUESTION:If p ≠ 1 and if qp/(q - p) = 1, what is the value of q in terms of p?
options: A)(p+1)/p B)(p - 1)/p C)p/(p + 1) D)p/(1-p) E)(1 - p)/p
SOLUTION:This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
D #### D
QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h?
options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4
SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E #### E
<<<Examples ends
QUESTION:At an election 2 candidates are participated a candidate got 45% of votes and defeated by 9000 votes. 83 votes are invalid. Find the total polled votes?
options: A)100000 B)85236 C)89562 D)90083 E)95842
SOLUTION:winners votes = 100-45 = 55%
invalid votes = 83
polled votes = [(100*9000)/(2*55-100)]+83 = 90083
Answer is D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
options: A)3 1/2 sec B)3 5/2 sec C)3 7/2 sec D)8 1/2 sec E)3 1/8 sec
SOLUTION:D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 1/2 sec
Answer: D #### D
QUESTION:A rectangular block 15cm by 30cm by 75cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
options: A)6 B)40 C)15 D)10 E)22
SOLUTION:Volume of the block = 15*30*75 = 33750 cm^3
Side of the largest cube = H.C.F of 15,30,75 = 15cm
Volume of the cube = 15*15*15 = 3375 cm^3
Number of cubes = 33750/3375 = 10
Answer is D #### D
QUESTION:In how many ways can the letters of the word REGULATION be arranged such that all the vowels always appear together?
options: A)10!*5! B)10!*6! C)10! D)6!*5! E)5!*5!
SOLUTION:The 10 letters can be grouped into 5 consonants and one set of 5 vowels.
The number of ways to arrange 6 units is 6!
Then, for each arrangement, the 5 vowels can be arranged in 5! ways.
The total number of arrangements is 6!*5!
The answer is D. #### D
QUESTION:How many factors of 60 are odd numbers greater than 1?
options: A)3 B)4 C)5 D)3 E)7
SOLUTION:prime factors of 60 are 2^2,3^1,5^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,) = (1+1)(1+1)=4
since we need odd divisors other than 1 =>4-1 = 3 odd divisors
D is the answer #### D
QUESTION:Two hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 400 selected numbers are odd?
options: A)20% B)25% C)40% D)50% E)80%
SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even.
The percentage of odd numbers is about (1/2)(200) / 400 = 25%
The answer is B. #### B
QUESTION:One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
options: A)180 min B)160 min C)280 min D)18 min E)190 min
SOLUTION:Let the slower pipe alone can fill the tank in x minutes
Then the faster pipe can fill the tank in x/4 minutes
Part filled by the slower pipe in 1 minute = 1/x
Part filled by the faster pipe in 1 minute = 4/x
Part filled by both the pipes in 1 minute = (1/x)+(4/x)
Answer is A
It is given that both the pipes together can fill the tank in 36 minutes
⇒ Part filled by both the pipes in 1 minute = 1/36
(1/x)+(4/x)=1/36
5/x=1/36
x=5×36=180
i.e.,the slower pipe alone fill the tank in 180 minutes #### A
QUESTION:Three partners A, B, C in a business invested money such that 3(A’s capital) = 6(B’s capital) = 9(C’s capital) then, The ratio of their capitals is
options: A)63 : 45 : 34 B)6 : 3 : 2 C)36 : 54 : 28 D)63 : 45 : 35 E)None of these
SOLUTION:Explanation:
Let3(A’s capital) = 6(B’s capital) = 9(C’s capital) = Rs.x
Then, A’s capital = Rs x/3, B’s capital = Rs. x/6 and C’s capital = Rs. x/9.
A : B : C = x/3 : x/6 : x/9
6 : 3 : 2
Answer: Option B #### B
QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show?
options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30
SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour.
The two clocks show 2:00 at 2 0'clock
At 3:00 -
Clock B is at 3:00
Clock A is at 3:20 (1 hour + gains 20 minutes)
AT 4:00 -
Clock B is at 4:00
Clock A is at 4:40 (2 hours + gains 40 minutes)
In 4 hours the clock A gains 4*20=80 minutes or 1 hour 20 minutes
If clock A is at 7:20 the clock B is at 6:00
Answer is B #### B
QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-4)(x+9)(2X+5) = 0?
options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2
SOLUTION:x = -2.5
Prob =1/12
Answer - A #### A
QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her
options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger
SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1996 has to be the ring finger
Answer is (D) #### D
QUESTION:An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
options: A)8877 B)3000 C)7787 D)1799 E)1711
SOLUTION:4 --- 2000
5 --- ? => 3000
Answer: B #### B
QUESTION:A, Band C are three contestants in a kmrace. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ?.
options: A)540 m B)178 m C)936 m D)234 m E)713 m
SOLUTION:While A covers 1000 m, B covers (1000 - 40) m = 960 m and
C covers (1000 - 64) m or 936 m.
When B covers 960 m, C covers 936 m
Option C #### C
QUESTION:A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.15,000 earned at the end of 2years from the startingof the business?
options: A)s. 5,000 B)s. 4,500 C)s. 5,700 D)s. 6,500 E)s. 7,500
SOLUTION:A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 15000 x 3/10 = Rs. 4,500.
B #### B
QUESTION:If 75 percent of 600 is 50 percent of x, then x=?
options: A)800 B)900 C)1000 D)1100 E)1200
SOLUTION:0.75 * 600 = 0.5 * x
x = 7.5/5 * 600 = 900 #### B
QUESTION:A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
options: A)23 Years B)21 Years C)20 Years D)25 Years E)22 Years
SOLUTION:Let present age of the son =x=x years
Then, present age the man =(x+24)=(x+24) years
Given that, in 22 years, man's age will be twice the age of his son
⇒(x+24)+2=2(x+2)⇒x=22
ANSWER:E #### E
QUESTION:The odds against ram solving the problem are 6 to 3 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try?
options: A)1/4 B)5/21 C)16/21 D)23/28 E)13/18
SOLUTION:Odds against Ram are 6:3 so probability that he will solve the problem is 1/3.
Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12
It will be solved means that either Ram or Krishna or both will be able to solve it.
P(A or B) = P(A) + P(B) - P(A and B) = 1/3 + 7/12 - (1/3)*(7/12) = 13/18
E #### E
QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job?
options: A)6 B)13 1â„2 C)17 D)Data inadequate E)None of these
SOLUTION:12 M × 18 = 12 W × 18 × 3/1
\ w = 1/3 M
10M + 8W = 10M + 8 × 1/3M = 12 2/3 M
\12 2/3 men can complete the same work
in 12×18/12 2/3=17days
Answer C #### C
QUESTION:A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
options: A)4 sec B)6 sec C)7 sec D)3 sec E)2 sec
SOLUTION:Speed of train relative to man
= 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men
= 110 * 3/55 =6 sec.
Answer:B #### B
QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.988] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
options: A)0 B)1 C)27 D)54 E)Cannot be determined
SOLUTION:It cannot be determined.As we do not know the actual value of K.
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
K=[lCM of 80 and 45] * (any integer)
for value of k(60) * any integer unit value will be always zero .
A #### A
QUESTION:A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
options: A)12 B)17 C)15 D)19 E)26
SOLUTION:Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P
= 19
Answer:D #### D
QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996?
options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3
SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A
QUESTION:In how many ways the word "KIT" can be arranged?
options: A)6 B)8 C)18 D)21 E)24
SOLUTION:Explanation :
The required number of ways = 3!
= 6
Answer : A #### A
QUESTION:If 9^y = 3^12, what is y?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:3^2y = 3^12
2y=12, therefore y=6
E #### E
QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
options: A)6 days B)4 days C)8 days D)5 days E)1 days
SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4
=> 4 days
Answer: B #### B
QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
options: A)10 B)99 C)787 D)62 E)22
SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer: A #### A
QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items?
options: A)15% B)12.16% C)13.4% D)20.2% E)None of these
SOLUTION:Explanation :
Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively.
And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively.
Overall loss percentage of the 1st two items = 14.33%
=>(0.21p+0.11q)/(p+q)=0.1433
=>p/q=1/2.
Overall loss percentage of the 2nd and 3rd item =10.4%
=>(0.11q+0.1r)/(q+r)=0.104.
=>q/r=2/3.
Therefore, the overall loss percentage is :
=>(0.21p+0.11q+0.1r)x100/(p+q+r).
=>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3).
=>0.1216×100.
=>12.16%.
Answer : B #### B
QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes?
options: A)6 min B)12 min C)10 min D)15 min E)16 min
SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 11 - 1 = 10 rounds per hour.
Time taken to complete one round at this speed = 1/10 hr = 6 min.
A #### A
QUESTION:The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home?
options: A)60% B)50% C)55% D)40% E)33.3%
SOLUTION:Increase = 168000-120000 = 48000
% increase = 48000*100/120000 = 40%
Answer: option D #### D
QUESTION:Find the value of 3 + 2 • (8 – 3)
options: A)(a) 25 B)(b) 13 C)(c) 17 D)(d) 24 E)(e) 15
SOLUTION:3 + 2 • (8 – 3)
= 3 + 2 (5)
= 3 + 2 × 5
= 3 + 10
= 13
Answer: (D) #### D
QUESTION:10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
options: A)2 B)1 C)7 D)6 E)4
SOLUTION:1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/10 + 10/140) = (1/14 + 1/14) = 1/7
5 women and 10 children will complete the work in 7 days.
Answer:C #### C
QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
options: A)3 B)5 C)6 D)4 E)9
SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 20 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 5. Answer: B #### B
QUESTION:Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?
options: A)24. B)28. C)36. D)42. E)48
SOLUTION:Diameter of tube= 5 inches
Height of wooden tube= 15 inches
Two tubes can stand in 31 inches height
Two tubes can fit in 11 inches length
Two tubes can fit in 10 inches width
So, one box can hold 8 tubes
Three boxes can hold= 8*3= 24 tubes
A is the answer #### A
QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle?
options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm
SOLUTION:let length = x and breadth = y then
2(x+y) = 46 x+y = 23
x²+y² = 17² = 289
now (x+y)² = 23²
x²+y²+2xy= 529
289+ 2xy = 529
xy = 120
area = xy = 120 sq.cm
Answer: B #### B
QUESTION:The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
options: A)76 B)88 C)66 D)55 E)35
SOLUTION:Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer:E #### E
QUESTION:A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 30 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
options: A) 2 hours, 225 miles B) 5.5 hours, 600 miles C) 4 hours, 450 miles D) 5 hours, 550 miles E) 6 hours, 650 miles
SOLUTION:Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.
Equation 1 - x= 100 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 120 (t-.5) subtracted .25 hrs because it is early or took less time than usual.
Now equating 12 we get 100(t+.5)=120(t-.5)
=> 10t +5 = 12t - 6
=> 2t=11 => t= 5.5 hrs.
Hence x= 100(5.5+.5) =>100 X 6 => 600 miles.
Hence correct answer B #### B
QUESTION:What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7?
options: A)397 B)401 C)403 D)405 E)364
SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=364.
Answer: E. #### E
QUESTION:What percent is 2 gm of 1 kg?
options: A)0.5 % B)0.2% C)1.5% D)2% E)3%
SOLUTION:1 kg = 1000 gm
2/1000 × 100 = 200/1000
=1/5 = 0.2 %
B) #### B
QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
options: A)5 B)6 C)7 D)1 E)2
SOLUTION:160 = (180*4*R)/100
R = 5%
Answer: A #### A
QUESTION:Find the L.C.M of 2^2 * 3^3 * 5 *7^2*11, 2^3 * 3^2* 5^2* 7^4*11, 2 * 3* 5^3* 7^4*11
options: A)2^3 * 3^3 * 5^3 * 7^4 * 11 B)2^2*3^3*5^3 * 7^4 * 11 C)2^2*3^3*5^2 * 7^4 * 11 D)2^3*3^3*5^2* 7^4 * 11 E)2^3*3^3*5^2* 7^3 * 11
SOLUTION:L.C.M= product of the highest powers of 2,3,5,7 and 11=2^3 * 3^3 * 5^3 * 7^4 * 11
Answer (A) #### A
QUESTION:A tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume. If 6,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 15%
SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-6,000=4,000 gallons and sodium chloride is 600 gallons (6% of initial solution of 10,000 gallons) then sodium chloride is 600/4,000*100=15% of the remaining solution of 4,000 gallons.
Answer: E. #### E
QUESTION:A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%
options: A)Rs 6.56 B)Rs 9.56 C)Rs 10.56 D)Rs 11.56 E)None of these
SOLUTION:Explanation:
80 : 5 = 105 : x
x= (5×105/80)
= Rs 6.56
Option A #### A
QUESTION:The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by?
options: A)2.0% B)3.2% C)3.9% D)4% E)5.1%
SOLUTION:Net growth on 1000 = 32-10 = 20
Net growth on 100 = 20*100/1000 = 2.0%
Answer is A #### A
QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour.
options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these
SOLUTION:Explanation:
We know Time = Distance/speed
So total time taken =
(120/60+160/80)=4hours
Time taken for 280 Km = 280/4=70.km/hr
Option A #### A
QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
options: A)80% B)100% C)116.7% D)120% E)180%
SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%.
Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%.
6 is 6/3.33*100 = 180% of 3.33.
Answer: E. #### E
QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
options: A)18/35 B)18/38 C)18/34 D)18/31 E)18/30
SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35.
Answer:A #### A
QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum.
options: A)800 B)700 C)600 D)500 E)None of them
SOLUTION:Let the sum be Rs. x Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40
= (7x/20)-(3x/10)=40
x = (40 * 20) = 800.
Hence, the sum is Rs. 800.
Answer is A. #### A
QUESTION:The present worth of Rs.676 due in 2 years at 4% per annum compound interest is
options: A)Rs.150.50 B)Rs.154.75 C)Rs.156.25 D)Rs.625 E)None
SOLUTION:Solution
Present Worth = Rs.[676/(1+4/100)²]
= Rs.(676x25/26x25/26)
= Rs.625
Answer D #### D
QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is
options: A)51:52 B)52:54 C)53:54 D)54:55 E)None of these
SOLUTION:Explanation:
Let the Cost price of article is Rs. x
Required ratio = (104% of x) / (108% of x)
=104/108
=52/54 = 52:54.
Answer: B #### B
QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten?
options: A)15 B)18 C)21 D)23 E)29
SOLUTION:There are two conditions:
1. Angel got at least one score of each of 1, 2, 3, and 4.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18.
Answer: B. #### B
QUESTION:If B and C are digits and 8BC is a 3-digit number that is divisible by 5, which of the following is a possible product of B and C?
options: A)1 B)2 C)5 D)7 E)14
SOLUTION:Try with the options -
A. If BC = 1 , both B and C must be 1
B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3
C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3
D. If BC = 6 , then we can have the following possibilities
i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3
ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3
E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 5
Thus answer is (D) #### D
QUESTION:5800 * 99
options: A)574580 B)574200 C)584250 D)576460 E)None of these
SOLUTION:Explanation:
5800 * (100 - 1)
= 580000 - 5800
= 574200
Option B #### B
QUESTION:If the two hands in a clock are 11 minutes divisions apart,then the angle between them is
options: A)66° B)18° C)24° D)60° E)None of these
SOLUTION:In a clock, each minute makes 6°
∴ 11 minutes will make 6 × 11 = 66°
Answer A #### A
QUESTION:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
options: A)671.5 B)600 C)672.5 D)673 E)773.5
SOLUTION:Many approaches are possible, one of them:
Let the distance be 1 kilometer.
Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds;
Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours;
So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: B. #### B
QUESTION:Evaluate 35 / .07
options: A)400 B)500 C)505 D)None of these E)506
SOLUTION:Explanation:
35/.07 = 3500/7 = 500
Option B #### B
QUESTION:Distances from you to Man united is written below.
CHELSEA and ARSENAL are 700 kms away
SPURS 1800 kms away
WOLVES 200 kms away
Based on the system , How far should it be to MANCITY ?
options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles.
SOLUTION:Solution:
2100 miles.
Each vowel equivalent to 500 and each consonant equivalent to -200
Answer C #### C
QUESTION:A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
options: A)8 B)9 C)4 D)18 E)None
SOLUTION:Ratio of rates of working of A and B = 2 : 1
So, ratio of times taken = 1 : 2
B's 1 day's work = 1/12
Therefore A's 1 day's work = 1/6
(A + B)'s 1 day's work = (1/6 + 1/12)= 1/4
So, A and B together can finish the work in 4 days.
Answer: C #### C
QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6?
options: A)300 B)992 C)772 D)552 E)280
SOLUTION:1/3:1/3:1/6 = 2:2:1
1/5*1400 = 280
560-280 = 280
Answer: E #### E
QUESTION:The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
options: A)3. B)7. C)10. D)16. E)15.
SOLUTION:Time taken by the birds to meet = 20/(4 + 1) = 4 mins
Distance traveled by the bird traveling from West-Town = 4 *4= 16
Answer: D #### D
QUESTION:The points A(0, 0), B(0, 4a - 4) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
options: A)88 B)98 C)108 D)78 E)90
SOLUTION:1/2bh=1/2(2a+1)(2a+6)
Now 4a-4=2a+6
2a=10 , a=5
Therefore,
A(0,0); B(0,16); C(11,16)
1/2*11*16=88
Answer: A #### A
QUESTION:x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b?
options: A)24 B)21 C)20 D)17 E)15
SOLUTION:Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20.
Answer: C. #### C
QUESTION:If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q
options: A)1 B)3 C)5 D)7 E)9
SOLUTION:3/7 = 0.428571... (a repeating pattern one digit long)
B #### B
QUESTION:In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?
options: A)a) 8 B)b) 23 C)c) 29 D)d) 32 E)e) 53
SOLUTION:Thats 29 in C. #### C
QUESTION:There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
options: A)1 B)10 C)125 D)50 E)20
SOLUTION:25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125
so 125 enrolled for swimming
Answer: C #### C
QUESTION:The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January?
options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500
SOLUTION:Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8600
= 34400 ----(2)
(2)-(1) i.e. May - Jan = 2400
Salary of May is Rs.6500
Salary of January = Rs.4100
Answer:A #### A
<<<Examples ends
QUESTION:On increasing the price of T.V. sets by 40%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
options: A)4 B)5 C)56 D)12 E)7
SOLUTION:Explanation:
Let the price be = Rs.100, and number of units sold = 100
Then, sale value = Rs.(100 × 100) = Rs.10000
New sale value = Rs.(140 × 80) = Rs.11200
Increase% = 1200/10000 × 100 = 12%
Answer: D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A man can row at 4 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
options: A)2.4 km B)2.9 km C)3.4 km D)1.9 km E)5.6 km
SOLUTION:Explanation:
Speed in still water = 4 kmph
Speed of the current = 1 kmph
Speed downstream = (4+1) = 5 kmph
Speed upstream = (4-1) = 3 kmph
Let the required distance be x km
Total time taken = 1 hour
⇒ x/5+x/3=1
⇒3x+5x=15
⇒8x=15
⇒x=1.9 km
Answer: Option D #### D
QUESTION:385, 462, 572, 396, 424, 671, 264
options: A)385 B)424 C)671 D)264 E)None of these
SOLUTION:Solution
In each number except 424,the middle digit is the sum of the other two. Answer B #### B
QUESTION:Enrollment in City College in 1980 was 210 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
options: A)- 10% B)- 16 2/3 % C)- 52.38% D)- 25% E)- 183 1/3%
SOLUTION:Assume 100 enrollments present in 1990
210 % of 1990 = enrollments on 1980
enrollments on 1980 = 210
% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)
=(100 - 210) *100 / 210
= -11000 / 210
= - 52.38 %
Ans - C #### C
QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads?
options: A)3/4 B)7/8 C)3/8 D)5/6 E)9/11
SOLUTION:Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E)=n(E)/n(S)
=7/8
The answer should be B #### B
QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
options: A)27% B)25% C)21% D)85% E)24%
SOLUTION:SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer:B #### B
QUESTION:If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in:
options: A)12 years B)18 years C)16 years D)14 years E)19 years
SOLUTION:Explanation:
The sum P becomes 3P in 4 years on compound interest
3P = P(1+R/100)4
⇒ 3 = (1+R/100)4
Let the sum P becomes 81P in n years
81P = P(1+R/100)n
⇒ 81 = (1+R/100)n
⇒ (3)4 = (1+R/100)n
⇒ ((1+R/100)4)4 = (1+R/100)n
⇒ (1+R/100)16 = (1+R/100)n
n=16
i.e, the sum will become 81 times in 16 years
ANSWER IS C #### C
QUESTION:Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are:
options: A)7, 6 B)5, 1 C)6, 3 D)8, 7 E)None of these
SOLUTION:Explanation :
Let A and B be such sets, i.e., n (A) = m, n (B) = n
So, n (P(A)) = 2m and n (P(B)) = 2n
Thus n (P(A)) – n (P(B)) = 56, i.e. 2m – 2n = 56
⇒ 2n (2m-n - 1) = 23 x 7
⇒ n = 3 , 2m-n – 1 = 7
⇒ m = 6
Answer : C #### C
QUESTION:Rs.1210 were divided among 3 person P, Q, R so that P:Q=5:4 and Q: R=9:10. Then R gets the amount.
options: A)Rs. 300 B)Rs. 400 C)Rs. 480 D)Rs. 490 E)Rs. 500
SOLUTION:P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9.
So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40
Sum of ratio terms is = ( 45 + 36 + 40 ) =121.
R share of amount is Rs (1210 x 40 / 121) = Rs. 400.
B #### B
QUESTION:Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
options: A)173 m B)200 m C)273 m D)300 m E)None of these
SOLUTION:xplanation:
Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, <ACB = 30º and <ADB = 45º.
AB/AC=tan30
Answer: C #### C
QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days?
options: A)700 B)666 C)600 D)400 E)800
SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C #### C
QUESTION:Which of the following can be expressed as a terminating decimal?
options: A)1/25 + 1/35 B)1/225 + 1/1,250 C)1/11,000 + 1/13,000 D)1/75 + 1/35 E)1/125 + 1/8
SOLUTION:In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first.
A. 1/25 + 1/35 = 12/175 = 12/25*1/7
1/7 does is not a terminating decimal.
E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000
This is a terminating decimal and our answer.
Correct Option: E #### E
QUESTION:A car covers a distance of 630 km in 6 hours. Find its speed?
options: A)105 B)7778 C)266 D)288 E)121
SOLUTION:624/6 = 105 kmph
Answer:A #### A
QUESTION:In "Clash Royal" App Game, Warrior "The Bomber" is a very good defensive options. It can be purchased from the card shop.
The cost of the bomber is quite interesting.
The Cost of 1st bomber is: 2
The Cost of 2nd bomber is: 4
The Cost of 3rd bomber is: 6
The Cost of 4th bomber is: 8
The Cost of 5th bomber is: 10
i.e to buy 5 bombers you need 2+4+6+8+10 = 30 coins.
How many bombers can you buy using 1000 coins ? ?
options: A)61 B)62 C)63 D)64 E)65
SOLUTION:Solution
62
The Cost of 1st bomber is: 2 i.e Total coins spend: 2
The Cost of 2nd bomber is: 4 i.e Total coins spend: 6
The Cost of 3rd bomber is: 6 i.e Total coins spend: 12
The Cost of 4th bomber is: 8 i.e Total coins spend: 20
The Cost of 5th bomber is: 10 i.e Total coins spend: 30
The Cost of 6th bomber is: 12 i.e Total coins spend: 42
The Cost of 7th bomber is: 14 i.e Total coins spend: 56
The Cost of 8th bomber is: 16 i.e Total coins spend: 72
The Cost of 9th bomber is: 18 i.e Total coins spend: 90
The Cost of 10th bomber is: 20 i.e Total coins spend: 110
The Cost of 11th bomber is: 22 i.e Total coins spend: 132
The Cost of 12th bomber is: 24 i.e Total coins spend: 156
The Cost of 13th bomber is: 26 i.e Total coins spend: 182
The Cost of 14th bomber is: 28 i.e Total coins spend: 210
The Cost of 15th bomber is: 30 i.e Total coins spend: 240
The Cost of 16th bomber is: 32 i.e Total coins spend: 272
The Cost of 17th bomber is: 34 i.e Total coins spend: 306
The Cost of 18th bomber is: 36 i.e Total coins spend: 342
The Cost of 19th bomber is: 38 i.e Total coins spend: 380
The Cost of 20th bomber is: 40 i.e Total coins spend: 420
The Cost of 21st bomber is: 42 i.e Total coins spend: 462
The Cost of 22nd bomber is: 44 i.e Total coins spend: 506
The Cost of 23rd bomber is: 46 i.e Total coins spend: 552
The Cost of 24th bomber is: 48 i.e Total coins spend: 600
The Cost of 25th bomber is: 50 i.e Total coins spend: 650
The Cost of 26th bomber is: 52 i.e Total coins spend: 702
The Cost of 27th bomber is: 54 i.e Total coins spend: 756
The Cost of 28th bomber is: 56 i.e Total coins spend: 812
The Cost of 29th bomber is: 58 i.e Total coins spend: 870
The Cost of 30th bomber is: 60 i.e Total coins spend: 930
The Cost of 31st bomber is: 62 i.e Total coins spend: 992
Answer B #### B
QUESTION:Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart?
options: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm
SOLUTION:Total distance, which should be covered by both cars is 190+35=225 miles.
Let t be the time so the equation will be 46t+54t=225 thus,
t=2.25 hours
Answer: D #### D
QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
options: A)6 hrs 21 min B)6 hrs 91 min C)6 hrs 01 min D)6 hrs 23 min E)3 hrs 21 min
SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer:A #### A
QUESTION:Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed?
options: A)10 pm B)1 pm C)2 pm D)3 pm E)4 pm
SOLUTION:Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the Printer were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm
B #### B
QUESTION:Half of 2 percent written as decimal is
options: A)5 B)0.01 C)0.05 D)0.005 E)None of these
SOLUTION:Explanation:
It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01
Answer: Option B #### B
QUESTION:A customer pays 40 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
options: A)50 B)40 C)70 D)60 E)20
SOLUTION:Let x be the original price.
x - 20 = 40
x - 20 + 20 = 40 + 20
x + 0 = 60
x = 60
Answer is D #### D
QUESTION:If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 5.
II. x is an integer multiple of 3
III. x is an integer multiple of 6
options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only
SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6.
Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.
Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even
Answer E #### E
QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is
options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12
SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
= 4/13
Answer:D #### D
QUESTION:Rs.6160 were divided among B, C & D in such a way that B had Rs.320 more than C and D had Rs 240 more than B . How much was C’s share?
options: A)Rs.2300 B)Rs.2310 C)Rs.2320 D)Rs.2330 E)Rs.2340
SOLUTION:Let C gets Rs x. Then We can say B gets Rs (x + 320 ) and D gets Rs ( x + 280) .
x + 320 + x + x + 560 = 6160
3x = 5280
x = 1760 .
C’s share = Rs ( 1760+560 ) = Rs.2320
C #### C
QUESTION:If a is a number such that –2 ≤ a ≤ 2, which of the following has the largest possible absolute value?
options: A)3a – 1 B)x^2 + 1 C)3 – x D)x – 3 E)x^2 – x
SOLUTION:Ans is A .. leads to the max value of 7 for a = -2 #### A
QUESTION:The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid.
options: A)9: 8 B)9: 5 C)9: 1 D)9: 2 E)9: 4
SOLUTION:a1 : a2 = 3 : 1
6 a12 : 6 a22 = 9: 1
Answer:C #### C
QUESTION:A train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
options: A)45 kmph B)50 kmph C)55 kmph D)60 kmph E)70 kmph
SOLUTION:Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 100/((x+5)×5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55
Speed of the train is 55 kmph.
Answer: Option C #### C
QUESTION:In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning?
options: A)1/48 B)11/16 C)11/12 D)5/16 E)23/48
SOLUTION:First lets get the overview
Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2)
Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6)
Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4)
So now as above we have three events A,BC.
1st method(This is lengthy method)
Possible cases in which it's a win( the highlighted green event is a win and red is loose.
1.ABC= 1/2*5/6*3/4
OR
2.ABC= 1/2*1/6*3/4
OR
3.ABC= 1/2*5/6*1/4
OR
4.ABC= 1/2*1/6*3/4
OR
5.ABC= 1/2*5/6*1/4
OR
6.ABC= 1/2*5/6*1/4
OR
7.ABC= 1/2*1/6*1/4
As we now OR means add
Adding up all of them we'll get the probability of winning ie 11/16
Answer : B #### B
QUESTION:A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days B will the work get over?
options: A)60 B)70 C)B=75 D)B=80 E)100
SOLUTION:We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75
Ans: C (75 days) #### C
QUESTION:The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
options: A)279 B)283 C)308 D)318 E)342
SOLUTION:Other number = (11 x 7700)/275 = 308.
Answer: Option C #### C
QUESTION:January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
options: A)Monday B)Tuesday C)Wednesday D)Friday E)Sunday
SOLUTION:The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 1 day beyond Monday
Hence, It will be Tuesday. answer : B #### B
QUESTION:A committee of three students has to be formed. There are six candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
options: A)3 B)4 C)5 D)6 E)8
SOLUTION:Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE.
D #### D
QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
options: A)100 B)250 C)260 D)416 E)None of these
SOLUTION:Explanation:
Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 × 32 = 416.
Answer: D #### D
QUESTION:If C + D = 9 and C and D are positive integers, which of the following is a possible value for 5C + 8D?
options: A)55 B)61 C)69 D)90 E)97
SOLUTION:c + d = 11
5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 45 + 3d=D=15
D=15
c+d=9=C+15=9=C=9-15=-6
C=-6
5C + 8D=5(-6)+8(15)=-30+120=90
Hence, D is the right answer. #### D
QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
options: A)25 B)34 C)50 D)67 E)50
SOLUTION:Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 6 oz can = 300 oz/6 oz = 50
Answer E, 50 cans #### E
QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit?
options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these
SOLUTION:30,000 *12=45,000*8
1:1
Madhu's share=1/2*60,000
i.e. Rs. 30,000
ANSWER:C #### C
QUESTION:Consider two statements
Statement 1 => If R is an integer and R=2p+1 where p is not an integer.
Statement 2 => If S is an integer and S=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of R and S respectively
options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined
SOLUTION:answer will be E
R = integer
R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even R would odd
if n odd R would be even
ANSWER IS E #### E
QUESTION:A girl has exactly 5 quarters, 9 dimes, and 10 nickels in her pocket. If she withdraws a number of these coins at random, how many coins would she have to withdraw to ensure that she has at least a 50 percent chance of withdrawing at least one quarter?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:When the probability of NOT drawing a quarter is 50% or less, then the probability of drawing a quarter is at least 50%.
P(not drawing a quarter with 2 coins) = 19/24 * 18/23 = 57/92 > 50%
P(not drawing a quarter with 3 coins) = 57/92 * 17/22 = 969/2024 < 50%
The answer is B. #### B
QUESTION:For 1rs 4p interest
wat will be for 5000rs?
options: A)350Rs B)450Rs C)200Rs D)30Rs E)448Rs
SOLUTION:For 1rs , 4p interest
for 5000rs, x
x= 5000/1 * 4p ==> 20000 paise
To express in rs, 20000/100 = 200rs
ANSWER:C #### C
QUESTION:In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
options: A)7⁄19 B)2⁄3 C)3⁄4 D)9⁄21 E)None of these
SOLUTION:If the drawn ball is neither red nor green, then it must be blue, which can be picked in 7C1 = 7 ways. One ball can be picked from the total(8 + 7 + 6 = 21) in 21C1 = 21 ways.
∴ Reqd probability = 7⁄21 = 1⁄3
Answer E #### E
QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence?
I. w-6,x-6,y-6,z-6
II. 5w,2x,3y,5z
III. 5w,5x,5y,5z
options: A)II and III B)III only C)I and III D)I and II E)II only
SOLUTION:lets look at the three choices...
I. w-6,x-6,y-6,z-6
since the difference is constant, it is an arithmetic sequence...
II. 5w,2x,3y,5z
since the difference is not constant, it is not an arithmetic sequence
III. 5w,5x,5y,5z
since the difference is constant it is an arithmetic sequence...
Answer is A) #### A
QUESTION:Average age of students of an adult school is 46 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
options: A)1200 B)120 C)360 D)168 E)None of these
SOLUTION:Explanation :
Let the original no. of students be x.
According to situation, 46x + 120*32 = (x + 120)36 ⇒ x = 48
So, Required no. of students after joining the new students
= x + 120 = 168.
Answer : D #### D
QUESTION:Sum of the numbers from 1 to 25 is
options: A)210 B)325 C)320 D)105 E)None of these
SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2
Substitute n = 25.
So S20=25×26/2=325
Correct Option: B #### B
QUESTION:Carol budgeted 18 dollars for gifts for each of the 15 people on her Christmas list. After a disagreement with some of her neighbors, she reduces her Christmas list to 10 people. How much can she spend on each?
options: A)20 B)27 C)18 D)23 E)30
SOLUTION:A1*P1=A2*P2
18*15=A2*10 => A2=27
Answer:B #### B
QUESTION:The divisor is 12, the quotient is 4 and the remainder is 1.
What is the dividend?
options: A)48 B)49 C)96 D)97 E)72
SOLUTION:D = d * Q + R
D = 12 * 4 + 1
D = 48 + 1
D = 49
Answer: B #### B
QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300
SOLUTION:Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 616
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 616
⇒ y[12/10 + 1] = 616
⇒ 22y/10 = 616
⇒ 22y = 6160
⇒ y = 6160/22 = 560/2 = Rs.280
B #### B
QUESTION:Replace X with the appropriate number in
2 , 4 , 6 , 30 , 32 , 34 , X
options: A)38 B)8 C)5 D)36 E)37
SOLUTION:D
list of consecutive numbers that does not contain a 'e' in the spelling #### D
QUESTION:A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played?
options: A)50 B)60 C)70 D)80 E)90
SOLUTION:60% is 20%-points above 40% and 20%-points below 80%.
Thus the ratio of "the first 30 games" to "remaining games" is 1:1.
So the team played a total of 30+30 = 60 games.
The answer is B. #### B
QUESTION:In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A?
options: A)2 B)3 C)5 D)6 E)8
SOLUTION:I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have A=2*3*5*7 = 840
Thus, answer B #### B
QUESTION:19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
options: A)286 B)342 C)422 D)540 E)618
SOLUTION:2*19C2 = 2*171 = 342
The answer is B. #### B
QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight.
options: A)22 B)10 C)88 D)26 E)18
SOLUTION:M + D + I = 74 - - - (1)
(D + I) - M = 46 - - - (2)
I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3)
Adding (1) and (2) we get 2D + 2I = 120
Substituting the value of I in the above equation,
2D+2(2D5)=1202D+2(2D5)=120
⇒⇒ 14D = 600
⇒⇒ D = 300/7 = 42.8
Ans:B #### B
QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 10 per cent larger than the original. By what percentage has the area of the logo increased?
options: A)50 B)80 C)100 D)125 E)21
SOLUTION:Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 4.4 , so radius is 2.2
New area = 4.84π
Increase in area is 0.84π
% increase in area = 0.84/4*100
So, % increase is 21%
Answer will be (E) #### E
QUESTION:For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
options: A)12% B)26% C)29% D)32% E)60%
SOLUTION:In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated.
In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.
Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%.
Answer: D. #### D
QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28
SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 70 students =
800 + 3000 = 3800
Average marks of all the students = 3800/70 = 54.28
ANSWER:B #### B
QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
options: A) 5/6*d B) 7/3*d C) 10/3*d D) 7/2*d E) 9/2*d
SOLUTION:Favid has d books;
Jeff has d/3 books;
Paula has 2d books;
Total = d+d/3+2d=10d/3.
Answer: C. #### C
QUESTION:A person was fined for exceeding the speed limit by 10 km/hr.Another person was also fined for exceeding the same speed limit by twice the same.If the second person was traveling at a speed of 35 km/hr,find the speed limit.
options: A)487 B)15 C)76 D)29 E)12
SOLUTION:If x is speed limit,
Speed of first person = x + 10
Speed of 2nd person = x + 20
But speed of 2nd person = 35 kmph
x + 20 = 35
x = 15 kmph.
so speed limit is 15 kmph option D
Answer: B #### B
QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
options: A)300 km B)320 km C)360 km D)390 km E)400 km
SOLUTION:Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C) #### C
QUESTION:Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 45 miles per hour. How many miles from the station was train A overtaken by train B?
options: A)100 B)120 C)140 D)160 E)180
SOLUTION:After two hours, Train A is ahead by 60 miles.
Train B can catch up at a rate of 15 miles per hour.
The time to catch up is 60/15 = 4 hours.
In 4 hours, train A travels another 30*4 = 120 miles for a total of 180 miles.
The answer is E. #### E
QUESTION:What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
options: A)$788 B)$812 C)$864 D)$878 E)$912
SOLUTION:After one year: 1.2 * $500
After two years: (1.2)^2 * $500
After three years: (1.2)^3 * $500 = $864
The answer is C. #### C
QUESTION:√(36)^2
options: A)6 B)14 C)36 D)21 E)None of these
SOLUTION:explanation
√(36)^2 =?
or, ? = 36
Answer C #### C
QUESTION:Little Praveen had $50.50. He spent $12.25 on sweets and gave same money to his two friends and the amount left with him is $31.25. Find how much he spent to two of his friends?
options: A)$ 16.65 B)$ 18.65 C)$ 19.25 D)$ 16.55 E)$ 17.65
SOLUTION:Praveen spent and gave to his two friends a total of
12.25 + 2x= $4.65, x is the amount spent to one friend.
Money left
50.50 -2x = $31.85. Then 2x=$18.65.
correct answer is B) $ 18.65 #### B
QUESTION:The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :
options: A)4 B)8 C)12 D)16 E)18
SOLUTION:Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8 Answer: B #### B
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 50 years now, the son's age five years back was?
options: A)18years B)19years C)20years D)21years E)22years
SOLUTION:Let the son's present age be x years. Then, (50 - x) = x
2x = 50.
x = 25.
Son's age 5 years back (25 - 5) = 20 years.
C) #### C
QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
options: A)288 B)165 C)881 D)1277 E)121
SOLUTION:Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 25 = 375 m.
Let the length of the platform be x m . Then,
(x + 375)/36 = 15 => x = 165 m.
Answer: B #### B
QUESTION:What is 35% of 4/13 of 585?
options: A)52 B)63 C)74 D)85 E)96
SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 585 is between 540 and 630, so (1/9)*585 will be about 65.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The closest answer is 63, so this is the answer to choose.
The answer is B. #### B
QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
options: A)72 min B)25.11628 min C)70 min D)74.11682 min E)76 min
SOLUTION:x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
185x+15*2x=180
x=180/215
x=0.837209
time taken for type A problem=15*2*0.837209=25.11628min
ANSWER:B #### B
QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is :
options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None
SOLUTION:Explanation:
Ratio of rents
=(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3)
=72:50:140:63
Let total rent = Rs.x
Then, A's share = Rs.(x×72/325)= Rs.(72x/325)
72x/325=360 or x = 325×360/72=1625
Correct Option: C #### C
<<<Examples ends
QUESTION:What is x if x + 5y = 24 and y = 2?
options: A)1 B)3 C)5 D)7 E)14
SOLUTION:Substitute y by 2 in x + 5y = 24
x + 5(2) = 24
x + 10 = 24
If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence
x = 14 correct answer E #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 10'o clock.
options: A)60sec B)62sec C)66sec D)64sec E)54sec
SOLUTION:At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
.
.
9'o clock 8 *6=48sec
10'o clock 9 *6=54sec
So, 54sec at 10'o clock.
ANSWER:E #### E
QUESTION:A boat having a length 7 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
options: A)100 kg B)120 kg C)89 Kg D)80 Kg E)210 Kg
SOLUTION:Volume of water displaced = (7 x 3 x 0.01) m3
= 0.21 m3.
Mass of man = Volume of water displaced x Density of water
= (0.21 x 1000) kg
= 210 kg.
Answer: E #### E
QUESTION:In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
options: A)6^6 ways B)8^9 ways C)7^8 ways D)8^7 ways E)8^6 ways
SOLUTION:6 people can be prized with distinct prizes in 6^6 ways
ANSWER:A #### A
QUESTION:In 20 years, A will be twice as old as B was 20 years ago. If A is now 10 years older than B, the present age of B is?
options: A)35yrs B)40yrs C)50yrs D)60yrs E)70yrs
SOLUTION:Let B's present age = x years
Then A's present age = x+10 years
x+10+20 = 2(x-20)
x + 30 = 2x - 40
x = 70years
Answer is E #### E
QUESTION:Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE?
options: A)1/15 B)1/14 C)1/12 D)1/13 E)1/17
SOLUTION:Explanation :
Let two digit number that Shiwani thought be 'xy', where x and y are single digit number.
Therefore, 10x+y=p(x+y)+3, where p is a natural number
p=10x+y−3x+y.
Also, y+x>3.
Possible values of x and y for which p is a natural number are :-
(x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9),
(x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null),
(x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4)
There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits.
Probability that Devesh thought of the same number as Shiwani = 1/14
Answer : B #### B
QUESTION:The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 4. If the project took 90 hours, how many more hours did the hardest working person work than the person who worked the least?
options: A)18 hours B)22 hours C)25 hours D)26 hours E)20 hours
SOLUTION:Let the persons be A, B, C.
Hours worked:
A = 2*90/9 = 20 hours
B = 3*90/9 = 30 hours
C = 4*90/9 = 40 hours
C is the hardest worker and A worked for the least number of hours. So the difference is 40-20 = 20 hours.
Answer : E #### E
QUESTION:A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?
options: A)77 days B)21 days C)88 days D)55 days E)44 days
SOLUTION:WC = 1:2
2x + x = 1/14 => x = 1/42
2x = 1/21 => 21 days
Answer: B #### B
QUESTION:The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
options: A)277 B)268 C)287 D)480 E)281
SOLUTION:Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer:D #### D
QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600:
options: A)200 B)250 C)300 D)350 E)400
SOLUTION:X = Rs.5000/-
Y = Rs.15000/-
X share 1 part & Y share 3 parts
Total 4 parts -----> Rs.1600/-
----> 1 part -------> Rs.400/-
X share = 1 part -----> Rs.400/-
E #### E
QUESTION:In an election between two political leaders 10% of the voters did not cast their vote. 10% of the votes polled were found invalid. The successful political leader got 54% of the valid, votes and won by a majority of 3240 votes. The number of voters enrolled on the voters list was :
options: A)30000 B)50000 C)33000 D)40000 E)45000
SOLUTION:Explanation :
Solution: Let the number of voters be x. then, votes polled = 90% of x.
Valid votes = 90% of(90% of x)
.'. 54% of[90% of(90% of x)] - 46% of[90% of(90% of x)] = 3240.
8% of[90% of(90% of x)] = 3240.
8/100 * 90/100 * 90/100 * x = 3240
x = (3240*100*100*100)/(8*90*90) = 50000
Answer : B #### B
QUESTION:The number of positive integer solutions for the equation x +y +z + t = 18 is
options: A)640 B)780 C)380 D)540 E)680
SOLUTION:The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1)- where k is the number and n is number of variable in the equation.
18-1 C 4-1 = 17C3 = 680
Answer : E #### E
QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5)
SOLUTION:3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5.
Answer: D. #### D
QUESTION:(1/5)^q * (1/4)^18 = 1/(2(10)^35). What is q?
options: A)17 B)18 C)34 D)35 E)36
SOLUTION:We need to arrive at a common base. -->
(5)^(-q) * 2^(-36) = 2^(-36)*5^(-35)
5^(-q)=5^(-35)
-q=-35
q=35=D #### D
QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters)
options: A)92 B)90 C)82 D)78 E)75
SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
O=12.5*6 = 75=E #### E
QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
options: A)81.6 B)88.6 C)81.1 D)81.5 E)81.2
SOLUTION:SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer: A #### A
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
options: A)11% B)25% C)87% D)19% E)12%
SOLUTION:800 --- 200
100 --- ? => 25%
Answer: B #### B
QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 87°, what fraction of the wheel’s area is represented by the smallest sector?
options: A)1/120 B)1/100 C)1/80 D)1/60 E)1/40
SOLUTION:The largest angle is 87.
Let d be the difference between any two angles in the progression.
The sum of all the angles will be:
87 + (87-d) + (87-2d) + ... + (87-7d) = 696 - 28d
The sum of all the central angles in a circle = 360
696 - 28d = 360
d = 336/28 = 12
The smallest sector is (87-7d) = 87-7*12 = 3
3/360 = 1/120
The answer is A. #### A
QUESTION:Thomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer?
options: A)10 B)14 C)19 D)21 E)25
SOLUTION:The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5
The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0
Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5
The % of profit in selling a single computer=(4545.5/45454.5)*100=10%
Answer:A #### A
QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15
SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B
QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water
options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr
SOLUTION:still in water=1/2(98+10)km/hr
=54km/hr
correct option is :B #### B
QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players?
options: A)45 B)56 C)64 D)78 E)90
SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players.
=> Required number of ways = 13C11
= 78
D #### D
QUESTION:If x is a positive integer, which of the following must be odd?
options: A)x+1 B)x^2+x C)x^2+x+7 D)x^2−1 E)3x^2−3
SOLUTION:A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 7 = ODD
Hence C. #### C
QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of :
options: A)45 hours B)47 hours C)48 hours D)50 hours E)None
SOLUTION:Explanation:
Basic rate per hour = Rs.(20/40)= Rs.1/2
Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8
Suppose he worked x hours overtime.
Then,20+5/8x=25 or 5/8x=5
x=5×8/5=8 hours
So he worked in all for (40+8) hours = 48 hours.
Correct Option: C #### C
QUESTION:walking at ¾ of his usual speed ,a man is late by 2 ½ hr.
the usual time is.
options: A)7 B)8 ½ C)7 ½ D)7 ¾ E)9 ½
SOLUTION:Usual speed = S
Usual time = T
Distance = D
New Speed is ¾ S
New time is 4/3 T
4/3 T – T = 5/2
T=15/2 = 7 ½
Answer is C. #### C
QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.)
Can somebody explain?
options: A)6720 B)7720 C)7820 D)7950 E)8120
SOLUTION:First ring can be worn in 4 ways (on any of the four fingers);
Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1);
Third ring can be worn in 6 ways (the same logic as for the second ring);
Fourth ring can be worn in 7 ways;
Fifth ring can be worn in 8 ways;
Total: 4*5*6*7*8=6720. ANS:A #### A
QUESTION:If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is
options: A)not an even B)an even C)a perfect square D)an odd E)a prime
SOLUTION:x^2 - 2x + 2y + 3 = 2x^2 - 3x + y + 1
y = x^2 - x - 2
y = (x-2)(x+1) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B. #### B
QUESTION:A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy
options: A)s. 600 B)s. 800 C)s.500 D)s.900 E)s. 1300
SOLUTION:Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 27300.
Gain = SP – CP
3X = 27300 – 18X
21X = 27300
X = Rs. 1300.
ANSWER : OPTION E #### E
QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 60 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?
options: A)12 B)15 C)20 D)24 E)30
SOLUTION:Let x be the number of new boarders.
The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10.
60 / (60+x) = 4/5
x = 15
The answer is B. #### B
QUESTION:Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:
options: A)Rs. 4800 B)Rs. 5000 C)Rs. 5400 D)Rs. 5600 E)Rs. 6600
SOLUTION:let investment is x... den remaining investment is (9800-x)
x*9/75= (9800-x)*10/80
x=4800
9800-x=5000
ANSWER:B #### B
QUESTION:Evaluate 28% of 550 + 45% of 280
options: A)232 B)242 C)252 D)262 E)280
SOLUTION:Explanation:
= (28/100) * 550 + (45/100) * 280
= 154 + 126 = 280
Answer: Option E #### E
QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers
options: A)2 B)4 C)8 D)12 E)14
SOLUTION:Explanation:
Let the ten digit be x, unit digit is y.
Then (10x + y) - (10y + x) = 36
=> 9x - 9y = 36
=> x - y = 4.
Option B #### B
QUESTION:John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam four years ago?
options: A)2 B)4 C)6 D)8 E)16
SOLUTION:j= 3s
after 6 years
j +6 = 2(s+6)
j= 2s+6
2s +6 = 3s
s= 6
four years ago
s= 6-4= 2
A is the answer #### A
QUESTION:A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B?
options: A)38 metre B)28 metre C)23 metre D)15 metre E)36 metre
SOLUTION:Clearly, A beats B by 4 seconds
Now find out how much B will run in these 4 seconds
Speed of B = Distance/Time taken by B=288/32=9 m/s
Distance covered by B in 4 seconds = Speed × time =9×4=36 metre
i.e., A beat B by 36 metre
Answer is E #### E
QUESTION:A city with a population of 173,460 is to be divided into 9 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
options: A)17,400 B)17,500 C)17,600 D)17,700 E)17,800
SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.
Let p be the population of the least populated district.
Then 173,460 = p + 8(1.1)p
9.8p=173,460
p = 17,700
The answer is D. #### D
QUESTION:One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel?
options: A)400 B)450 C)500 D)550 E)600
SOLUTION:The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour.
The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours.
The answer is A. #### A
QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?
options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150
SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15.
Hence, the probability that at least one light bulb fails is 1-0.94^15.
Answer: A.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A
QUESTION:The profit earned by selling on article for 900 is double the loss incurred when the same article is sold for 450. At what price should the article be sold to make 25% profit?
options: A)750 B)800 C)850 D)860 E)890
SOLUTION:Let ‘x’ be the CP of the article;
Then 900 – x = 2(x – 450); :. x= 600.
25% of 600 = 150
:. New SP = 600 + 150 = 750
Option 'A' #### A
QUESTION:If logx y = 10 and log2 x = 1000, what is the value of y?
options: A)210002 B)277889 C)210000 D)27788 E)788291
SOLUTION:Explanation:
log2 x = 1000
=> x = 21000
logx y = 10
=> y = x10
= (21000)10
= 2(1000 × 10)
= 210000
Answer: Option C #### C
QUESTION:In a camp, there is a meal for 110 men or 200 children. If 140 children have taken the meal, how many men will be catered to with remaining meal?
options: A)41 B)30 C)35 D)33 E)36
SOLUTION:D
33
There is a meal for 200 children.
140 children have taken the meal.
Remaining meal is to be catered to 60 children.
Now, 200 children 110 men.
60 children = (110/200)x 60= 33 men. #### D
QUESTION:Jimmy has 20% more cookies than Janice. What percentage of cookies should Jimmy give to Janice so that both Jimmy and Janice have the same number of cookies?
options: A)7.5% B)7.7% C)7.9% D)8.1% E)8.3%
SOLUTION:An easy way to solve this question is by number plugging. Assume Janice has 100 cookies then Jimmy has 120 cookies. Now, for both Jimmy and Janice to have equal amounts of cookies we should give Janice 10 of Jimmy's cookies, which is 10/120=~8.3% of Jimmy's cookies.
Answer: E. #### E
QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed.
options: A)32 B)15 C)18 D)20 E)25
SOLUTION:Relative speed = (420/18)m/s = (420/18)*(18/5) = 84 kmph
speed of goods train = 84-64 = 20 kmph
Answer is D #### D
QUESTION:In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 8,000 have been vaccinated against both, how many have been vaccinated only against rubella?
options: A)2,5000 B)7,500 C)10,000 D)15,000 E)16,000
SOLUTION:Use a single variable as far as possible.
Number vaccinated only against mumps = x
Number vaccinated against both = 2x = 8000 (so x = 4000)
Then, number vaccinated against mumps (including both) = x + 2x = 3x
Number vaccinated against rubella = 2*3x = 6x
Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*4000 = 16,000
Answer (E) #### E
QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
options: A)65 B)44 C)18 D)16 E)14
SOLUTION:Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer:C #### C
QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A.
options: A)256 B)388 C)379 D)277 E)122
SOLUTION:Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 672 = 256
Answer: A #### A
QUESTION:Vijay bought 160 shirts at the rate of Rs. 220 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
options: A)s.225 B)s.288 C)s.485 D)s.279 E)s.282
SOLUTION:Total CP per shirt = 220 + 1400/160 + 1.75 + 320/160 = Rs. 232.5
SP = CP[(100 + profit%)/100]
= 232.5 * [(100 + 20)/100] = Rs.279.
Answer:D #### D
QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund?
options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000
SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5
1/5 of fund = 841---
Fund = 5 * 841---
Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it.
Answer (E). #### E
QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs?
options: A)362880 B)340009 C)250909 D)345008 E)1000
SOLUTION:number of ways =9! = 362880
Answer is A #### A
QUESTION:Sara works 5 days a week at d dollars per day for m weeks out of the month. Which of the following represents her monthly pay?
options: A)m/(5d) B)20d C)5d D)5dm E)20d/m
SOLUTION:Total income of Sara in a month = d*5*m dollars. = d*5*m = 5dm Answer is D #### D
QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2
SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer: B #### B
QUESTION:If the cost price is 96% of the selling price, then what is the profit percent?
options: A)4.17% B)5% C)6.12% D)3.25% E)5.75%
SOLUTION:Let S.P. = $100
C.P. = $96
Profit = $4
Profit% = 4/96 * 100 = 25/6 = 4.17%
Answer is A #### A
QUESTION:Eight years ago, Rhea was half of Rick in age. If the ratio of their present ages is 3:4, what is the total of their present ages?
options: A)25 years B)28 years C)32 years D)26 years E)28 years
SOLUTION:let rhea age be x
rick age be y
given
x-8=1/2(y-8)......a
also given
x/y=(3/4)
=>x=3/4(y).......b
by solving a and b
we get y=16
x=12
then x+y=12+16=28
ANSWER:B #### B
QUESTION:If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 4?
options: A)1/4 B)3/8 C)1/2 D)5/8 E)3/4
SOLUTION:I get 5/8 as well
1 to 96 inclusive means we have 48 odd and 48 even integers
E O E / 4 = Integer, therefore we have 48 / 96 numbers divisible by 8
O E O / 4 = Not Integer
We cannot forget multiples of 8 from 1 to 96
We have 24 numbers that are multiple of 4
Therefore, 48/96 + 24/96 = 72/96 = 3/4
answer : E #### E
QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years?
options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11
SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320
C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5
Difference = (360.5 - 320) = Rs. 40.5
Answer: C #### C
QUESTION:In how many ways letters of the word LEADER be arranged?
options: A)5 B)78 C)69 D)58 E)120
SOLUTION:LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways
E #### E
QUESTION:Find the smallest four-digit number which is a multiple of 112.
options: A)896 B)1008 C)1120 D)1024 E)None of these
SOLUTION:The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104.
112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112.
ANSWER:B #### B
QUESTION:There is a group of persons each of whom can completea piece of work in 16 days, when they are working individually. On the 1st day 1 person works, on the second day another person joins him, on the third day one more person joins them & this process continues till the work is completed. How many days are needed to complete the work?
options: A)5 1⁄2 days B)5 1⁄3 days C)5 1⁄6 days D)6 1⁄6 days E)7 1⁄6 days
SOLUTION:Work completed in 1st day = 1/16
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16
…
An easy way to attack such problems is from the choices. You can see the choices are
very close to each other. So just see one by one.
For instance, The first choice given in 3 1⁄4
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.
(Just for your reference, work done in 5 days = 15/16.
Pending work in 6th day = 1 – 15/16 = 1/16.
In 6th day, 6 people are working and work done = 6/16.
To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.
Hence total time required = 5 + 1/6 = 5 1⁄6 days
C #### C
QUESTION:A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
options: A)6.4 days B)4.4 days C)5.4 days D)8.4 days E)2.4 days
SOLUTION:A
6.4 days
1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300
So, all three together will complete the work in 300/47 = 6.4 days.- #### A
QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
options: A)33 1/8% B)33 3/3% C)33 1/3% D)39 1/3% E)33 4/3%
SOLUTION:675 ---- 225
100 ---- ? => 33 1/3%
Answer:C #### C
QUESTION:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 45min will be.
options: A)60 km/h B)53 km/h C)40 km/h D)70 km/h E)65 km/h
SOLUTION:Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=45/60hr=3/4hr
New speed = 40* 4/3 kmph= 53kmph
Answer : B #### B
QUESTION:How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?
options: A)20 B)31 C)42 D)53 E)64
SOLUTION:Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers
Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers
So required number= 62-20 = 42
Choice C #### C
QUESTION:A three digit number divisible by 7 becomes divisible by 3 when 7 is added to it. The largest such number is :
options: A)891 B)896 C)882 D)867 E)864
SOLUTION:Out of all the 5 options, only 896 is NOT divisible by 3. All others are divisible
So Answer = B(No further calculation required)
Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3
7 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3
Applying the above rule,It means that the number which we are going to add should be non-divisible by 3
So comes the answer = 896
Answer : B #### B
QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760
SOLUTION:After one year: 1.2 * $2500
After two years: (1.2)^2 * $2500
After three years: (1.2)^3 * $2500 = $4320
The answer is D. #### D
QUESTION:What is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
options: A)1200 B)1256 C)1349 D)1456 E)1590
SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C #### C
QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals?
options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6
SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15
ANSWER:D #### D
<<<Examples ends
QUESTION:Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 3 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
options: A)1/24 B)1/8 C)1/4 D)1/3 E)3/8
SOLUTION:I hope you are familiar with basic probability fundas -
Let's say you have just ONE letter and TWO envelopes ONE of which is correctly addressed and the other addressed incorrectly.
What's the probability of putting the Letter in the correctly addressed envelope -
To answer this question - we see IN HOW MANY WAYS can the letter be put into the envelope - you could put it (assuming you don't know which envelope is which) in either of the two - so in total you have TWO ways of shoving the letter in. However, there's only ONE way in which it can go into the correctly addressed envelope -
so 1/2 is the prob of putting in correct envelope. This is easy.
Now in our current problem - let's say we have just ONE letter but FOUR envelopes. Only one of these envelopes has the address corresponding to the letter. The remaining three envelopes are incorrectly addressed.
So the probability that you will put the letter correctly is 1/4. Right?
What happens if i ask you the reverse question? what is the prob for putting it in the incorrect envelope. Suddenly you have three envs that are incorrect so you can put the letter incorrectly with a prob of 3/4. Right?
The whole problem can be broken down into Four Events that will fulfill the requirement of the question
Event 1 - E1
We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the first letter goes into the correct envelope) we have the remaining THREE Letters and THREE envelopes.
Event 2 - E2
Let's take letter number 2 now - what is the probability that it LANDS in the INCORRECT envelope. Again by the same logic as above - there are 3 envelopes remaining out of which ONLY ONE has the correct address for LETTER number 2. The remaining 2 have INCORRECT address and LETTER NUMBER 2 could go in either of these 2 to meet our condition.
Thus the probability of this event is 2/3
So till now what we have done is -
we have calculated the prob of shoving Letter number 1 in correct env -- 1/4
we have calculated the prob of shoving Letter number 2 in INcorrect env --- 2/3
Event 3 - E3
Now let's take letter number 3 - again according to question we want to shove this in the WRONG envelope. There are 2 remaining envelopes and hence the prob of shoving this in the wrong env (or equally in the RIght env) is 1/2.
Finally we come to event E4 - the Letter number 4. This has only one way of going in so its probability of being put into the WRONG envelope is 1.
ok so we can see that our grand event is actually a combination of FOUR EVENTS happening - each with a probability of its own. So to calculate the total probability of the Grand Event itself we just multiply the individual probabilities since each event happens INDEPENDENTLY of each other
Egrand = 1/4 * 2/3 * 1/2 * 1/1 = 1/12
However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result.
If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 and worked thru the remaining letters, we could have equally well started out with letter L2 or L3 or L4.
Thus since each of these events ARE MUTUALLY EXCLUSIVE, meaning THEY CAN NEVER HAPPEN ALL THE SAME TIME BUT ONLY ONE LETTER AT A TIME, to calculate the TOTAL PROBABILITY of we will add the individual probabilities 1/12 + 1/12 + 1/12 + 1/12 which works out to 1/8.
B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
options: A)3 months B)4 months C)5 months D)6 months E)7 months
SOLUTION:S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = (100x80)/(1600x15)= 1/3 year = 4 months
answer : B #### B
QUESTION:what is the radius of a circle that has a circumference of 3.14 meters?
options: A)0.5 mtr B)1.5 mtr C)2.3 mtr D)0.2 mtr E)1.2 mtr
SOLUTION:circumference of a cirlce = 2nr, given circumference= 3.14 mtr.
2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (A) #### A
QUESTION:What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-79)*(50-80)?
options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000
SOLUTION:One of the terms is (50-50) so the product is 0.
The answer is C. #### C
QUESTION:A no.when divided by 223 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
options: A)2 B)7 C)9 D)11 E)15
SOLUTION:223 + 43 = 266/17 = 11 (Remainder)
D #### D
QUESTION:If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips?
options: A)1/8 B)1/16 C)1/32 D)1/64 E)1/128
SOLUTION:P(HHHHTT) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64
The answer is D. #### D
QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet?
options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m
SOLUTION:D = 50 * 1 ½ = 75 km
RS = 75 – 50 = 25
T = 75/25 = 3 h
3.30 + 3 h = 6.30 p.m.
Answer: C #### C
QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
options: A)12, 9 B)10, 5 C)12, 7 D)11, 6 E)12, 6
SOLUTION:x – y = 5
4x – 6y = 6
x = 12 y = 7
ANSWER:C #### C
QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
options: A)15 B)19 C)20 D)21 E)22
SOLUTION:A's 1day work=1/10;
B's 1day work=1/30;
(A+B) 1day work=(1/10+1/30)=2/15;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 2/15 work in 1 day...
They did 2/3 w in 5 days.
Total days=(5+10) = 15
ANSWER:A #### A
QUESTION:An arithemetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 12th member of this sequence?
options: A)A)37 B)B)40 C)+ 13 D)D)34 E)+ 13
SOLUTION:Common difference of an arithmetic series is constant.
2p+2-p=4p+3-2p-2
p=1
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
Ans:D #### D
QUESTION:A 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
options: A)6%. B)7.5%. C)9.2%. D)10.5%. E)14%.
SOLUTION:Denominator:
340+10+3.2+6.8=360
Numerator:
340(1-.80-.06)+3.2
340(0.14)+3.2
47.6+3.2
50.8
Ratio:
50.8/360=0.14
Answer: E #### E
QUESTION:In how many a committee of 5 members can be selected from 6 men 5 ladies consisting of 3 men and 2 ladies
options: A)250 B)150 C)100 D)50 E)200
SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
ANSWER E #### E
QUESTION:In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
options: A)8 B)9 C)10 D)11 E)12
SOLUTION:The total number of books the students borrowed is 20*2=40.
The students who borrowed zero, one, or two books borrowed 8*1+3*2=14 books.
The 7 students who borrowed at least three books borrowed 40-14=26 books.
If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books.
The answer is A. #### A
QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone?
options: A)4 2/3 B)7 C)9 D)24 E)21
SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 6 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/7+6*1/x=1
5x+42=7x
2x=42
x=21 days.
Ans:E #### E
QUESTION:In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
options: A)1/6 B)2/9 C)6/20 D)13/20 E)3/4
SOLUTION:Method- 1
There are 9 fine pieces of pen and 3 defective in a lot of 16 pens
i.e. Probability of first pen NOT being defective = (13/16)
i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective]
Probability of Both pen being NON-defective = (12/15)*(13/16) = 13/20
Answer: option D #### D
QUESTION:A fruit drink is made of orange, watermelon, and grape juice, where 25 percent of the drink is orange juice and 40 percent is watermelon juice. If the drink is made with 105 ounces of grape juice, how many ounces is the drink total?
options: A)220 B)250 C)280 D)300 E)340
SOLUTION:Let the total number of ounces in the drink be x.
% of orange = 25%
% of watermelon = 40%
% of grape = 100% - 65% = 35%
0.35x = 105
x = 300
Therefore there are a total of 300 ounces in the drink.
The answer is D. #### D
QUESTION:On Monday Joshua sold 90 phones, Rob sold 30% more phones than Joshua, Prerna sold 11 more phones than Rob, and Declan sold 3/4 of what Prerna sold. How many phones did Declan sell?
options: A)111 B)75 C)29 D)128 E)96
SOLUTION:E
96
Joshua sold 90 phones.
Rob sold 30 % more phones than Joshua
Rob = 90 + 90 × 30%
= 90 + 90 × 0.30
= 90 + 27
= 117
Prerna sold 11 more phones than Rob
Prerna = 117 + 11
= 128
Declan sold 3/4 of what Prerna sold.
Declan= 128 x 3/4
=96
Declan sold 96 phones.
The correct answer is E. #### E
QUESTION:The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?
options: A)14 M B)20 M C)18 M D)12 M E)15 M
SOLUTION:LB = 460 M2
LET BREATH = B
L = B * (100 + 15)/100 = 115B/100
FROM THESE 115B/100 * B = 460
B2 = 46000/115 = 400
B = ROOT OF 400 = 20 M
ANSWER B #### B
QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
options: A)388 B)299 C)266 D)400 E)2871
SOLUTION:2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400.Answer: D #### D
QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam?
options: A)52% B)64% C)72% D)76% E)80%
SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A
QUESTION:How many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14?
options: A)30 B)31 C)32 D)33 E)34
SOLUTION:250/15 = 16 (plus remainder) so there are 16 multiples of 15
250/14 = 17 (plus remainder) so there are 17 multiples of 14
We need to subtract 1 because 15*14 is a multiple of both so it was counted twice.
The total is 16+17-1 = 32
The answer is C. #### C
QUESTION:In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive?
options: A)None B)One C)Two D)Three E)Four
SOLUTION:Non - Negative ( zero to positive infinity )
Solution to the question :
-4,-3,-2,-1,0 , 1,2,3
Hence ans is 3 ..option D #### D
QUESTION:Zeeshan having a certain number of one rupee,fifty paise and twenty
five paise coins are in the ratio of 3:2:4, add up to
Rs 75. Then how many 1 rupee coins he have?
options: A)10 B)20 C)45 D)128 E)49
SOLUTION:Explanation :
Given ratio = 3:2:4.
Let us assume that there are 3 one rupee coins,2
fifty paise coins and 4 twenty-five paise coins in all.
Their value=(3*1)+(2*.50)+(4*.25)=3+1+1=Rs 5
If the total is Rs 5, number of 1 rupee coins are 3.
If the total is Rs 75, number of 1 rupee coins would be 75*3/5=45.
Answer : C #### C
QUESTION:The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
options: A)76 kg B)76.5 kg C)85 kg D)Data inadequate E)None of these
SOLUTION:EXPLANATION
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer C #### C
QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16
SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C #### C
QUESTION:The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ?
options: A)31 kg B)63 kg C)61 kg D)62 kg E)91 kg
SOLUTION:let c=coach's avg. weight
original total weight=(30 friends)(30 kg avge)=900kg
(900+3c)/(30+3)=33 kg avg.
c=63 kg
Answer B #### B
QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
options: A)220 B)250 C)320 D)420 E)560
SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7.
We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers.
Hence , answer is D. #### D
QUESTION:Find the area of a parallelogram with base 20 cm and height 10 cm?
options: A)287 cm2 B)887 cm2 C)200 cm2 D)250 cm2 E)668 cm2
SOLUTION:Area of a parallelogram = base * height
= 20 * 10
= 200 cm2
Answer: C #### C
QUESTION:The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares
options: A)22 cm B)24 cm C)26 cm D)28 cm E)None of these
SOLUTION:Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 10*10 - 8*8
= 36 cm
So side of third square = 6 [because area of square = side*side]
Perimeter = 4*Side = 4*6 = 24 cm
Option B #### B
QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola
y = x2 + x + 4 at exactly one point. Compute the intersection point.
options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10)
SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution
in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4.
Therefore, k = -3 or k = 5.
Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection
point is (2, 10) .
correct answer A #### A
QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is?
options: A)11 B)72 C)36 D)99 E)27
SOLUTION:Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240)/12 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72 km/hr.
Answer: B #### B
QUESTION:The ratio of boys to girls is 6:4.60% of the boys and 40% of girls take lunch in the canteen.What % of class takes lunch?
options: A)51% B)52% C)53% D)54% E)55%
SOLUTION:let total no of students 100, boy 60 and girl 40, so lunch taken by boy and girl respectively 60* 60/100=36 and 40* 40/100=16
so total 52 students takes lunch out of 100 students..so required % is 52%
ANSWER:B #### B
QUESTION:Two numbers are in the ratio of 7:6. If 18 be subtracted from each, they are in the ratio of 6:5. Find the numbers?
options: A)5,9 B)7,9 C)4,7 D)7,6 E)6,9
SOLUTION:(7x-18):(6x-18) = 6:5
x = 1 => 7,6
Answer: D #### D
QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?
options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000
SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager.
Average company salary * Number of employees = Total company salary
>>> $80,000 * 10 = $800,000
Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000)
>>> $800,000 - $300,000 - $240,000 = $260,000.
The correct answer is C. #### C
QUESTION:A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be
options: A)7744 B)2388 C)3778 D)2992 E)2888
SOLUTION:Explanation:
length of wire = {\color{Blue}2 \Pi r}= 2 *(22/7 )*56 = 352 cm
side of the square = 352/4 = 88cm
area of the square = 88*88 = 7744sq cm
Answer: A) 7744 #### A
QUESTION:If n = 20! + 15, then n is divisible by which of the following?
I. 15
II. 17
III. 19
options: A)I only B)II only C)III only D)I and II E)II and III
SOLUTION:15 divides 20! so 15 also divides 20! + 15.
17 and 19 divide 20! so they do not divide 20! + 15.
The answer is A. #### A
QUESTION:The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?
options: A)6.06% B)6.07% C)6.08% D)6.09% E)6.19%
SOLUTION:Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09%
ANSWER:D #### D
QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?
options: A)120 B)350 C)1470 D)2,520 E)5,040
SOLUTION:Number of ways to choose 2 colors among 7 - 7c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))
Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]
Total number of combinations - 7c2 * 2* 7c4 = 1470
C #### C
QUESTION:The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ?
options: A)148 B)134 C)156 D)144 E)None
SOLUTION:Solution:
Ratio of Ducks and Frogs in Pond,
= 37 : 39.
Average of Ducks and Frogs in Pond,
= 132.
So, total number of Ducks and Frogs in the Pond,
= 2* 132 = 262.
Therefore,
Number of Frogs, = (262*39)/76 = 134.
Answer: Option B #### B
QUESTION:If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years?
options: A)(1+k/100)^n B)(1+k)^n C)(1+kn/100) D)(1+k/100)^4n E)(1+kn)
SOLUTION:Amount after 7n years will be = x ( 1 + k/100)^4n
Amount after 3n years will be = x ( 1 + k/100)^3n
So, required ratio will be -
{ x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n
Hence answer will be a. (1+k/100)^4n
D #### D
QUESTION:Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?
options: A)24. B)28. C)36. D)42. E)48
SOLUTION:Diameter of tube= 5 inches
Height of wooden tube= 15 inches
Two tubes can stand in 31 inches height
Two tubes can fit in 11 inches length
Two tubes can fit in 10 inches width
So, one box can hold 8 tubes
Three boxes can hold= 8*3= 24 tubes
A is the answer #### A
QUESTION:A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight?
options: A)20 lb B)11 lb C)10 lb D)15 lb E)5 lb
SOLUTION:Sol.
66÷6 = 11.
Answer : B #### B
QUESTION:In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
options: A)7000 B)7200 C)7400 D)7600 E)8000
SOLUTION:State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
E) #### E
QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200
SOLUTION:Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000)
= 60720
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 60720 = 5280
Hence, A. #### A
QUESTION:A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
options: A)4 B)5 C)6 D)7 E)8
SOLUTION:The rate of the pump + leak = 5/14
1/2 - leak's rate = 5/14
leak's rate = 1/2 - 5/14 = 1/7
The leak will empty the tank in 7 hours.
The answer is D. #### D
QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
options: A)15% B)25% C)15.125% D)27.78% E)none
SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options.
The correct answer is (D). #### D
QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?
options: A)15.5 B)15.4 C)15.25 D)15.3 E)15.6
SOLUTION:Total age of 20 men = 15.6 x 20 = 312
Now, total age of 25 men = 389.
Total age of five men added later = 389 - 312 = 77.
Hence, the total average of five men = 77/5 = 15.4
ANSWER:B #### B
QUESTION:Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers?
options: A)21, 12 B)9, 0 C)15, 6 D)10, 1 E)14, 5
SOLUTION:the larger number: x
the smaller number: y
twice the larger: 2x
three more than five times the smaller: 5y + 3
relationship between ("is"): 2x = 5y + 3
four times the larger: 4x
three times the smaller: 3y
relationship between ("sum of"): 4x + 3y = 71
Now I have two equations in two variables:
2x = 5y + 3
4x + 3y = 71
I will solve, say, the first equation for x:
x = (5/2)y + (3/2)
Then I'll plug the right-hand side of this into the second equation in place of the "x":
4[ (5/2)y + (3/2) ] + 3y = 71
10y + 6 + 3y = 71
13y + 6 = 71
13y = 65
y = 65/13 = 5
Now that I have the value for y, I can solve for x:
x = (5/2)y + (3/2)
x = (5/2)(5) + (3/2)
x = (25/2) + (3/2)
x = 28/2 = 14
Answer: E #### E
QUESTION:How many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number?
options: A)4 B)10 C)11 D)12 E)15
SOLUTION:The Question basically asks how many positive odd integers less than 100 are odd multiples of 5
So we have 5,15,25,35,45,55,65,75,85,95
=10
Ans B #### B
QUESTION:Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
options: A)21 B)16 C)16 D)28 E)12
SOLUTION:Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D #### D
QUESTION:What is the perimeter of a square with area 9p^2/25 ?
options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3
SOLUTION:Area of square, (side)^2 = (3p/5)^2
Therefore side of the square = 3p/5
Perimeter of square = 4*side = 4* (3p/5) = 12p/5
Answer is C. #### C
QUESTION:A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
options: A)4/19 B)7/19 C)12/19 D)21/99 E)26/77
SOLUTION:Solution
P( None is defective)
= 18C2 / 22C2
= 51/77
P( at least one is defective)
= (1- 51/77)
= 26/77.
Answer E #### E
QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered?
options: A)60% B)28% C)30% D)56% E)73%
SOLUTION:Let C.P. be Rs. 100.
Then, S.P. = Rs. 121.60
Let marked price be Rs. x. Then, 95/100 x = 121.60
x = 12160/95 = Rs. 128
Now, S.P. = Rs. 128, C.P. = Rs. 100
Profit % = 28%.
Answer: B #### B
QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss?
options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents
SOLUTION:50 % profit on $ 1
= $ 50/100 × 1
= $ 0.50× 1
= $ 0.50
Similarly, 40 % loss on $ 1
= $ 40/100 × 1
= $ 0.40× 1
= $ 0.40
Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40
So profit by amount $0.40.
Answer is E. #### E
QUESTION:Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 res. The ratio in which these two mixtures be mixed to get a new mixture containing milk and a water in the ratio 9:4?
options: A)2:8 B)2:1 C)2:2 D)2:3` E)2:7
SOLUTION:Step (i) : Let C.P. of milk be Re.1 Given ratio of mixture in A = 8:5 Milk in 1 lit mixture in A = 8/13 lit C.P of 1 lit mixture in A = Rs. 8/13 Ratio of Mixture in B = 5:2 milk in 1 litre mixture in B – 5/7 lit C.P of 1 lit mixture in B = Rs. 5/7 Ratio of new mixture = 9:4 milk in 1 lit mixture = 9/13 C.P of 1 lit mixture = Rs/ 9/13 (Mean price) Step (ii) : By the rule of allegation, i. C.P of 1 liter of mixture in A =8/13 ii. C.P of 1 liter of mixture in B = 5/7 iii. Mean price (p) = 9/13 iv. d – m = 9/13 – 5-7 = 2/91 v. m – c = 9/13 – 8/13 = 1/13 Required ratio = 2/91 : 1/13 = 2:7
Answer:E #### E
QUESTION:If x and y are positive integers, find which of the following CANNOT be the greatest common divisor of 25x and 20y?
options: A)5 B)5(x-y) C)20x D)20y E)35x
SOLUTION:We are looking for a choice that CANNOT be the greatest common divisor of 25x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer.
lets check
a. 5 25x/5 = 5x and 20y/5 = 4y both are integers so eliminate
b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate
c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 25x and 20y ...
or 25x/20x = 5/4 which is not a integer.
so answer is C. #### C
QUESTION:Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
options: A)16 sec B)13 sec C)17 sec D)21 sec E)23 sec
SOLUTION:Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 12 + 6 = 18 m/sec.
Required time = (120 + 120)/18 = 13 sec.
Answer: B #### B
QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.18000?
options: A)6620 B)2888 C)2776 D)2997 E)5958
SOLUTION:A = 18000(11/10)^3
= 23958
= 18000
----------
5958
Answer: E #### E
QUESTION:A person purchased a TV set for Rs. 18000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 46000. What percentage of profit did he make?
options: A)100% B)90% C)140% D)115% E)120%
SOLUTION:The total CP = Rs. 18000 + Rs. 5000
= Rs. 2300 and SP
= Rs. 46000
Profit(%)
= (46000 - 23000)/23000 * 100
= 100%
Answer:A #### A
QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d?
options: A)2 B)8 C)10 D)11 E)14
SOLUTION:1155 = 3 * 5 * 7 * 11
a = 11
d = 3
a - d = 8
Answer is B #### B
QUESTION:If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers?
options: A) 3 B) 4 C) 5 D) 9 E) 12
SOLUTION:If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct.
Answer: C. #### C
QUESTION:A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
options: A)2 1/7 hours B)2 1/2 hours C)2 7/2 hours D)4 1/2 hours E)2 1/5 hours
SOLUTION:Required time = (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer:B #### B
QUESTION:How many 9 digit numbers are possible by using the digits 1, 2, 3, 4, 5 which are divisible by 4 if the repetition is allowed?
options: A)77 B)26 C)88 D)27 E)99
SOLUTION:: If A number has to be divisible by 4, the last two digits must be divisible by 4. So possibilities are, 12, 24, 32, 44, 52. And the of the remaining 7 places, each place got filled by any of the five digits. So these 7 places got filled by 5 x 5 x .....(7 times) = 5757 ways. So total ways are 5 x 5757 = 5/8
Answer:A #### A
QUESTION:A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)
options: A)$15,360 B)$17,360 C)$25,560 D)$21,360 E)$27,360
SOLUTION:For every $3 earn above $9360, the recipient loses $1 of benefit.
OR
For every $1 loss in the benefit, the recipient earns $3 above $9360
If earning is; 9360+3x
Benefit = 12000-x
Or the vice versa
If benefit is 12000-x, the earning becomes 9360+3x
He lost 50% of the benefit;
Benefit Received= 12000-0.55*12000 = 12000-6600
x=5400
Earning becomes 9360+3x=9360+3*5400=25560
Ans:C #### C
QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is?
options: A)36.7 B)36.1 C)36.5 D)36.9 E)36.3
SOLUTION:Correct sum
= (36 * 50 + 48 - 23)
= 1825.
Correct mean = 1825/50
= 36.5
Answer:C #### C
<<<Examples ends
QUESTION:Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 35%. What fraction of the original paint was replaced?
options: A)1/35 B)1/5 C)2/3 D)3/5 E)4/5
SOLUTION:35% is 10%-points above 25% and 15%-points below 50%.
Thus the ratio of 25%-solution to 50%-solution is 3:2.
3/5 of the original paint was replaced.
The answer is D. #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
options: A)1/6 B)2/9 C)6/20 D)13/20 E)3/4
SOLUTION:Method- 1
There are 9 fine pieces of pen and 3 defective in a lot of 16 pens
i.e. Probability of first pen NOT being defective = (13/16)
i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective]
Probability of Both pen being NON-defective = (12/15)*(13/16) = 13/20
Answer: option D #### D
QUESTION:A grocery store bought some apples at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples?
options: A)1:7 B)1:5 C)1:4 D)1:2 E)2:5
SOLUTION:To avoid fractions, assume there were 45 apples. So the store bought them for 45/5 = 9 dollars.
To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these.
45 split in the ratio 1:4 gives 9 and 36.
9 apples split into 3 apples each will give $3.
36 apples split into 6 apples each will give $6.
They add up to $9 so we have hit the right answer.
Answer (C) #### C
QUESTION:man is 36 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
options: A)14years B)26 years C)17 years D)34 years E)22 years
SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 36) + 2 = 2(x + 2)
x + 38 = 2x + 4
x = 34.
answer :D #### D
QUESTION:In a class of 100 students, there are 50 who play soccer, 45 who play
basketball, and 50 who play volleyball. Only 15 of these students play all
three sports. Everyone plays at least one of these sports. How many of
the students play exactly two of these sports?
options: A)15 B)20 C)25 D)30 E)35
SOLUTION:Let S1 be the number of students who play exactly one of the three sports; S2 - the
number of students who play exactly two of the three sports; and let S3 be the number
of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100
(the total number of students). Also in the sum 50+45+50 (soccer players + basketball
players + volleyball players), each student who plays exactly one sport is counted once,
the ones who play exactly two sports are counted twice, and those who play all three
sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that
S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15
correct answer A #### A
QUESTION:Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely?
options: A)15 sec B)19 sec C)12 sec D)10 sec E)11 sec
SOLUTION:Explanation:
D = 250 m + 250 m = 500 m
RS = 80 + 40 = 120 * 5/18 = 100/3
T = 500 * 3/100 = 15 sec
Answer: Option A #### A
QUESTION:If 0.5% of A =85 paise, then the value of A is ?
options: A)Rs. 170 B)Rs. 17 C)Rs. 1.70 D)Rs. 4.25 E)None
SOLUTION:Answer
∵ 0.5/100 of A = 85/100
∴ A = Rs. (85 / 0.5) = Rs. 170
Correct Option: A #### A
QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease
SOLUTION:100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B #### B
QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
options: A)14years B)26 years C)17 years D)18 years E)22 years
SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 20) + 2 = 2(x + 2)
x + 22 = 2x + 4
x = 18.
answer :D #### D
QUESTION:How many multiples of 5 are there between 50 and 500 ?
options: A)128 B)91 C)89 D)61 E)60
SOLUTION:It should be mentioned whether 50 and 500 are inclusive.
If 50 and 500 are inclusive, then the answer is (500-50)/5+1=91.
If 50 and 500 are NOT inclusive, then the answer is (495-55)/5+1=89.
Since OA is C, then we have NOT inclusive case. #### C
QUESTION:The present ages of three persons in proportions 5 : 6 : 4. Five years ago, the sum of their ages was 60. Find their present ages (in years).
options: A)8, 20, 28 B)16, 28, 36 C)25,30,20 D)18, 24, 32 E)None of these
SOLUTION:Explanation:
Let their present ages be 5x, 6x and 4x years respectively.
Then, (5x - 5) + (6x - 5) + (4x - 5) = 60
15x-15 = 60
x = 5
Their present ages are 5x = 25 years, 6x = 30 years and 4x = 20 years respectively.
Answer: C #### C
QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?
options: A)11 B)12 C)22 D)24 E)44
SOLUTION:22 times in a day.
12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes)
ANSWER:C #### C
QUESTION:The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
options: A)5 B)4 C)1/2 D)1/5 E)1/8
SOLUTION:If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5.
The answer is D. #### D
QUESTION:Find the highest common factor of 36 and 84.
options: A)4 B)6 C)12 D)18 E)19
SOLUTION:36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.
Answer: Option C #### C
QUESTION:Ravi can do a piece of work in 15 days while Prakash can do it in 30 days. In how many days will they finish it together?
options: A)11 days B)9 days C)8 days D)12 days E)10 days
SOLUTION:1/15 + 1/30 = 3/30
10/1 = 10 days
ANSWER:E #### E
QUESTION:A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is
options: A)280 B)285 C)290 D)295 E)275
SOLUTION:Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25 / 30)=(8550 / 30)=285
Option B #### B
QUESTION:Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 55
options: A)55 B)6 C)15 D)31 E)91
SOLUTION:1(result) + (1*1) = 2.
2(result) + (2*2) = 6.
6(result) + (3*3) = 15.
15(result) + (4*4) = 31.
31(result) + (5*5) = 56.
Now we are getting 56 not 55.. So 55 is the wrong number of the given.
answer : A #### A
QUESTION:A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
options: A)5 kmph B)7 kmph C)9 kmph D)8 kmph E)1 kmph
SOLUTION:Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer:D #### D
QUESTION:A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
options: A)22887 B)2677 C)2987 D)8925 E)17711
SOLUTION:Principal = (100 * 4016.25) / (9 * 5)
= Rs. 8925.
Answer:D #### D
QUESTION:Given that 268x74= 19632, find the value of 2.68x.74.
options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None
SOLUTION:Solution
Sum of decimals places =(2+2)
= 4.
Therefore, = 2.68×.74
= 1.9632
Answer A #### A
QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions?
options: A)2112 m B)2704 m C)2278 m D)2288 m E)2378 m
SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions.
= 1500 * 2 * 22/7 * 22.4 = 211200 cm
= 2112 m
Answer: A #### A
QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years?
options: A)30 B)35 C)40 D)50 E)60
SOLUTION:Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 20 years = (20 + 20) years =40 years.
Answer : C #### C
QUESTION:575.104 x 15.98 ÷ 9.001 + 21.25 = ?
options: A)983.578 B)1043.65 C)1033.65 D)656.112 E)456.512
SOLUTION:Explanation:
? = 575.104 x 15.98 ÷ 9.001 + 21.25
≈ (575.104 x 16/9) + 21.25 ≈ 1022.40 + 21.25 ≈ 1043.65
Answer: Option B #### B
QUESTION:A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long?
options: A)40 sec B)11 sec C)88 sec D)33.33 sec E)10 sec
SOLUTION:Speed = 54 * 5/18 = 15 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 1/15 = 33.33 sec
Answer: D #### D
QUESTION:A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A?
options: A)Rs.240 B)Rs.340 C)Rs.260 D)Rs.280 E)Rs.440
SOLUTION:LCM = 180
Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c
= (180/15)/(180/15 +180/20 + 180/45)
= (12/25) * 500
= Rs.240
ANSWER:A #### A
QUESTION:As a bicycle salesperson, David earns a fixed salary of $25 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>1
options: A)I,III only B)III only C)I only D)II only E)II,III only
SOLUTION:II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>1 --> if David sold 3 bicycles this week then this week he earned 25+3*6=$43, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $25. So y must be more than 1;
I. y<3x --> is not always true.
Answer: E #### E
QUESTION:A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these
SOLUTION:Explanation:
Volume of water displaced = (8 x 2 x 0.01) m3
= 0.16 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.16 x 1000)kg
= 160 kg.
Answer: D #### D
QUESTION:Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
options: A)5/7 B)5/3 C)5/1 D)5/6 E)5/2
SOLUTION:P(at least one graduate) = 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer: D #### D
QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?
options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000
SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager.
Average company salary * Number of employees = Total company salary
>>> $80,000 * 10 = $800,000
Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000)
>>> $800,000 - $300,000 - $240,000 = $260,000.
The correct answer is C. #### C
QUESTION:A hall 36m long and 15m broad is to be paved with stones, each measuring 8dm by 5 dm. The number of stones required is:
options: A)180 B)1800 C)18 D)18000 E)1350
SOLUTION:Area of the hall= 3600*1500
Area of each stone= (80*50)
Therefore, number of stones= (3600*1500/ 80*50)= 1350
ANSWER:E #### E
QUESTION:The sum of three integers A, B and C is 60. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
options: A)40 B)45 C)35 D)50 E)55
SOLUTION:A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=60
so 1/3(B+C)+B+C=60
4(B+C)/3= 60
B+C =60*3/4 = 45
A=60-45=15
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=60
so 1/5(A+C)+A+C=60
A+C=60*5/6=50
but A=15, so C=50-15=35
Answer :C #### C
QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
options: A)22 B)45 C)66 D)88 E)12
SOLUTION:Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: B #### B
QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
options: A)8% B)6% C)9% D)10% E)11%
SOLUTION:Rs 1552 income = Rs 128
By investing Rs 97 income = 128/1552*97 = Rs 8
Divdend = 8%
ANSWER A #### A
QUESTION:When 2/3 of the garments in the shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 80 percent of the garments in the shipment pass?
options: A)6 B)9 C)8 D)7 E)5
SOLUTION:B = 9
2/3x= 20
x=30
for 80% approval we need 24 garments approved.
already approved = 18
we need 6 more.
Answer : A #### A
QUESTION:If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a + b + c > a^3
II. a × b × c < a^3
III. 5b > bc
options: A)I only B)II only C)III only D)II and III E)I, II, and III
SOLUTION:Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4
Putting the values in the answers only 'A' seems valid. #### A
QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h?
options: A)6 B)12 C)24 D)36 E)48
SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24.
ANS :C #### C
QUESTION:What is the smallest positive integer that can be multiplied by 605 to make it a perfect square?
options: A)2 B)3 C)5 D)7 E)11
SOLUTION:605 is multiplied by 5 gives 3025
Its a square root of 55
Answer is 5 -Option C #### C
QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60?
options: A)10 B)15 C)8 D)12 E)20
SOLUTION:4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 60
4n< 53
n < 13. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13)
Combining the two
-1.5 < n<13.25
n = 1 to 13 (48 integers)
and n = -1 and 0
so 15 integers.
B #### B
QUESTION:In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
options: A)8*9! B)8*8! C)7*9! D)9*8! E)None
SOLUTION:Solution: No. of ways in which 10 paper can arranged is 10! Ways.
When the best and the worst papers come together, regarding the two as one paper, we have only 9 papers.
These 9 papers can be arranged in 9! Ways.
And two papers can be arranged themselves in 2! Ways.
No. of arrangement when best and worst paper do not come together,
= 10!- 9!.2! = 9!(10-2) = 8.9!.
Answer A #### A
QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares?
options: A)$37.5 B)$40 C)$50 D)$48 E)$52
SOLUTION:Dividend on 1 share = $(10/100*50)
=$5
$12.5 is an income on an investment of $100
$5 is an income on an investment of $(100*2/25*5)=40
Thus, cost of 1 share =$40
option B #### B
QUESTION:There are two sections C and D of a class, consisting of 18 and 22 students respectively. If the average weight of sections C is 20 kg and that of sections D is 18 kg. Find the average weight of the whole class
options: A)18.7 B)18.8 C)18.9 D)19.9 E)None
SOLUTION:Solution
Total weight of(18+22)Students = (18x20+22x18)Kg
= 756 kg.
Average weight of the whole class = (756 /40 )
= 18.90.
Answer C #### C
QUESTION:8, 24, 12, 36, 18, 54, (....)
options: A)72 B)68 C)108 D)27 E)86
SOLUTION:8 × 3 = 24
24 ÷ 2 = 12
12 × 3 = 36
36 ÷ 2 = 18
18 × 3 = 54
54 ÷ 2 = 27
Answer is D. #### D
QUESTION:an article with cost price of 192 is sold at 25% profit. what is the selling price?
options: A)198 B)200 C)204 D)240 E)210
SOLUTION:sp=1.25*192=240
ANSWER:D #### D
QUESTION:A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in :
options: A)13 1/3 days B)16 days C)15 days D)20 days E)30 days
SOLUTION:C alone can finish the work in 80 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/80) = 1/16
All the three together will finish it in 16 days.
ANSWER:B #### B
QUESTION:In the coordinate plane, points (x, 1) and (12, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
options: A) 4.5 B) 7 C) 8 D) 11 E) 12
SOLUTION:Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.
Thus: (x, 1)=(2, 1) and (12, y) = (12,6) --> x+y=2+6=8.
Answer: C. #### C
QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded?
options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV
SOLUTION:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN.
so this way CAMEL becomes OVNZX
ANSWER:C #### C
QUESTION:The maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
options: A)91 B)81 C)1001 D)1911 E)None
SOLUTION:olution
Required number of students.
= H.C.F of 891 and 810.
‹=› 81.
Answer B #### B
QUESTION:A company plans to gradually replace its fleet of 20 cars with newer models. At the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models.How many years did it take before the number of older cars left in the company's fleet was less than 50 percent of the fleet?
options: A)6 B)3 C)2 D)4 E)5
SOLUTION:Total fleet--20
End of year 2000 -- (retires 5 and buys 6) total fleet--21(15 old 6 new).
End of year 2001 -- (retires 5 and buys 6) total fleet--22(10 old 12 new).
Answer is C--after 2 years the company has a total of 22 cars (10 old 12 new), the old cars are already less than 50% of its fleet. #### C
QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam.
options: A)15 B)25 C)30 D)45 E)55
SOLUTION:Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 92(x - 5)
80x - (5 * 20) = 92(x - 5)
360 = 12x => x = 30
ANSWER:C #### C
QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3?
options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10
SOLUTION:arrangement = 5!/3!=20
Probability of getting all 3 balls=
3 from 5=5c3
1 from 3 red ball,1 green,1 yellow
(3c1*1c1*1c1)/5c3 =3/10
ANSWER:A #### A
QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 370440, then population in 1978 was?
options: A)320000 B)120029 C)187899 D)178968 E)789698
SOLUTION:X * (105/100) * (105/100) * (105/100) = 370440
X = 370440/1.157625
X = 320000
Answer:A #### A
QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740
SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All two
2. One symmetry and other two non
4. All the two letters can be arranged in 2 ways
( 11c2+ 11c1 * 15c2) *2
( 11*10/ 2 + 11 * 15 * 14 / 2 ) * 2
2420
IMO option D is the correct answer..
OA please...will correct if I missed anything..D #### D
QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is?
options: A)150 m B)778 m C)200 m D)276 m E)971 m
SOLUTION:2(l + 150)
= 600 => l
= 150 m
Answer:A #### A
QUESTION:A local bank that has 8 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 8 codes?
options: A)4 B)6 C)5 D)3 E)7
SOLUTION:Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Total = 9 Codes. Enough.
Answer: D #### D
QUESTION:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?
options: A)3x+32 B)5x-1 C)(7x+15)/2 D)(9x-4)/2 E)6x+2
SOLUTION:We can take
X+1 = 9
X= 8
So 4c envelopes will be 6
and 5c envelopes will be 3
So total cost will be 39
Then that is our target
Plug x =8 in answer choices
Only B works
Correct Answer : B #### B
QUESTION:The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
options: A)180.27 cm B)180.29 cm C)978.29 cm D)178.89 cm E)176.29 cm
SOLUTION:Calculated average height of 35 boys = 182 cm.
Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182cm - (166 cm - 106 cm)/35
= 182 cm - 60 /35 cm
= 182 cm - 1.71 cm = 180.29 cm.
Answer: B #### B
QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle?
options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm
SOLUTION:let length = x and breadth = y then
2(x+y) = 46 x+y = 23
x²+y² = 17² = 289
now (x+y)² = 23²
x²+y²+2xy= 529
289+ 2xy = 529
xy = 120
area = xy = 120 sq.cm
Answer: B #### B
QUESTION:Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE?
options: A)1/15 B)1/14 C)1/12 D)1/13 E)1/17
SOLUTION:Explanation :
Let two digit number that Shiwani thought be 'xy', where x and y are single digit number.
Therefore, 10x+y=p(x+y)+3, where p is a natural number
p=10x+y−3x+y.
Also, y+x>3.
Possible values of x and y for which p is a natural number are :-
(x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9),
(x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null),
(x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4)
There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits.
Probability that Devesh thought of the same number as Shiwani = 1/14
Answer : B #### B
QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
options: A)Rs. 51.25 B)Rs. 51.22 C)Rs. 51.219 D)Rs. 51.18 E)Rs. 51.11
SOLUTION:Explanation:
Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500) = Rs. 51.25.
Answer:A #### A
QUESTION:Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 36 have long fur, 27 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
options: A)26 B)19 C)11 D)8 E)6
SOLUTION:No of dogs=45
Long fur=36
Brown=27
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=36+27-Both
Both=26
Answer A #### A
QUESTION:Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 16, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
options: A) 4/11 B) 1/2 C) 15/22 D) 144/17 E) 11/4
SOLUTION:P1 takes 12 hrs
Rate for P2P3 together = 1/16 + 1/18 = 17/144
Therefore they take 144/17
Ratio = 144/17 = D #### D
QUESTION:One pump drains one-half of a pond in 5 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
options: A)1 hour B)1.2 hour C)3 hours D)5 hours E)1.1 hours
SOLUTION:The tricky part here, I believed is one half hour = 1/2. Then everything would be easy.
We have the 1st pump working rate/hour = 1/2 : 5 = 1/10
Working rate of 2 pumps: 1/2 : 1/2 = 1.
Working rate of 2nd pump: 1 -1/10 = 9/10 --> Time taken for the 2nd pump to finish: 1 : 9/10 = 10/9 = 1.1 hours.
E #### E
QUESTION:Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months.
options: A)Rs. 9009 B)Rs. 9008 C)Rs. 9002 D)Rs. 9202 E)Rs. 9001
SOLUTION:Explanation:
P = Rs. 78000, R = 77/5 % p.a and T = 9/12 years = ¾ years
Therefore,
S.I = (P*R*T)/100
= (78000* 77/5 * ¾ * 1/100)
= Rs. 9009
ANSWER: A #### A
QUESTION:Which of the following must be subtracted from 2^96 so that the resulting integer will be a multiple of 3?
options: A)2 B)5 C)3 D)1 E)4
SOLUTION:{4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : D #### D
QUESTION:In how many ways can a group of 4 men and 2 women be made out of a total of 6 men and 4 women?
options: A)63 B)67 C)70 D)90 E)80
SOLUTION:We need to select 4 men from 6 men and 2 women from 4 women. Number of ways to do this
= 6C4 × 4C2
90
D) #### D
<<<Examples ends
QUESTION:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
options: A)18 B)20 C)24 D)36 E)42
SOLUTION:Use weighted average:
2% and 12% solutions mix to give 5% solution.
w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3
You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution.
If total 5% solution is actually 60 litres, you need 7*6 = 42 litres of 2% solution and 3*6 = 18 litres of 12% solution.
Answer (E) #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Speed of boat in water is 12km/hr. and the speed of the stream is 3km/hr. Find the time taken by the boat to go upstream a distance of 45km.
options: A)3 B)4 C)5 hrs. D)6 E)2
SOLUTION:US =speed of the boat - speed of the stream 12-3 =9km/hr. Time taken to cover 45km =45/9 = 5hrs. Answer : C #### C
QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525
SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
A) #### A
QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was
options: A)Rs. 2000 B)Rs. 10000 C)Rs. 15000 D)Rs. 20000 E)None of these
SOLUTION:Explanation :
Principal = Rs. (100×5400 / 12×3)
=> Rs. 15,000.
Answer : C #### C
QUESTION:What is the unit’s digit of 7^5
options: A)1 B)3 C)5 D)7 E)9
SOLUTION:7^1=7
7^2=49
7^3=343
7^4=1(last digit)
7^5=7(last digit) and the cycle repeats after every 4 powers
Therefore, last digit of 7^5=7
Answer D #### D
QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
options: A)5/9 B)5/12 C)1/36 D)7/12 E)4/9
SOLUTION:Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
ANSWER:B #### B
QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages.
options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12
SOLUTION:Explanation:
Let the present ages of A and B be 'a' and 'b' respectively.
3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1)
a-b = 5 -------(2) Solving (1) and (2) we get b=8
Substituting b = 8 in second equation, we get a= 13. Answer : C
=> 2a = 32 => a = 16.
Answer: C #### C
QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.
options: A)I only B)I and II C)II and III D)I, II, and III E)IV only
SOLUTION:This is a very good 'trap question'.
Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3
If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'.
Ans: E #### E
QUESTION:A ship sails out to a mark at the rate of 15 kmph. and sails back at the rate of 10 kmph. The average rate of sailing is ?
options: A)5 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None
SOLUTION:Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 15 x 10 ) / (15 +10 ) km/hr.
= 12 km/hr.
Correct Option: B #### B
QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages.
options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these
SOLUTION:Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 136
20x = 160 => x = 8
Their present ages are 32, 56 and 72 years respectively.
ANSWER:D #### D
QUESTION:The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 15 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
options: A)28% B)40% C)68% D)70% E)72%
SOLUTION:Let initial price be 1000
Price in day 1 after 10% discount = 900
Price in day 2 after 15% discount = 765
Price in day 3 after 20% discount = 612
So, Price in day 3 as percentage of the sale price on day 1 will be = 612/900*100 => 68%
Answer will definitely be (C) #### C
QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean a. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than a+d?
options: A) 16% B) 32% C) 48% D) 84% E) 92%
SOLUTION:16%
________________________________________________ a+d
34%
________________________________________________ a
34%
________________________________________________ a-d
16%
since 68% lies one standard deviation from mean a, => 50% of 68% lies on either side as it is symmetric about a.
thus 16% lie below a-d and 16% lie above a+d
now below a+d = 16+34+34 = 84%
hence D #### D
QUESTION:What should be added to 4750 so that it may become a perfect square?
options: A)11 B)15 C)16 D)17 E)18
SOLUTION:69x69=4761
4761-4750 = 11
If added to 11 get perfect square
answer =A #### A
QUESTION:In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
options: A)266 B)86400 C)11760 D)5040 E)None of these
SOLUTION:Here, 5 men out of 8 men and 6 women out of 10 women can be chosen in
8C5 × 10C6 ways, i.e., 11760 ways.
Answer C #### C
QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
options: A)19 B)18.7 C)19.9 D)21.7 E)22.8
SOLUTION:Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 36 Paise is given as tax
=> Total tax incurred = 36 Paise = Rs.36/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−36/100−x)6/100 = 36/100
⇒ 6(25 −0.36 −x) = 36
⇒ (25 − 0.36 − x) = 6
⇒ x = 25 − 0.36 − 6 = 18.7
B) #### B
QUESTION:George can do 3/5 of work in 9days.He then calls in pauls and they completed the work in 4days.How long paul would take long to complete the work?
options: A)32 B)28 C)35 D)30 E)22
SOLUTION:George work is (5/3)*9 =15;
1 day work of george is 1/15 ;
remaining is 2/5th;
paul & george work is 5/2*4=10 ;
their 1 day work is 1/10;
and only paul work is (1/10)-(1/15)=30
ANSWER:D #### D
QUESTION:The sum of four consecutive even numbers is 292. What would be the smallest number?
options: A)74 B)76 C)70 D)68 E)65
SOLUTION:Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
ANSWER:C #### C
QUESTION:Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart?
options: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm
SOLUTION:Total distance, which should be covered by both cars is 190+35=225 miles.
Let t be the time so the equation will be 46t+54t=225 thus,
t=2.25 hours
Answer: D #### D
QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
options: A)4 B)8 C)16 D)17 E)None of these
SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B #### B
QUESTION:What should come in place of the question mark (?) in the following equation?
5978 + 6134 + 7014 = ?
options: A)19226 B)16226 C)19216 D)19126 E)None of these
SOLUTION:? = 5978 + 6134 + 7014 = 19126
Answer D #### D
QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years?
options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 %
SOLUTION:Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11)
= 100/11 = 9.09 %
ANSWER:A #### A
QUESTION:Among the members of the Malmo family, there are three times as many members who do not wear glasses as members who do. Half of the Malmo family members have blue eyes, and 4/5 of the family members who have blue eyes do not wear glasses. What percent of the Malmo family members wear glasses and do not have blue eyes?
options: A)10 B)15 C)20 D)25 E)35
SOLUTION:Number in black are given and in red are calculated.
Now, since x+3x=100, then x=25 and therefore =25−10=15
Answer: B. #### B
QUESTION:The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is
options: A)64 sq.m B)70 sq.m C)78 sq.m D)84 sq.m E)None
SOLUTION:Solution
Perimeter of the rhombus = 56 m
Each side of the rhombus = 56 / 4 m
= 14 m.
Height of the rhombus = 5 m
Area = (14 x 5) m²
= 70 m²
Answer B #### B
QUESTION:A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
options: A)2 B)4 C)6 D)8 E)12
SOLUTION:To fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible
so we will take the base as 12 feet by 8 feet
Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less.
Therefore the radius of the cylinder will become Diameter 2===>8/2=4 Diameter
ANSWER:D #### D
QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places?
options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5
SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.
Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300
Number CA possible = 1C1 = 1
Number FL possible = 1C1 = 1
Number HI possible = 1C1 = 1
Number other possible = 47C1 = 47
Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)
P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900
Answer: D #### D
QUESTION:Express a speed of 90 kmph in meters per second?
options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps
SOLUTION:90 * 5/18
= 25 mps
Answer:E #### E
QUESTION:A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 8.30 a.m. ?
options: A)7 B)2 C)9 D)2 E)8
SOLUTION:B
2
Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 2 times before 8.30 a.m. #### B
QUESTION:Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
options: A)175.5 B)170 C)169.5 D)180 E)190
SOLUTION:Since first and second varieties are mixed in equal proportions.
average price = 126+135/2 = 130.50
o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x - 153 = 22.50
x = 175.50
ANSWER A #### A
QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3%
SOLUTION:675 ---- 225
100 ---- ? => 33 1/3%
Answer:C #### C
QUESTION:Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age.
options: A)60 years B)80 years C)70 years D)76 years E)86 years
SOLUTION:Let Kumar’s present age be x years and Sailesh’s present age be y years.
Then, according to the first condition,
x - 10 = 3(y - 10) or, x - 3y = - 20 ..(1)
Now. Kumar’s age after 10 years = (x + 10) years
Sailesh’s age after 10 years = (y + 10)
(x + 10) = 2 (y + 10) or, x - 2y = 10 ..(2)
Solving (1) and (2), we get x = 70 and y = 30
Kumar’s age = 70 years and Sailesh’s age = 30 years.
ANSWER:C #### C
QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy
SOLUTION:Payment of a week for 2 days a week = $2x
Payment of 4 weeks for 2 days a week = $2x*4 = $8x
Payment of a week for y days overtime a week = $3x+$2xy
Payment of 3 weeks for y days overtime a week = ($3x+$2xy)*3
Total Earnings = $8x + ($3x+$2xy)*3 = 17x+6xy
Answer: option E #### E
QUESTION:What percent is 4 gm of 1 kg?
options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 %
SOLUTION:1 kg = 1000 gm
4/1000 × 100 = 400/1000
=2/5 = 0.4 %
B) #### B
QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash?
options: A)A)1000 B)B)3000 C)C)3500 D)D)2500 E)E)2250
SOLUTION:For 20 staffs: 300*100*20 = 60000
for driver and cleaning staff: 300*100*2 =6000
From petty Cash : 1000
Answer is 1000 Answer is A #### A
QUESTION:A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 10 seconds. Find the length of the train and its speed.
options: A)10 m/sec B)15 m/sec C)18 m/sec D)19 m/sec E)25 m/sec
SOLUTION:If length of train is l and speed of train is s, then
l/s = 10
(l+180)/s = 20
(l+180)/l = 20/10 =2
l+180 =2l
l= 180
l=180 mtrs
s= l/10 = 180/8 = 10 m/sec
ANSWER:A #### A
QUESTION:A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
options: A)9:32 B)9:30 C)32:9 D)19:32 E)18:30
SOLUTION:Water:soap = 3:4
Soap:Salt=15:20
=> For 15 soap, salt = 20
=> For 4 Soap, salt = (20/15)*4 = 80/15=16/3
So, water:soap:salt = 3:4:16/3= 9:12:16
After open container, water:soap:salt =4.5:12:16
So, water:salt = 4.5:16 = 9:32
ANSWER:A #### A
QUESTION:A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
options: A)1/2 B)3/5 C)3/8 D)4/9 E)7/10
SOLUTION:The total possible choices are 10C3 = 120
The ways to choose 3 apples: 5C3 = 10
The ways to choose 2 apples: 5C2 * 5C1 = 50
P(at least 2 apples) = 60/120 = 1/2
The answer is A. #### A
QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
options: A)87 B)67 C)23 D)75 E)25
SOLUTION:Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer: C #### C
QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9?
options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21
SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15
E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2
probability = 2/15
Answer is A #### A
QUESTION:A and B are two circles. The radius of A is thrice as large as the diameter of B. What is the ratio between the areas of the circles?
options: A)1:18. B)1:20. C)1:4. D)1:36. E)1:16.
SOLUTION:Given : The radius of A is thrice as large as the diameter of B. => R(a) = 3*D(b) = 3*2*R(b) = 6R(b). The radius are in ratio of 1:6 thus the area will be in the ratio of square of radius. 1:36. Hence D. #### D
QUESTION:Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
options: A)99:61 B)99:160 C)61:160 D)61:99 E)99:160
SOLUTION:Vessel A = 300 gallons --> milk = 120, water = 180;
Vessel B = 500 gallons --> milk = 375, water = 125;
Vessel A + B = 800 gallons --> milk = 495, water 305.
The ratio = 495/305 --> reduce by 5 = 99/61.
Answer: A. #### A
QUESTION:How many different positive integers are factors of 196 ?
options: A) 1 B) 2 C) 3 D) 49 E) 36
SOLUTION:15, 14×15, 14=7^2 × 2^2
So total factors = (6+1)(6+1) = 49
Answer: D #### D
QUESTION:There are 145 bananas lying in a shop which is to be divided equally among 12 candidates. Find the extra number of bananas lying with the shop owner after distribution.
options: A)1 B)2 C)3 D)4 E)9
SOLUTION:145 divided by 12 = 12x12+1. That is, 1 banana will be extra after distributing 12 bananas to each candidate (12 in number). Answer A. #### A
QUESTION:Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do
the same job in 9 hours. If Tina Works independently at the job for 8 hours and then Ann works
independently, how many hours will it take Ann to complete the remainder of the jobs?
options: A)2/3 B)3/4 C)1 D)2 E)3
SOLUTION:Work done by Tina in 1 hr=1/12
Work done by Tina in 8 hr=1/12*8 which is 2/3
Now,the remaining work is 1/3 which is completed by Ann in 1/3*9 which is 3hr
ANSWER:E #### E
QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time?
options: A)70 min B)94 min C)110 min D)112 min E)120 min
SOLUTION:First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
And now we have 4 robots
So Total = (1) + (2) = 70 minutes
Answer - A #### A
QUESTION:If you add all the numbers on your mobile phone , what is the answer?
options: A)45 B)50 C)55 D)100 E)60
SOLUTION:0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are in your mobile phone.
Therefore 0+1+2+3+4+5+6+7+8+9=45
Answer is A #### A
QUESTION:9, 16, 18, 25, 36,49
options: A)9 B)16 C)18 D)25 E)36
SOLUTION:Each of the numbers except 18, is perfect square.
Answer: Option C #### C
QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
options: A)25 B)29 C)48 D)26 E)54
SOLUTION:A
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. #### A
QUESTION:If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x?
options: A)308 B)154 C)70 D)44 E)21
SOLUTION:If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that.
LCM of 2,7,11= 154
Hence x must be divisible by 154
Hence B #### B
QUESTION:There are 36 students in a certain geometry class. If one third of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
options: A)9 B)12 C)18 D)24 E)27
SOLUTION:Total Students = 36
One third of the students are boys = 1/3*36 = 12
Three fourths of the boys are under six feet tall = 3/4*12 = 9 ...
Therefore Number of boys in the class under six feet tall = 9 ... Answer A....
Alternatively... Number of boys in the class under six feet tall = 3/4 of 1/3 of Total Students = 3/4*1/3*36 = 9...
Answer A #### A
QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr?
options: A)25 B)30 C)99 D)88 E)61
SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr.
= 72 * 5/18 = 20 m/sec.
Time taken to pass the man = 500 * 1/20 = 25 sec.
Answer: A #### A
QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.899] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
options: A)0 B)1 C)27 D)54 E)0
SOLUTION:K=[lCM of 80 and 45] * (any integer)
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
for value of k(60) * any integer unit value will be always zero .
E #### E
QUESTION:(128.5 x 32) + (13.8 x 30) = ? x 25
options: A)524.48 B)556.02 C)574.36 D)181.04 E)595.46
SOLUTION:Explanation :
? = (128.5 x 32) + (13.8 x 30)/25
= 4112 + 414/25 = 181.04
Answer : Option D #### D
QUESTION:A runs 25% faster than B and is able to allow B a lead of 7 meters to end a race in dead heat. What is the length of the race?
options: A)10 meters B)25 meters C)45 meters D)15 meters E)35 meters
SOLUTION:Answer
A runs 25% as fast as B.
i.e., if B runs 100 m in a given time, A will run 125 m in the same time.
In other words, if A runs 5 m in a given time, then B will run 4 m in the same time.
Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat.
Ratio of length of start given : length of race :: 1 : 5
In this question, we know that the start given is 7 m.
Hence, the length of the race will be 7 * 5 = 35 m.
Choice E #### E
QUESTION:If x and y are different integers, both divisible by 11, then which is not necessarily true?
options: A)x^2 + y^2 is divisible by 11 B)x - y is divisible by 11 C)xy is divisible by 11 D)x + y is divisible by 11 E)x + y is divisible by 22
SOLUTION:Let x = 11k and let y = 11j.
Then x+y = 11(k+j) and k+j could be even or odd.
Thus 11(k+j) is not necessarily divisible by 22.
The answer is E. #### E
QUESTION:A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.157. Find the unknown rate of two blankets?
options: A)420 B)550 C)490 D)450 E)520
SOLUTION:10 * 157 = 1570
3 * 100 + 5 * 150 = 1050
1570 – 1050 = 520
Answer:E #### E
QUESTION:P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
options: A)8/15 B)7/15 C)6/15 D)5/15 E)4/15
SOLUTION:Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
Answer is A. #### A
QUESTION:Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil.
options: A)12 B)10 C)15 D)19 E)20
SOLUTION:Let the cost of a pen ands a pencil be Rs. X and Rs. Y respectively.
Then, 2x + 3y = 86 ….(i) and 4x + y =112.
Solving (i) and (ii), we get: x = 25 and y = 12.
Cost of a pen =Rs. 25 and the cost of a pencil =Rs. 12.
Answer is A. #### A
QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result?
options: A)132 B)127 C)125 D)152 E)112
SOLUTION:C
125
96 passes out of 125 give an average of 76.8% #### C
QUESTION:If c is 20% of a and 10% of b, what percent of a is b?
options: A) 2.5% B) 15% C) 25% D) 35% E) 200%
SOLUTION:Answer = E
20a/100 = 10b/100
b = 20a/10 = 200a/100 = 200% #### E
QUESTION:John and David work at a hospital with 8 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen?
options: A)1/30 B)1/25 C)1/20 D)1/28 E)1/30
SOLUTION:Probability that John and David will both be chosen out of 8 workers
= (2/8)*(1/7)
= 1/28
Answer D #### D
QUESTION:A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price
options: A)Rs.450/- B)Rs.451/- C)Rs.440/- D)Rs.455/- E)Rs.445/-
SOLUTION:Loss = 500*10/100 = 50
S.P = C.P - Loss
= 500- 50
=Rs.450/-
Answer : A #### A
QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 9 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
options: A)15 litres B)10 litres C)30 litres D)22 litres E)18 litres
SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+9)=4/5
20x=4(3x+9)
8x=36
x=4.5
Quantity of alcohol = (4 x 4.5) litres = 18 litres.
Answer is E #### E
QUESTION:If it is true that x > -3 and x < 7, which of the following must be true?
options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above.
SOLUTION:the range is -3 < x < 7
A. x > 3 - no because x can be between -3 < x < 3
B. x < -7 - no because the values of x are always >-7
C. x < 3 - no because x can be between 3 < x < 7
D. -7 < x < 3 - no because x can be between 3 < x < 7
E. none of the above.
Answer: E #### E
QUESTION:The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is
options: A)3 10 B)2 10 – 1 C)3 10 – 1 D)2 10 E)None of these
SOLUTION:Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions.
Hence, the number of all possible selections is 3 10 – 1.
Answer C #### C
QUESTION:The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches?
options: A)66 B)83.5 C)84 D)95 E)76
SOLUTION:sum of last 4 matches = (10 × 66) – (6 × 54)= 336
Average =
336/4
= 84
ANSWER:C #### C
<<<Examples ends
QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job?
options: A)4 days B)6 days C)8 days D)2 days E)9 days
SOLUTION:Sandy can do 1/6 of the job each day.
Molly can do 1/12 of the job each day.
The combined rate is 1/6 + 1/12 = 1/4 of the job each day.
The job will take 4 days.
The answer is A. #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If x = 4 and y = −2, what is the value of (x − 2y)^y?
options: A)−100 B)0.015 C)0.25 D)4 E)8
SOLUTION:Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
by inversing and squaring 0.015
Answer: B #### B
QUESTION:A bus started from bus stand at 8.00a m and after 30 min staying at destination, it returned back to the bus stand. The destination is 27 miles from the bus stand. The speed of the bus 50 percent fast speed. At what time it returns to the bus stand.
options: A)11a.m B)12a.m C)10a.m D)10.30p.m E)11.30p.m
SOLUTION:bus started after 30min ie .5hrs
Now,
Time=distance/speed ie Time=27/18 during going ie 1.5 hrs
now during the return journey speed increasd by 50% so new speed 27mph
Time=27/27 ie 1(RETURN journey)
so total time=1+.5+1.5=3hrs
so the bus will reach at 11am
ANSWER:A #### A
QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years
options: A)27 B)24 C)40 D)32 E)35
SOLUTION:sameer and anand be 5x years and 4x years respectively
(5x+3)/(4x+3)=11/9
9(5x+3)= 11(4x+3), 45x+27=44x+33
45x-44x=33-27
x=6, therefore anand's present age : 4x=24 years
correct answer(B) #### B
QUESTION:Solve below question 2x + 1 = -17
options: A)-8 B)-9 C)9 D)8 E)-7
SOLUTION:1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B #### B
QUESTION:On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $20,000, in how many years total will the total value of the investment plus interest increase to $40,000?
options: A)15 B)16 C)18 D)20 E)24
SOLUTION:5,000(1 + x)^10 = 20,000
(1+x)^10 = 4 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
5000(1 + x)^n = 40,000
(1+x)^n = 8
(1+x)^n = 2^3
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A. #### A
QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:
options: A)14 hrs B)15 hrs C)10 hrs D)8 hrs E)9 hrs
SOLUTION:work done by leak in 1 hr = (1/2-3/7)=1/4
=>14 hrs
ANSWER A #### A
QUESTION:The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.2.0 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
options: A)s.1014 B)s.1332 C)s.999 D)s.1085 E)s.1020
SOLUTION:a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 2.0 = 1332
ANSWER:B #### B
QUESTION:A chair is bought for Rs.800/- and sold at a loss of 10% find its selling price
options: A)Rs.500/- B)Rs.510/- C)Rs.515/- D)Rs.720/- E)Rs.540/-
SOLUTION:Loss = 800*10/100 = 80
S.P = C.P - Loss
= 800- 80
=Rs.720/-
Answer :D #### D
QUESTION:The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 360 m, its area is?
options: A)180 B)882 C)277 D)261 E)281
SOLUTION:5x + 12x + 13x = 360 => x = 12
a = 60, b = 144, c = 156
S = (60 + 144 + 156)/2 = 180
Answer: A #### A
QUESTION:Find the average of first 20 natural numbers?
options: A)5.5 B)7.2 C)10.5 D)12.3 E)15.5
SOLUTION:Sum of first n natural numbers = n(n+1)/2
sum of first 20 natural numbers = 20*21/2 =210
average = 210/20 = 10.5
Answer is C #### C
QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers?
options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr
SOLUTION:speed of man = 20km/hr
number of rests = (120/30)-1 = 3
time taken for the man = (120/20)+3*(20/60) = 7 hr
Answer is D #### D
QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
options: A)Rs.51.25 B)Rs.51.27 C)Rs.51.79 D)Rs.51.8 E)Rs.51.93
SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500)
= Rs.51.25.
Answer: A #### A
QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg?
options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42
SOLUTION:1000*(25/100) = 250 ---- 5
? ---- 1
=> Rs.50
Answer: A #### A
QUESTION:John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish?
options: A) 24 B) 34.8 C) 37.8 D) 40 E) 84
SOLUTION:The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40.
Answer: D. #### D
QUESTION:A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 680 dollars, and, in a third, loses 80. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ?
options: A)-280 B)300 C)-350 D)-380 E)None
SOLUTION:In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 680 - 80 = 250
And x = -350.
Answer C #### C
QUESTION:How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example
options: A)100 B)610 C)729 D)900 E)1000
SOLUTION:The hundred-thousand's digit won't be zero or else it's no longer a 6 digit integer (you could form a palindromic number with five digits though). The subesquent two digits, ten-thousand's and thousand's digit, can be 10 different numbers each, zero - nine. Thus,
9∗10∗10∗1∗1∗1=9009∗10∗10∗1∗1∗1=900 Answer D #### D
QUESTION:The average of eleven ten prime numbers which are odd is?
options: A)17.72 B)18.52 C)19.63 D)16.53 E)15.63
SOLUTION:Explanation:
Sum of first 11 prime no. which are odd = 195
Average = 195/11 = 17.72
Answer:A #### A
QUESTION:In how many ways can the letters of the CHEATER be arranged
options: A)20160 B)2520 C)360 D)80 E)None of these
SOLUTION:Explanation:
As we can see the letter "E" is twice in given word, so Required Number
=7!/2!=7∗6∗5∗4∗3∗2!/2!=2520
Option B #### B
QUESTION:A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
options: A)720 B)760 C)680 D)780 E)880
SOLUTION:On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is
10 x 9 x 8 = 720
ANSWER:A #### A
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train?
options: A)500 m B)620 m C)872 m D)150 m E)765 m
SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 30) m
= 500 m.
Answer: A #### A
QUESTION:A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails?
options: A)1/8 B)1/4 C)3/8 D)1/2 E)9/16
SOLUTION:We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.
Using the binary formula and defining a head as a success,
P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2
t= 6/16
= 3/8
The answer is therefore (C) #### C
QUESTION:8^100 is divisible by 17. Find the remainder?
options: A)8 B)12 C)16 D)18 E)20
SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 = (816)6×8417
Now this problem simply boils down to (1)6×8417 = 8417
84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.
C #### C
QUESTION:A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 3 percent and 6 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
options: A) 3/8 B) 21/25 C) 1/2 D) 3/5 E) 3/4
SOLUTION:x * 3/100 * 1 + (20000 - x) * 8/100 * 1 = 1440
3x - 8x = 144000 - 160000
=> -5x = -16000
=> x = 32000
So 16800/20000 = 21/25
Answer - B #### B
QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)?
options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5
SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57)
4.5/(4.5 - 2) = 9/5 (1.8)
3.5/(3.5 - 2) = 7/3 (~2.33)
2.5/(2.5-2) = 5
1.5/(1.5 - 2) = -3
Thus, the answer is D. #### D
QUESTION:The tax on a commodity is diminished by 10% and its consumption increased by 15%. The effect on revenue is?
options: A)2% decrease B)3.5% increase C)9% decrease D)3% decrease E)2% increase
SOLUTION:100 * 100 = 10000
90 * 115 = 10350
-----------
10000-----------350
100-----------? => 3.5% decrease
Answer: B #### B
QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
options: A)122443 B)154546 C)165454 D)186545 E)220030
SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
E #### E
QUESTION:The radius of a semi circle is 6.3 cm then its perimeter is?
options: A)35.4 cm B)32.4 cm C)32 cm D)30 cm E)35 cm
SOLUTION:Explanation:
36/7 r = 6.3 = 32.4
ANSWER IS B #### B
QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
options: A)20% B)40% C)50% D)60% E)70%
SOLUTION:70 + 55 + 35 = 160%
The number is 60% above 100% because 60% of the counties were counted twice.
The answer is D. #### D
QUESTION:A conference is to have eight presentations over the course of one day, consisting of three long presentations, and five short presentations. If the conference organizer doesn't want consecutive long presentations, and the conference is to start with a short presentation, how many schedules of presentations are possible?
options: A)1200 B)7200 C)2880 D)5760 E)11520
SOLUTION:S*S*S*S*S*
5 short presentations can be arranged in 5!=120 ways.
As for 3 long presentations: each can be placed instead of any of the 5 star, so in C35=10C53=10 ways, and they also can be arranged in 3!=6 ways.
Total = 120*10*6 = 7,200
Ans:B #### B
QUESTION:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of t feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?
options: A)5,280(x/t) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280
SOLUTION:In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet.
The number of revolutions = distance/circumference = 5,280x/t.
Answer: A. #### A
QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments.
options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3
SOLUTION:The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:21.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6.
ANSWER:A #### A
QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600:
options: A)200 B)250 C)300 D)350 E)400
SOLUTION:X = Rs.5000/-
Y = Rs.15000/-
X share 1 part & Y share 3 parts
Total 4 parts -----> Rs.1600/-
----> 1 part -------> Rs.400/-
X share = 1 part -----> Rs.400/-
E #### E
QUESTION:If the positive integer x is a multiple of 1 and the positive integer y is a multiple of 7, then xy must be a multiple of which of the following?
I. 7
II. 2
III. 3
options: A)II only B)I and II only C)I only D)II and III only E)I, II, and III
SOLUTION:x=1a
y=7b
xy=7ab
where a,b are integers
Hence , xy will always be divisible by 7 .
C is the answer. #### C
QUESTION:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
options: A) 6x B) 4x C) 5x/3 D) 3x/2 E) 3x/5
SOLUTION:Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<D<5x --> only option B fits.
Answer: B. #### B
QUESTION:Find the simple interest on Rs.300 for 9 months at 6 paisa per month?
options: A)142 B)152 C)162 D)172 E)182
SOLUTION:I = (300*9*6)/100 = 162
ANSWER:C #### C
QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 160 km/hr?
options: A)2.5 sec B)2.9 sec C)2.7 sec D)8.7 sec E)8.5 sec
SOLUTION:Speed = 160 * 5/18 = 44 m/sec
Time taken = 120/44 = 2.7 sec.
Answer: C #### C
QUESTION:If x+|x|+y=4 and x+|y|-y=6 what is x+y=?
options: A)11 B)-1 C)3 D)5 E)13
SOLUTION:If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.
If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).
Answer: C.
Adding both eqn we get 2x +IxI+IyI = 13
Now considering X <0 and y>0
2x-x +y = 13
we get x+y =11
Hence answer should be A #### A
QUESTION:E = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set E and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
options: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33
SOLUTION:The total number of pairs E,B possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.
Answer: B. #### B
QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test.
You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it?
options: A)48% B)55% C)60% D)71% E)80%
SOLUTION:C
60%
In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability.
In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already.
Therefore, P(Second/First) = P (First and Second)/ P (First)
= 0.25/0.42
=0.60
=60 % #### C
QUESTION:The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles?
options: A)20° B)70° C)60° D)120° E)140°
SOLUTION:If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence
3x + 6x = 90
9x = 90
x = 10
Measures of the two acute angles are
3x = 3 × 10 = 30°
6x = 6 × 10 = 60°
C #### C
QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase?
options: A) 45% B) 125% C) 145% D) 150% E) 180%
SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80
So the approximate answer is E #### E
QUESTION:How many three letter words are formed using the letters of the word TIME?
options: A)28 B)21 C)26 D)24 E)29
SOLUTION:The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃
= 4 * 3 * 2 = 24.
Answer: D #### D
QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 5-letter code words?
options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1
SOLUTION:Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5
Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6
Ratio: 5 to 1
Answer : D #### D
QUESTION:The volume of a cube is 3375 cc. Find its surface.
options: A)1350 B)1150 C)1456 D)1254 E)1489
SOLUTION:a3 = 3375 => a = 15
6a2 = 6 * 15 * 15 = 1350
Answer: A #### A
QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
options: A)2200 B)1897 C)8799 D)2000 E)2782
SOLUTION:P(11/10)4 - P(6/5)2 = 482
P = 2000
Answer: D #### D
QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 5 years ago?
options: A)152460 B)214560 C)138214 D)210000 E)200000
SOLUTION:population 2 years ago = 176400/(1 + 5/100)^5
Answer is C #### C
QUESTION:A box contains 3 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
options: A)4/7 B)3/5 C)5/8 D)2/3 E)3/4
SOLUTION:Each ball has an equal chance (1/9) of being selected fourth.
The probability that a black ball is selected fourth is 6/9 = 2/3.
The answer is D. #### D
QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40
SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35
P(at least one graduate) = 1- 1/35 = 34/35
The answer is D. #### D
QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed?
options: A)21005 B)10500 C)25200 D)5376 E)None of these
SOLUTION:Solution
Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4)
8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224
Number of group,each having 3 consonants and 1 vowels = 224 .
Each group contains 4 letter.
Number of ways of arranging 5 letters among themselves
= 4 ! = (4 × 3 × 2 × 1) = 24 .
So, Required number of words = (24 × 224) = 5376 .Answer D #### D
QUESTION:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ?
options: A)23/30 B)11/15 C)7/10 D)1/6 E)2/15
SOLUTION:Let total Housing Units = 5x.
As per question, Equipped with Cable TV = x
Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6.
So, Cable TV + VCR = x + x/6 = 7x/6
No Cable TV and VCR = 5x - 7x/6 = 23x/6.
Fraction = 23x/(6 * 5x) = 23/30. Hence, A #### A
QUESTION:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.)
options: A)4 B)5 C)6 D)12 E)24
SOLUTION:Let's start with 4 minimum number of colors
So single color code we can make 4 nos.
Now if we need to make 2 color combination out of 4 we can do so in 4!/2!*2! or 4*3/2 or 6
So total we can make 4+6=10 color combinations but we have 12 boxes
So let's look at 5 we get 5 single color codes
and out 5 color choices, we can choose 2 in 5!/2!*3! ways or 10 ways.
So total we can have 5+10=15 color combinations.
So, minimum number we need will be 5
Ans is B....... #### B
QUESTION:How many terminating zeroes T does 200! have?
options: A) 40 B) 48 C) 49 D) 55 E) 64
SOLUTION:You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C #### C
QUESTION:A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
options: A)287 B)298 C)350 D)726 E)267
SOLUTION:D = 72 * 5/18 = 25
= 500 – 150
= 350
Answer: C #### C
QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero?
options: A)472392 B)648421 C)720756 D)729951 E)810364
SOLUTION:All six digits are different and first digit is not zero.
So first digit can be filled in 9 ways.
And, second digit can be filled in 9 ways.
And, third digit can be filled in 9 ways.
And, fourth digit can be filled in 9 ways.
And, fifth digit can be filled in 9 ways.
And, sixth digit can be filled in 8 ways.
Total ways = 9*9*9*9*9*8
= 472392
Hence option (A). #### A
QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle?
options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm
SOLUTION:let length = x and breadth = y then
2(x+y) = 46 x+y = 23
x²+y² = 17² = 289
now (x+y)² = 23²
x²+y²+2xy= 529
289+ 2xy = 529
xy = 120
area = xy = 120 sq.cm
Answer: B #### B
QUESTION:If x is positive integer,y is negative integer, and 5x+2y=4, which of the following could be the value of x ?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Use answer options to solve this problem -
Put x = 2
So, 5x+2y=4
Or, 5(2)+2y=4
Or, 10+2y=4
Or, 2y=4-10;2y=-6
Or, y=-3(y is negative integer)
Answer will be (C) #### C
QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining?
options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25
SOLUTION:20000*2+8*x=15665*10
8x=156650-40000
x=116650/8
x=14581.25
ANSWER:C #### C
QUESTION:A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg?
options: A)s.7.7 B)s.7.4 C)s.7.5 D)s.7.1 E)s.7.9
SOLUTION:100*(20/100) = 20 --- 10
? --- 1 => Rs.2
300 --- 80
? --- 2 => Rs.7.5
Answer:C #### C
QUESTION:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
options: A)1/15 B)4/5 C)4/15 D)1/5 E)2/5
SOLUTION:tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x)
hence 1/5
D #### D
QUESTION:A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the end nearest to the cow. Seeing this cow ran towards the train and managed to escape when the train was 2m away from the bridge. If it had run in opposite direction(i.e away from the train) it would have been hit by the train 2m before the end of the bridge. What is the length of bridge in meters assuming speed of the train is 4 times that of the cow.
options: A)32 B)36 C)40 D)44 E)50
SOLUTION:Explanation :
Explation:
Let length of bridge is X
then middle of bridge is X/2.
and Cow is standing at X/2-5 from the end so
After seeing the train it would run opposite direction and cover distance of X/2-5 when the train is 2m away from other side.
So, the bridge from one side to cow is {(X/2-5)+(X/2-5)}=X-10
so remaining distance is 10m
the cow is hit before 2m i.e cow covers 8m and train will cover 32 m.
Answer : A #### A
QUESTION:If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
options: A)3 B)8 C)9 D)6 E)4
SOLUTION:96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B #### B
QUESTION:The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
options: A)6 B)8 C)9 D)10 E)12
SOLUTION:Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B #### B
QUESTION:Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
options: A)2 B)4 C)6 D)8 E)10
SOLUTION:P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
880/x = 880/1.1x + 10
1.1(880) = 880 + 11x
11x = 88
x = 8
The answer is D. #### D
QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
options: A)15 B)19 C)20 D)21 E)22
SOLUTION:A's 1day work=1/10;
B's 1day work=1/30;
(A+B) 1day work=(1/10+1/30)=2/15;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 2/15 work in 1 day...
They did 2/3 w in 5 days.
Total days=(5+10) = 15
ANSWER:A #### A
<<<Examples ends
QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution?
options: A)45 B)33 1/3 C)27 D)16 2/3 E)15
SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution?
3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x:
1.5/x = 1/20
x = 30
Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution.
Answer is A. #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ?
options: A)23/30 B)11/15 C)7/10 D)1/6 E)2/15
SOLUTION:Let total Housing Units = 5x.
As per question, Equipped with Cable TV = x
Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6.
So, Cable TV + VCR = x + x/6 = 7x/6
No Cable TV and VCR = 5x - 7x/6 = 23x/6.
Fraction = 23x/(6 * 5x) = 23/30. Hence, A #### A
QUESTION:The arithmetic mean of the set S = {8, K, 7, 13, M, 8} is 9. If K and M are integers, and K ≠ M, what is the median of the numbers in the set?
options: A)7 B)7.5 C)8 D)8.5 E)9
SOLUTION:The sum of the numbers is 6*9 = 54
K+M = 54 - 13 - 8 - 8 - 7 = 18
Since K ≠ M, K and M do not equal 9.
Thus one of the two numbers is 8 or less and one is 10 or more.
Then middle two numbers in the set are 8 and 8.
The median is 8.
The answer is C. #### C
QUESTION:A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?
options: A)7 km/hr B)7.2 km/hr C)7.4 km/hr D)7.8 km/hr E)8.9 km/hr
SOLUTION:Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B #### B
QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning?
options: A)$360 B)$380 C)$300 D)$280 E)$275
SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation?
Not really!
Keep in mind that the interest earned each year will be the same in Simple Interest.
At the end of 2 years, Amount = $350
At the end of 5 years, Amount = $425
This means she earned an interest of $75 in 3 years. Or $25 in each year.
We know that the interest earned each year will be the same.
Therefore she must have earned $50 in 2 years.
Hence Principal Amount = $350 - $50 = $300 Option C #### C
QUESTION:A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500?
options: A)s. 1991 B)s. 2991 C)s. 3991 D)s. 4991 E)s. 5991
SOLUTION:Explanation:
Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009.
Required sale = Rs. [ (4500 x 6) – 24009 ]
= Rs. (27000 – 24009)
= Rs. 2991.
Answer B #### B
QUESTION:If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
options: A)s.575 B)s.595 C)s.590 D)s.580 E)s.585
SOLUTION:80 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
ANSWER:E #### E
QUESTION:If 1535/1038 = a +1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?
options: A)165/2 B)175/2 C)178/3 D)187 by 2 E)197/2
SOLUTION:by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/(2+42/497)}
=1+{1/ (2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b *b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D #### D
QUESTION:Let S be the set of values which can be written as the sum of 5 consecutive perfect squares.
What is the smallest element of S which is divisible by 17?
options: A)255 B)355 C)522 D)355 E)664
SOLUTION:Each element of S can be written in the form
(x- 2)2 + (x - 1)2 + x2 + (x + 1)2 + (x + 2)2 = x2 + 2x2 + 2 + 2x2 + 8
= 5x2 + 10
= 5(x2 + 2)
where x is some positive integer with x 3. By iterating over values of x, we observe that when
x = 7, x2 + 2 = 51 = 3 * 17; no smaller value of x exists which satisfies the problem statement.
Hence, the solution is 5(x2 + 2) = 5 *51 = 255
correct answer A #### A
QUESTION:If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ?
options: A)7.2 kg. B)10.8 kg. C)12.4 kg. D)18.0 kg E)None
SOLUTION:Answer
∵Weight of 13 m long rod = 23.4 kg
∴ Weight of 1 m long rod = 23.4 / 13 kg
∴ Weight of 6 m long rod = 23.4 x 6 / 13
= 10.8 kg
Option: B #### B
QUESTION:The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica?
options: A)48 B)47 C)46 D)49 E)52
SOLUTION:let their ages are 9x,15x and 25x respectively.
difference between the ages of Patrick and Monica = 25x-9x=16x where
49x=147 or x=3
so diff in ages = 16x=16*3=48 yrs
ANSWER:A #### A
QUESTION:Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
options: A)28 B)10 C)28 D)27 E)13
SOLUTION:4/12 + x/15 = 1
x = 10
Answer:B #### B
QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ?
options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None
SOLUTION:Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.9 - 19 x 15) kg
= 13 kg.
Correct Option: D #### D
QUESTION:How many integers less than 100 have exactly 4 odd factors but no even factors?
options: A)11 B)13 C)15 D)17 E)19
SOLUTION:Two cases are possible:
x1y1=xy=odd<100x1y1=xy=odd<100, where xx and yy are odd prime numbers, then # of factors will be (1+1)(1+1)=4(1+1)(1+1)=4;
If x=3, then y can be: 5, 7, 11, 13, 17, 19, 23, 29, 31 - 9 numbers.
If x=5, then y can be: 7, 11, 13, 17, 19 - 5 numbers.
If x=7, then y can be: 11, 13 - 2 numbers.
OR:
x3=odd<100x3=odd<100, where xx is odd prime number, then # of factors will be (3+1)=4(3+1)=4.
x can be only 3 - 1 number.
Total 9+5+2+1=179+5+2+1=17 .
Answer: D. #### D
QUESTION:If f(x)= 5x^2- 2x+6 and g(y)= 3y-8, then g(f(x))
options: A)82x^2-9x+38 B)15x^2-6x+10 C)58x^2-4x+58 D)87x^2-5x+96 E)98x^2-7x+94
SOLUTION:g(f(x))=3(5x^2-2x+6)-8
=15x^2-6x+18-8
=15x^2-6x+10
the answer is B #### B
QUESTION:I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
options: A)280 B)670 C)230 D)67 E)120
SOLUTION:A
x*(85/100) = (480 - x)119/100
x = 280 #### A
QUESTION:A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000
options: A)3336,1667 B)3339,1667 C)3333,1666 D)3333,1668 E)3333,1669
SOLUTION:they invested in the ratio 1:2
a's share =1/3*5000=1666
b's share=2/3*5000=3333
ANSWER:C #### C
QUESTION:What is the maximum number of points that 10 circles of different radii intersect?
options: A)24 B)26 C)33 D)90 E)100
SOLUTION:the maximum number of points that two circles intersect is two.
therefore, each of these 10 circles intersect two point with each of the other 9 circles.
as a consequence, the number of these points is equal to two times the number of combination of the 10 circles.
2∗(10!)/(2!∗10!)=90
Answer: D #### D
QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed?
options: A)21005 B)10500 C)25200 D)5376 E)None of these
SOLUTION:Solution
Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4)
8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224
Number of group,each having 3 consonants and 1 vowels = 224 .
Each group contains 4 letter.
Number of ways of arranging 5 letters among themselves
= 4 ! = (4 × 3 × 2 × 1) = 24 .
So, Required number of words = (24 × 224) = 5376 .Answer D #### D
QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?
options: A)80.5 B)82 C)81.5 D)85 E)81.25
SOLUTION:Weighted mix method is best here....
Ratio is 1:10 for 88:80.5...
So the answer required = 80.5+ (88-80.5)*1/10=80.5+7.5*1/10
80.5+0.75=81.25
E #### E
QUESTION:If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be
options: A)2 B)4 C)6 D)7 E)14
SOLUTION:i just tried plugging in the numbers and found out that
4*11025 = 44, 100, which is a square of 210
B #### B
QUESTION:How much is 90% of 40 is greater than 4/5 of 25?
options: A)29 B)776 C)66 D)16 E)99
SOLUTION:(90/100) * 40 – (4/5) * 25
36 - 20 = 16
Answer: D #### D
QUESTION:Johnop went up a certain hill at the rate of one and a half kilometers per hour and came down at the rate of four and a half kilometers per hour, so that it took just four hours to make the double journey. How far was it to the top of the hill ?
options: A)3 km B)6 km C)4.5 km D)km E)none of the above
SOLUTION:Assume the distance to the top of the hill (1 way) as: x
Now, speed=distance/time => time=distance/speed
So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5.
For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5
Now, the total time for the trip is given as 4 hrs.
Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km
So, the distance one side is = 4.5 km.
The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km
Can someone assist me in understanding where am I wrong here? #### C
QUESTION:The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount?
options: A)Rs. 432 B)Rs. 422 C)Rs. 419 D)Rs. 442 E)None of these
SOLUTION:Explanation :
F = Rs. 2560
TD = Rs. 360
PW = F - TD = 2560 - 360 = Rs. 2200
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 2200 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time
=360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C #### C
QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be
options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11
SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 14
x = 2
Mini’s age = 8 years
And Minakshi’s age = 6 years
Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7
ANSWER:C #### C
QUESTION:A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?
options: A)1/3 B)2/9 C)9/46 D)7/19 E)1/6
SOLUTION:The first thing to notice is that A is faster than B and B is faster than C.
Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.
If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.
Therefore total work done = (2*2) + (1*1) + (1/3*1/3) = 46/9
Proportion of work done by B = (1*1) / (46/9) = 9/46
Hence Answer C. #### C
QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
options: A)6 B)9 C)36 D)120 E)144
SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways
Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places
Second Place, Physics Book - in 4 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.
Total no of ways = 4*3*3*2*2*1*1 = 144 ways
E #### E
QUESTION:A coin is tossed live times. What is the probability that there is at the least one tail?
options: A)1/15 B)31/32 C)1/10 D)30/32 E)25/27
SOLUTION:Probability of getting least one tail at the coin tossed five times.
= There is not even a single tail.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
ANSWER B #### B
QUESTION:In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
options: A)7000 B)7200 C)7400 D)7600 E)8000
SOLUTION:State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
E) #### E
QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
options: A)5760 lr B)6000 lr C)6500 lr D)4000 lr E)4500 lr
SOLUTION:1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
ANSWER A #### A
QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?
options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c
SOLUTION:Answer D - m, c, w
c ~ 1/3
w ~ 1/2
and m+w+c = 1 hence m ~ 1/6
Hence increasing order would be m -> c -> w
Aswer D #### D
QUESTION:Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
options: A)4 B)6 C)5 D)7 E)9
SOLUTION:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
Answer: Option A #### A
QUESTION:Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?
options: A)14 mph B)20 mph C)70/3 mph D)80/3 mph E)30 mph
SOLUTION:Average speed for first two hours, S1 = 30 mph
Distance travelled in these two hours, D1 = 60 miles
Average speed for the entire 5 hour ride, S = 30 mph
Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90
Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30
Hence, the correct answer is E #### E
QUESTION:A batsman had a certain average of runs for 16 innings. In the 17th innings, he made a score of 87 runs thereby increasing his average by 3. What is his average after 17 innings?
options: A)39 B)88 C)266 D)278 E)221
SOLUTION:Explanation:
Assume his initial average = xx
His total runs after 16 innings = 16xx
After scoring 87 runs his average got increased by 3 to xx + 3
So his total runs after 17 innings = 17 × (xx+3)
But it was given that the difference in the total scores after 16 innings and 17 innings = 87
Therefore 17×(x+3)−16x=87⇒x=3617×(x+3)−16x=87⇒x=36
His new average = 36 + 3 = 39
Answer:A #### A
QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke?
options: A)16 B)17 C)18 D)19 E)20
SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree.
From the diagram, (36−x)2=x2+122(36−x)2=x2+122
⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144
⇒72x=1296−144⇒72x=1296−144
⇒x=16
Answer:A #### A
QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?
options: A)57% B)60% C)58% D)50% E)20%
SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years
=> C.I - S.I
=> 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100
=> 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5
=> 16r/100 + 8r2/(100)2 = 20r/100
=> 4r/10 = 8r2/(100)2
=> 8[r/100]2 - 4r/100 = 0
=> r/100 {8r/100 -4} = 0
=> r = 0% of 50%
Since r!= 0%, r =50%
Answer:D #### D
QUESTION:In how many ways can you line up 7 apples in a row if one of them cannot be in the middle or at the either end?
options: A)1,790 B)52 C)2,880 D)98 E)2,560
SOLUTION:Since the apple cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.
Answer: C. #### C
QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
options: A)8 B)9 C)7 D)6 E)5
SOLUTION:2x * x = 128 => x= 8
Answer: A #### A
QUESTION:How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
options: A)5040 B)40 C)400 D)5000 E)6000
SOLUTION:LOGARITHM => 10 diff letters
req no of words = No of arrangements of 10 letters taking 4 at a time
=> 10P4 = (10*9*8*7)
==> 5040
ANSWER A #### A
QUESTION:The average of a couple was 26Yrs when they were married 6Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 22Yrs now. How old is the
child now ?
options: A)2 Yrs B)4 Yrs C)3 Yrs D)1 Yrs E)None of these
SOLUTION:(a+b-6-6)/2=26;
a+b=64;
a+b+c/3=22;
solving both c=2
ANSWER:A #### A
QUESTION:The side of a cube is 8 m, Find the voiume?
options: A)515 B)509 C)502 D)508 E)512
SOLUTION:Cube Volume = a(power)3
a(power)3 = 8(power)3
= 512 m(power)3.
Answer is E. #### E
QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.)
Can somebody explain?
options: A)6720 B)7720 C)7820 D)7950 E)8120
SOLUTION:First ring can be worn in 4 ways (on any of the four fingers);
Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1);
Third ring can be worn in 6 ways (the same logic as for the second ring);
Fourth ring can be worn in 7 ways;
Fifth ring can be worn in 8 ways;
Total: 4*5*6*7*8=6720. ANS:A #### A
QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?
options: A)30 B)42 C)120 D)360 E)720
SOLUTION:5 people ,7 seats, only 2 can drive
if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways
since any one can drive total ways = 24 *2= 48 ways
4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways
48*15=720
ANSWER:E #### E
QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
options: A)20 B)30 C)35 D)40 E)50
SOLUTION:Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D #### D
QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
options: A)230 m B)210 m C)260 m D)320 m E)330 m
SOLUTION:Relative speed = (120 + 80) km/hr
= (200 x(5/18))m/sec
= (500/9)m/sec.
Let the length of the other train be x metres.
Then, (x + 290)/9 = 500/9
x + 290 = 500
x = 210.
B #### B
QUESTION:When a number is divided by 31, the remainder is 29. When the same number is divided by 16, what will be the remainder?
options: A)11 B)13 C)15 D)Data inadequate E)None of these
SOLUTION:Number= (31 * Q)+ 29. Given data is inadequate.
Answer: D #### D
QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
options: A)5 B)10 C)24 D)32 E)120
SOLUTION:If it were a line/column combination/permutation problem, the solution would be : 5! = 120.
However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24.
ANS:C #### C
QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is
options: A)10% B)50% C)25% D)17.6% E)None of these
SOLUTION:Explanation:
cost price = (225 + 30) = 255 sell price = 300
gain = (45/255)*100 = 17.6%. Answer: D #### D
QUESTION:If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is
options: A)48 km B)50 km C)40 km D)22 km E)70 km
SOLUTION:B
50 km.
Let the actual distance travelled be x km.
Then x/10=(x+20)/14
--> 14x = 10x + 200
--> 4x = 200
--> x = 50 km. #### B
QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 60 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?
options: A)12 B)15 C)20 D)24 E)30
SOLUTION:Let x be the number of new boarders.
The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10.
60 / (60+x) = 4/5
x = 15
The answer is B. #### B
QUESTION:The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
options: A)279 B)283 C)308 D)318 E)342
SOLUTION:Other number = (11 x 7700)/275 = 308.
Answer: Option C #### C
QUESTION:A company organzied a help desk.there have been done 24 hrs work on software,17 hrs on help user nd 40% on other services.find the total no. of hrs have been worked on that day?
options: A)68 B)69 C)70 D)67 E)76
SOLUTION:let total no of hrs = x
they have done 24+17=41
40% of x is 40/100=2/5
x=41+2x/5
x=68.3
ANSWER:A #### A
QUESTION:Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 7.5 km apart, if they walk in the same direction?
options: A)12 hrs B)14 hrs C)15 hrs D)17 hrs E)None
SOLUTION:Sol.
to be 0.5 km apart, they take 1 hour.
To be 7.5 km apart, they take [1/0.5 * 7.5] hrs = 15 hrs.
Answer C #### C
QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have?
options: A)9 B)12 C)18 D)28 E)36
SOLUTION:Lets take an example: find the number of factors of 100
try to represent 100 in least possible prime numbers
100= 2^2 * 5^2=p^a*q^b
no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9
similarly find the number of factors of p^3 * q^6--->a=3,b=6
(3+1)(6+1)=28 Ans D. #### D
QUESTION:Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.
options: A)Rs. 610 B)Rs. 612 C)Rs. 614 D)Rs. 616 E)None of these
SOLUTION:Explanation:
Amount=[7500×(1+4100)2]=(7500×2625×2625)=8112
So compound interest = (8112 - 7500) = 612
Answer: B #### B
QUESTION:The largest 4 digit number exactly divisible by 88 is?
options: A)9930 B)9936 C)9944 D)9952 E)9960
SOLUTION:Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
C) #### C
QUESTION:15 + sqrt(- 6 + 8×5÷4) =?
options: A)31 B)32 C)33 D)34 E)35
SOLUTION:According to order of operations, inner brackets first where 8x5÷4 is first calculated since it has a multiplication and a division.
8x5÷4 = 40÷4 = 10
Hence
15 + sqrt(- 6 + 8×5÷4) = 15+ sqrt(- 6 + 10)
= 15 + sqrt(4) = 15 + 16 = 31
correct answer A)31 #### A
QUESTION:Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
options: A)11:5 B)3 : 2 C)1:2 D)3:5 E)7:8
SOLUTION:Answer: Option B
Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. #### B
QUESTION:One boy forgot the last digit of a 7 digit no. If he randomly dialthe final 3 digits aftercorrectly dialing the 1st 4, then what is the chance of dialing the correct no.?
options: A)1/890 B)2/465 C)1/1000 D)1/3453 E)2/1454
SOLUTION:it is given that last 3 digits are randomly dialed
Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability
= 1/(10)3 = 1/1000
C #### C
QUESTION:How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
options: A)12 sec B)30 sec C)36 sec D)16 sec E)18 sec
SOLUTION:Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 600 * 3/50
= 36 sec.
Answer: C #### C
QUESTION:If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12.
options: A)6 B)1 C)3 D)8 E)7
SOLUTION:Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3
If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3
When divided by 12, it must leave a remainder of 3.
The answer is C. #### C
QUESTION:In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?
options: A)3:1 B)3:5 C)7:8 D)7:9 E)9:11
SOLUTION:First mixture: milk and water in the ratio of 3x:4x.
Second mixture: milk and water in the ratio 5y:2y.
We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3.
Answer: A. #### A
QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth?
options: A)$69 B)$78 C)$90 D)$86 E)$77
SOLUTION:C
$90
SP of 1m of cloth = 8925/85 = $105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= $105 - $15 = $90. #### C
QUESTION:How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number?
options: A)26 B)30 C)34 D)38 E)42
SOLUTION:The first number is 22 = 16+6(1).
We can continue adding 6 to make a list: 22, 28, 34,...
The last number is 196 = 16+6(30)
There are 30 numbers in the list.
The answer is B. #### B
QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92?
options: A)60 B)70 C)80 D)90 E)100
SOLUTION:(4*90+x)/5=92
x=(5*92)-(4*90)
x= 460 - 360
total score required 460 - 360=100
Correct answer is E #### E
<<<Examples ends
QUESTION:Carol is four times Alice’s age but only twice as old as Betty. Alice is thirty-six years younger than Carol. How old is Betty?
options: A)36 B)39 C)42 D)48 E)24
SOLUTION:Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.
We're told 3 facts about the relative ages of 3 people:
1) Carol's age is 4 times Alice's age
2) Carol's age is 2 times Betty's age
3) Carol is 36 years older than Alice
We're asked for BETTY'S age.
Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST smaller answer first.
IF....
Betty = 24
Then Carol = 2(24) = 48
Then Alice = 48 - 36 = 12 AND 48/4 =12
All of these values mesh perfectly with the facts and with one another, so Betty MUST be 24
E #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent?
options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these
SOLUTION:Let CP of an book = 100
MP of an book = 120
Discount 30 % on 120 = 36
SP of the book = 120 - 36 = 84
loss = 16%
Answer : C #### C
QUESTION:For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?
options: A)18.1 B)21.1 C)36.5 D)42.2 E)84.4
SOLUTION:Let x and z be the smallest and largest of the original set, respectively.
z - x = 84.4
The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.
Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1
The answer is B. #### B
QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
options: A)18% B)19% C)28% D)68% E)48%
SOLUTION:1500 ---- 270
100 ---- ? => 18%
Answer: A #### A
QUESTION:Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is?
options: A)6 km B)8 km C)9 km D)11 km E)12 km
SOLUTION:Let total distance =D=D
Distance travelled at 4 kmph speed =(23)D=(23)D
Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D
Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr
We know,
Time=DistanceSpeedTime=DistanceSpeed
Total time
2115=2/34D+1/35D2115=2/34D+1/35D
2115=2D12+D152115=2D12+D15
84=14D84=14D
D=6 km
Option A is correct #### A
QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing?
options: A)191 B)400 C)737 D)840 E)1,560
SOLUTION:Let weight of side of beef before processing = x
(60/100)*x = 240
=> x = (240 * 100)/60 = 400
Answer B #### B
QUESTION:Solve 8x – 4 = 4x + 11
options: A)5(1/3) B)6(1/3) C)7(1/3) D)3(3/4) E)9(1/3)
SOLUTION:Sol.
8x – 4 = 4x + 11
=> 8x – 4x = 11 + 4
=> 4x = 15 => x = 15/3 = 3(3/4).
Answer D #### D
QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam?
options: A)52% B)64% C)72% D)76% E)80%
SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A
QUESTION:If a square mirror has a 20-inch diagonal, what is the approximate perimeter E of the mirror, in inches?
options: A) 40 B) 60 C) 80 D) 100 E) 120
SOLUTION:if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter E must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B #### B
QUESTION:A person spent Rs. 5,040 from his salary on food and 5,000 on house rent. After that he was left with 20% of his monthly salary. What is his monthly salary ?
options: A)22,550 B)32,550 C)52,550 D)62,550 E)12,550
SOLUTION:Total money spent on food and house rent = 5,040+5,000 = 10,040
Which is 100 - 20 = 80% of his monthly salary
∴ His salary = 10040x100/80 = 12550
Answer : E #### E
QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made?
options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these
SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000
ANSWER:C #### C
QUESTION:A ship sails out to a mark at the rate of 19 kmph. and sails back at the rate of 13 kmph. The average rate of sailing is ?
options: A)15 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None
SOLUTION:Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 19 x 13 ) / (19 +13 ) km/hr.
= 15 km/hr.
Correct Option: A #### A
QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table?
options: A)11*10! B)9*8! C)8*7! D)7*6! E)6*5!
SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=12
(n-1)!=11!=11*10!
Ans:A #### A
QUESTION:39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
options: A)9 B)12 C)10 D)13 E)15
SOLUTION:Explanation:
Let the required number of days be x
More persons, less days (indirect proportion)
More hours, less days (indirect proportion)
Hence we can write as
(persons)39:30
(hours) 5:6}:: x:12
⇒39×5×12=30 × 6 × x
⇒39×5×2=30 × x
⇒39=3×x
⇒x=13
Answer: Option D #### D
QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube.
options: A)36 B)48 C)45 D)360 E)55
SOLUTION:16200 = 23 * 34 * 52
A perfect cube has a property of having the indices of all its prime factors divisible by 3.
Required number = 32 * 5 = 45.
ANSWER:C #### C
QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase?
options: A)$32 B)$50 C)$320 D)$400 E)$500
SOLUTION:Property tax as a percentage of its assessed value = 8%
Increase in assessed value of the property = 24000 - 20000 = 4,000 $
Increase in property tax = (8/100)* 4000 = 320 $
Answer C #### C
QUESTION:Henry answered 4/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?
options: A)x B)(85/12)*x C)(85/24)*x D)(85/36)*x E)(85/48)*x
SOLUTION:Let Q be the number of homework questions.
Q = 4Q/5 + (5/17)(Q/5) + x
Q = 68Q/85 + 5Q/85 + x
12Q/85 = x
Q = (85/12)*x
The answer is B. #### B
QUESTION:A basket has 6 apples and 6 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
options: A)1/2 B)1/3 C)1/4 D)2/5 E)3/10
SOLUTION:The total possible choices are 12C3 = 220
The ways to choose 3 apples: 6C3 = 20
The ways to choose 2 apples: 6C2 * 6C1 = 90
P(at least 2 apples) = 110/220 = 1/2
The answer is A. #### A
QUESTION:A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 7 minutes less than they can row it in still water. How long would they take to row down with the stream
options: A)45 or 23 minutes B)73 or 12 minutes C)77 minutes D)19 minutes E)25 minutes
SOLUTION:A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-7))
giving t = 77
C #### C
QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is?
options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5
SOLUTION:3:1
Answer:B #### B
QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent?
options: A)10% B)20% C)30% D)40% E)50%
SOLUTION:5*SP = 7*CP
SP = 1.4*CP
The profit percent is 40%.
The answer is D. #### D
QUESTION:A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half?
options: A)14 B)15 C)18 D)22 E)33
SOLUTION:The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.
The time T2 to run the second half must be twice the time T1 to run the first half.
T2 = 2*T1 = T1+11
T1 = 11 and so T2 = 22.
The answer is D. #### D
QUESTION:Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
options: A)126 B)120 C)101 D)112 E)115
SOLUTION:8 shirts
9 pants
we can combine 2 shirts with (12-3) pants
2*9=18
we can combine the other shirts (6) with any pants (9)
9*12=54
Thus total :108+18=126 ANS:A #### A
QUESTION:For any non-zero a and b that satisfy |ab| = ab and |C| = -c
|b - 4| + |ab - b| = ?
options: A)a) ab - 4 B)b) b - 2b + 4 C)c) ab + 4 D)d) 2b - ab - 4a E)e) 4 - ab
SOLUTION:|a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b+4
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4
Answer: Option B #### B
QUESTION:In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true?
I) k=0
II) k=−1
III) k=−3
options: A)I only B)III only C)I and II only D)II and III only E)I and III only
SOLUTION:Please format the question properly.
Per the question, x^2+kx+1=0 with k=constant.
For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges.
B is the correct answer. #### B
QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is?
options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000
SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
M + O = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv)
Subtracting (ii) from (iv), we get M = 4000.
M's monthly income = Rs. 4000
C #### C
QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold?
options: A)6 B)4 C)8 D)10 E)12
SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies;
14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22
# of paperback copies sold is 30-22=8
Answer: C #### C
QUESTION:How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
options: A)5040 B)40 C)400 D)5000 E)6000
SOLUTION:LOGARITHM => 10 diff letters
req no of words = No of arrangements of 10 letters taking 4 at a time
=> 10P4 = (10*9*8*7)
==> 5040
ANSWER A #### A
QUESTION:A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in?
options: A)12 B)13 C)13 5/7 D)13 ¾ E)None of these
SOLUTION:Explanation:
(A+B)’s 2 day work = 1/16 + 1/12 = 7/18
work done in 6 pairs of days=7/48 x 6 = 7/8
remaining work = 1/8
work done by A on 13th day =1/16 remaining work = 1/16
on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day
total time taken =13 ¾ days
Answer: Option D #### D
QUESTION:The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
options: A)0.8% B)8.3% C)0.3% D)2.3% E)0.4%
SOLUTION:(1500 * R1 * 3)/100 - (1500 * R2 * 3)/100 = 13.50 4500(R1 - R2) = 1350
R1 - R2 = 0.3%
Answer:C #### C
QUESTION:The girl child birth in a town is 40% of boy child birth. What is the number of boy child as a percentage of girl child birth?
options: A)150% B)250% C)125% D)35% E)65%
SOLUTION:The number of girl child birth in a town is 40% of boy child birth
If the boy child birth=10
Girl child birth=4
We are asked to find the number of boy child birth as a percentage of girl child birth
B/G=10/4=2.50=250%
Answer is B #### B
QUESTION:Sum of 42 odd numbers is?
options: A)1764 B)1774 C)1784 D)1794 E)1754
SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 42 odd numbers = 42^2 = 1764
ANSWER:A #### A
QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 450. Find the total worth of the stock?
options: A)20029 B)22500 C)20289 D)20027 E)20026
SOLUTION:Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 450 => x = 22500
Answer: B #### B
QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.2 km long?
options: A)2 mins 14 sec B)2 mins 34 sec C)162 sec D)244 sec E)2 mins 44 sec
SOLUTION:D = 25 * 60 + 1200 = 2700 m
T = 2700/60 * 18/5 = 162 sec
ANSWER:C #### C
QUESTION:Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
options: A)broke even, B)lost 4 cents C)gained 4 cents D)lost 10 cents E)gained 10 cents
SOLUTION:Solution:
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer: A #### A
QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
options: A)Rs. 7500 B)Rs. 9000 C)Rs. 9500 D)Rs. 10,000 E)None of these
SOLUTION:Explanation:
A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs. 7500.
ANSWER IS A #### A
QUESTION:If the area of a square with sides of length 5 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
options: A)4 B)8 C)12 D)7 E)18
SOLUTION:Let length of rectangle = L
5^2 = L*4
=> L = 25/4 = 7
Answer D #### D
QUESTION:Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.?
options: A)8 B)12 C)14 D)16 E)18
SOLUTION:Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+30
3x + 6 = x + 30
2x = 24
\inline \therefore x = 12
\inline \therefore Middle number = x + 2 = 12+2 = 14
C #### C
QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
options: A)1/20 B)1/6 C)1/5 D)4/21 E)5/21
SOLUTION:series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 5*x
Hence, a1+a2+..+a20+n = 25x
So, the fraction asked = 5x/25x = 1/5
Answer C #### C
QUESTION:There are 3 people and 3 chairs. In how many different ways people can occupy the chairs?
options: A)6 B)15 C)24 D)36 E)120
SOLUTION:number of ways =3! = 6
Answer is A #### A
QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
options: A)600 B)2877 C)208 D)1882 E)191
SOLUTION:Explanation:
Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A #### A
QUESTION:If P = Q/R, -1 < R < 0 and 4 < Q, which of the following is correct?
options: A)P > 4. B)0 < P <4. C)-4 < P < 0. D)P < -4. E)P < -20.
SOLUTION:Q is +veR is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take Q=4.1P=-0.9
P=4.1/-0.9
P<-4
Ans D #### D
QUESTION:The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth?
options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 300 E)None of these
SOLUTION:Explanation :
T = 2 years
R = 10%
TD = (BG ×100)/TR = (24 × 100)/(2×10) = 12 × 10 = Rs. 120
TD = (PW × TR)/100
⇒ 120 = (PW × 2 × 10)/100
⇒ 1200 = PW × 2
PW =1200/2 = Rs. 600 Answer : Option A #### A
QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares?
options: A)$37.5 B)$40 C)$50 D)$48 E)$52
SOLUTION:Dividend on 1 share = $(10/100*50)
=$5
$12.5 is an income on an investment of $100
$5 is an income on an investment of $(100*2/25*5)=40
Thus, cost of 1 share =$40
option B #### B
QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 13260, how much money did he borrow?
options: A)13000 B)80288 C)2668 D)2600 E)2781
SOLUTION:Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 13260
18x + 45x + 39x = (13260* 100)
102x = 1326000 => x = 13000.
Answer:A #### A
QUESTION:Anderson has a phone plan that charges a
monthly rate of $50 for the first 1,000 minutes
plus $0.25 for each additional minute.
Which of the following functions models
Anderson’s plan for all m > 1,000, with m as
the number of minutes per month and f(m)
as the monthly charge?
options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000
SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee
based on the number of minutes used plus a flat rate of $50. With this information, you can
create the following function:
f(m) = Usage fee + 50
The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So
the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify:
f(m) = 0.25(m – 1,000) + 50
f(m) = 0.25m – 250 + 50
f(m) = 0.25m – 200
correct answer C)f(m) = 0.25m – 200 #### C
QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
options: A)22 B)80 C)40 D)77 E)12
SOLUTION:800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C #### C
QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1
SOLUTION:Explanation:
Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
Answer: D #### D
QUESTION:What is the probability that a leap year has 53 Sundays and 52 Mondays?
options: A)1/9 B)1/8 C)1/3 D)1/7 E)1/2
SOLUTION:A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:D #### D
QUESTION:At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
options: A)404 B)452 C)444 D)468 E)422
SOLUTION:312 + 222 - 112 (since 112 is counted twice )= 422
E is the answer #### E
QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
options: A)25 pounds B)46 pounds C)92 pounds D)100 pounds E)146 pounds
SOLUTION:Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*10 --> x = 100.
Answer: D. #### D
QUESTION:Machine W can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
options: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33
SOLUTION:Let the following be true:
W makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C #### C
QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class?
options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm
SOLUTION:The total height was 45 cm too much.
The average height should be reduced by 45 cm/30 = 1.5 cm
The answer is B. #### B
QUESTION:A woman is 18 years older than her son. In 4 years, her age will be twice the age of her son. The present age of her son is
options: A)12 B)14 C)16 D)18 E)20
SOLUTION:Explanation:
Let the son's present age be x years. Then, woman's present age = (x + 18) years
=> (x + 18) + 4 = 2(x + 4)
=> x + 22 = 2x +8
So, x = 14 Answer: B #### B
QUESTION:If xy > 0, which of the following must be negative?
options: A)-x/-y B)x/y C)-x/y D)2xy E)x+y
SOLUTION:- / + = -
Answer : C #### C
QUESTION:If the simple interest on Rs.3100 amount to Rs. 632.40 in 2 Years, What is the rate percent?
options: A)11.2% B)10.2% C)12.2% D)13.2% E)18.2%
SOLUTION:$632.40 = (3100*2*R)/100
R = 10.2%
Answer: B #### B
QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E?
options: A)60 B)80 C)40 D)120 E)160
SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30
(9/8)x - (3/4)x = 30
x = 80=E
Answer: B #### B
QUESTION:A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?
options: A)30 min B)35 min C)45 min D)50 min E)55 min
SOLUTION:there are 9 hours in between 9 a.m. to 6 p.m.
9*5=45 minutes.
ANSWER:C #### C
QUESTION:A Pharmacy company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 8 hrs and a machine of type S does the same job in 4 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
options: A)3 B)4 C)2 D)9 E)12
SOLUTION:Rate of machine R =1/8
Rate of machine S =1/4
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/8 +x/4 =1/2
3x/8=1/2
x=8/6=1.3=2
So no of machine R is 2
Answer C #### C
QUESTION:The smallest 2 digit prime number is?
options: A)A)11 B)B)13 C)C)19 D)D)113 E)E)None
SOLUTION:The smallest 3-digit number is 10, which is divisible by 2.
10 is not a prime number.
11 is a prime number.
Hence 11 is the smallest 2-digit prime number.
A) #### A
QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 160 km/hr?
options: A)2.5 sec B)2.9 sec C)2.7 sec D)8.7 sec E)8.5 sec
SOLUTION:Speed = 160 * 5/18 = 44 m/sec
Time taken = 120/44 = 2.7 sec.
Answer: C #### C
QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions?
options: A)2112 m B)2704 m C)2278 m D)2288 m E)2378 m
SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions.
= 1500 * 2 * 22/7 * 22.4 = 211200 cm
= 2112 m
Answer: A #### A
QUESTION:Set A contains all the even numbers between 8 and 50 inclusive. Set B contains all the even numbers between 108 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
options: A)2200 B)2550 C)5050 D)6275 E)11325
SOLUTION:Set A contains 8, 10, 12... 50
Set B contains 108 , 110 , 112 ... 150
Number of terms in each set = 22
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*22 = 2200
Answer A #### A
QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?
options: A)42 years B)41 years C)43 years D)40 years E)45 years
SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years
Answer C #### C
QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
options: A)1227 B)2088 C)26788 D)8112 E)1871
SOLUTION:A = 7500(26/25)2 = 8112
Answer: D #### D
<<<Examples ends
QUESTION:What is the greatest positive integer x such that 7^x is a factor of 343^10?
options: A)5 B)9 C)10 D)20 E)30
SOLUTION:343^10 = (7^3)^10 = 7^30
ANSWER:E #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The division of a whole number N by 14 gives a quotient of 18 and a remainder of 2. Find N.
options: A)797 B)254 C)597 D)997 E)297
SOLUTION:According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 18* 14 + 2 = 254 correc answer B #### B
QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture?
options: A)9! B)9×8! C)4x5! D)10!/2! E)10!
SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!*2! ways.
Total - Restriction =
= 6! - 5!*2! =
= 5!(6- 2!) =
= 4*5!.
Answer: C. #### C
QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3%
SOLUTION:Explanation:
Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens = Rs. 33
Profit% = 33/99 * 100 = 33 1/3%
Answer: A #### A
QUESTION:How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number?
options: A)26 B)30 C)34 D)38 E)42
SOLUTION:The first number is 22 = 16+6(1).
We can continue adding 6 to make a list: 22, 28, 34,...
The last number is 196 = 16+6(30)
There are 30 numbers in the list.
The answer is B. #### B
QUESTION:A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number?
options: A)297 B)187 C)278 D)200 E)267
SOLUTION:25 + 25 = 50
25% ------ 50
100% ----- ? => 200
Answer:D #### D
QUESTION:Pipe A can fill the tank in 30 minutes and pipe B in 20min and pipe C can empty the tank in 90 minutes. How long it will take to fill the tank if three of the pipes are operating together?
options: A)10.55 B)12.0 C)13.1 D)13.85 E)15.2
SOLUTION:Pipe A fills 1/30th of the tank in a minute and pipe B, 1/20th. Pipe C empties in 90min
(1/30)+(1/20)-(1/90)=(1/x)
13/180=1/x => x=180/13 => x=13.85 minutes
Answer: D #### D
QUESTION:What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 743.095 + ?
options: A)870 B)790 C)780 D)770 E)890
SOLUTION:? = 285 + 1895 – 655 – 745 or, ? = 780
Answer C #### C
QUESTION:From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x)
options: A)10 B)14 C)15 D)16 E)30
SOLUTION:Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations
E #### E
QUESTION:The sector of a circle has radius of 35 cm and central angle 135o. Find its perimeter?
options: A)91.5 cm B)11.5 cm C)91.8 cm D)92.5 cm E)152.5 cm
SOLUTION:Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 35) + 2(35)
= 49.5 + 70
= 152.5 cm
Answer:E #### E
QUESTION:The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability T that the next couple the maitre 'd seats will not order dessert?
options: A) 20% B) 25% C) 40% D) 60% E) 75%
SOLUTION:could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
T=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25% #### B
QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons?
options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20
SOLUTION:5p3 =5 x4= 20
Option 'E' #### E
QUESTION:A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
options: A)2 1/7 hours B)2 1/2 hours C)2 7/2 hours D)4 1/2 hours E)2 1/5 hours
SOLUTION:Required time = (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer:B #### B
QUESTION:You are filling up your car with gas. Your tank can hold 19 gallons. Your car started with x gallons in it. You paid $20 in gas. What was the cost of gas per gallon?
options: A)19/20 B)x/20 C)(19-x)/20 D)x-19)/20 E)19+20/x
SOLUTION:Amount of gas you added to your car: 19-x
Price per gallon: (19-x)/20
Answer: C #### C
QUESTION:In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 10 is
options: A)8 B)625 C)16 D)20 E)24
SOLUTION:I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 10
A. x+y+x-y = 10 --> x=5
B. x+y-x+y = 10 --> y=5
C. -x-y +x-y= 10 --> y=-5
D. -x-y-x+y=10 --> x=-5
The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be25*25=625
Answer: B #### B
QUESTION:Convert the 9/36 m/s into kilometers per hour?
options: A)0.9 kmph B)9.9 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph
SOLUTION:9/36 m/s = 9/36 * 18/5 = 9/10
= 0.9 kmph.
Answer: A #### A
QUESTION:Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 55% nuts, what percent of the combined mixture is dried fruit?
options: A)8.5% B)11.7% C)14.2% D)17.6% E)20.5%
SOLUTION:55% is 25%-points above 30% and 5%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 1:5.
1/6*70% = 11.7%
The answer is B. #### B
QUESTION:A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago?
options: A) 8 B) 10 C) 12 D) 14 E) 7
SOLUTION:Let's say
Age of Richard isR
Age of David isD
Age of Scott isS
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 7 years ago?
i.e. D-7 = 14-7 = 7 years
Answer: Option
E #### E
QUESTION:The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
options: A)10º B)75º C)90º D)130º E)180º
SOLUTION:Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º.
Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º.
Required angle = (130 - 120)º = 10º.
Answer A #### A
QUESTION:The probability of two events A and B are0.25 and 0.40 respectively. The probability that both A and B occur is 0.20. The probability that neither A nor B occur is _________
options: A)0.45 B)0.4 C)0.55 D)0.05 E)0.6
SOLUTION:we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.25+.40-.20
=.45
but the probability of neither A nor B=1-.45
=0.55
ANSWER:C #### C
QUESTION:44×98×101=?
options: A)435512 B)434431 C)548654 D)543286 E)546543
SOLUTION:44×(100-2)×(100+1)
(4400-88)×(100+1)
4312×(100+1)
431200+4312=435512
answer A #### A
QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 20% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
options: A)40% B)45% C)55% D)60% E)64%
SOLUTION:VERITAS PREPOFFICIAL SOLUTION:
D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 80% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5*(4/5) of the original price, which nets to 0.64 of the original price, or 64%.
E #### E
QUESTION:A box contains 4 chocobars and 4 ice creams. Tom eats 3 of them, by randomly choosing. What is the probability of choosing 2 chocobars and 1 icecream?
options: A)9/3 B)1/7 C)2/8 D)2/7 E)4/7
SOLUTION:Probability of choosing 1 chocobar = 4/8 = 1/2
After taking out 1 chocobar, the total number is 7.
Probability of choosing 2nd chocobar = 3/7
Probability of choosing 1 icecream out of a total of 6 = 4/6 = 2/3
So the final probability of choosing 2 chocobars and 1 icecream = 1/2 * 3/7 * 2/3 = 1/7
B #### B
QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three?
options: A)14 B)16 C)18 D)24 E)34
SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
ANSWER:A #### A
QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
options: A)2 months B)7 months C)8 months D)10 months E)12 months
SOLUTION:Explanation:
7 * 8 : 9 * x = 8:9 => x= 7 months
ANSWER:B #### B
QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020
SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10200 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv)
Subtracting (ii) from (iv), we get, P = 4050.
P's monthly income = Rs.4050.
Answer: A #### A
QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
options: A)38 B)41 C)30 D)31 E)29
SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: C #### C
QUESTION:In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
options: A)12 B)3 C)5 D)8 E)10
SOLUTION:Let the number of buffaloes be x and the number of ducks be y.
Then 4x+2y=2(x+y)+24
=>x=12
ANSWER A 12 #### A
QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased?
options: A) 100% B) 500% C) 300% D) 600% E) 800%
SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times.
The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%.
Answer: B. #### B
QUESTION:Deepak can read x pages in 10 minutes. At this rate, how long will it take him to read y pages?
options: A)(12/x)*y B)(5/x)*y C)(10/x)*y D)(10x)*y E)(13/x)*y
SOLUTION:x page in 10 mins
i.e. 1 page in 10/x mins
i.e. y pages in (10/x)*y
Answer: option C #### C
QUESTION:If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream
options: A)1.5kmph B)0.5kmph C)0.4kmph D)1.6kmph E)2.5kmph
SOLUTION:Speed upstream = 32/4 = 8 kmph
Speed down stream = 72/8 = 9 kmph
Speed of stream = ½ (9-8) = 0.5kmph
ANSWER:B #### B
QUESTION:Simple interest on a certain sum at a certain annual rate of interest is 1/3 of the sum. If the numbers representing Time is three times the Rate percent , then the Rate is:
options: A)1 1/3 %. B)2 1/3 %. C)3 1/3 %. D)4 1/3 %. E)5 1/3 %.
SOLUTION:Explanation :
Let sum = x. Then, S.I. = x/3
Let N =3R
[x * 3R * R / 100] = x/3? R^2 = 100/9
R = 10/3 = 3 1/3%.
Hence, Rate = 3 1/3 %.
Answer : C #### C
QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
options: A)270 B)252 C)272 D)292 E)285
SOLUTION:number of astronauts with previous experience = 7
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group
(7C1)*(9C2)
=7*36= 252
Answer : B #### B
QUESTION:While working alone at their respective constant rates, server J uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?
options: A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr
SOLUTION:Server J processes 480/4 files per hour = 120 per hour
Server Y processes 180/8 files per hour = 60 per hour
Total files processed per hour when J and Y work together = 120+60 per hour = 180 files per hour
480/180 = 2 2/3 hours=C #### C
QUESTION:In how many different number of ways a Committee of 4person of can be selected from 4boys and 4girls such that at least 1 girl is included in the committe
options: A)70 B)69 C)67 D)68 E)65
SOLUTION:1G 3B 2G 2B 3G 1B 4G
=(4C1*4C3)+(4C2*4C2)+(4C3*4C1)+4C4
= (4*4)+(6*6)+(4*4)+1
= 16+36+16+1=69
Total 4M 4W
8C4=70
4C4=1
At least one girl = total - with out girl
At least one girl =70-1=69
B) #### B
QUESTION:Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
options: A)7 min B)9 min C)4 min D)9 min E)1 min
SOLUTION:Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9
Answer:B #### B
QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :
options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 5
SOLUTION:Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 495
99c - 99a = 99(c - a) = 495
495 = 99*5 = 99(c - a)
So c - a = 5
Answer (E) #### E
QUESTION:If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF
options: A)13 - 11 - 9 - 7 - 8 B)13 - 11 - 9 - 7 - 6 C)13 - 11 - 9 - 7 - 7 D)13 - 11 - 9 - 7 - 3 E)13 - 11 - 9 - 7 - 1
SOLUTION:MLIGF = 13 - 11 - 9 - 7 - 8
Note: this is a dummy question. Dont answer these questions
Answer:A #### A
QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
options: A)20 B)15 C)25 D)18 E)12
SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
ANSWER B #### B
QUESTION:What percent is 4 gm of 1 kg?
options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 %
SOLUTION:1 kg = 1000 gm
4/1000 × 100 = 400/1000
=2/5 = 0.4 %
B) #### B
QUESTION:What is the area of a square field whose diagonal of length 20 m?
options: A)228 B)271 C)200 D)277 E)181
SOLUTION:d2/2 = (20 * 20)/2 = 200
Answer:C #### C
QUESTION:A word is defined as a sequence of five dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed?
options: A)124 B)150 C)212 D)243 E)316
SOLUTION:3^5 = 243
The answer is D. #### D
QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
options: A)3700 B)3890 C)88798 D)2789 E)2891
SOLUTION:Explanation:
Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700.
Answer: A) 3700 #### A
QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water?
options: A) 16 B) 72 C) 112 D) 128 E) 144
SOLUTION:Solution:
We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water.
2x + 16x = 162
18x = 162
x = 9
Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water.
Answer E. #### E
QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159
SOLUTION:46 + 28 + 10 = 84%
100 – 84 = 16%
850 * 16/100 = 136
Answer:A #### A
QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
options: A)1350 B)2997 C)2087 D)2697 E)9824
SOLUTION:Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5
=> 675
675 * 2
= Rs.1350
Answer:A #### A
QUESTION:What is the maximum number of pieces of birthday cake of size 5” by 5” that can be cut from a cake 15” by 15”?
options: A)5 B)10 C)16 D)20 E)9
SOLUTION:The prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 3 'pieces' each, we have (3)(3) = 9 total smaller squares (at maximum).
E #### E
QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 9 and 10. The larger of the two numbers is:
options: A)276 B)299 C)230 D)345 E)395
SOLUTION:Clearly, the numbers are (23 x 9) and (23 x 10).
Larger number = (23 x 10) = 230.
Answer: Option C #### C
QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2
options: A)I only B)I,II only C)II only D)I,III only E)III only
SOLUTION:12=2*2*3
16=2*2*2*2
GCF =2*2=4
Answer : C #### C
QUESTION:In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A?
options: A)2 B)3 C)5 D)6 E)8
SOLUTION:I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have A=2*3*5*7 = 840
Thus, answer B #### B
QUESTION:The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees.
options: A)$2291.7 B)$1546.8 C)$2546.5 D)$1879.3 E)$3125.3
SOLUTION:mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7
Answer is A #### A
QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
options: A)1/5 B)2/5 C)3/10 D)3/7 E)1/7
SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C #### C
QUESTION:The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface?
options: A)27 B)16 C)12 D)18 E)11
SOLUTION:2 * π * 2r * 3r = 12 πr2
Answer:C #### C
QUESTION:There are 22 students in a class. In how many different ways can a committee of 3 students be formed?
options: A)1180 B)1320 C)1540 D)1760 E)1920
SOLUTION:22C3 = 22*21*20 / 6 = 1540
The answer is C. #### C
QUESTION:A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
options: A)60 km/hr B)50 km/hr C)36 km/hr D)26 km/hr E)87 km/hr
SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 15 = 45 => x = 60 km/hr.
Answer:A #### A
QUESTION:The number of female students in a college in the previous year was 400. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year?
options: A)200 B)600 C)900 D)1600 E)2000
SOLUTION:Let x be the number of male students last year. The number of male students this year is 2x.
Let y be the number of female students this year.
x/400 = 2(2x/y)
y = 1600
The answer is D. #### D
QUESTION:A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
options: A)35.55 km/hr B)36 km/hr C)71 km/hr D)71.11 km/hr E)70 km/hr
SOLUTION:Total time taken =((160/64)+(160/80))hrs=9/2hrs.
Average speed =(320 x2/9)km/hr= 71.11 km/hr.
ANSWER D #### D
QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent?
options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3%
SOLUTION:750 ---- 50
50 ---- ? => 6 2/3%
Answer: E #### E
QUESTION:On the x-y coordinate plane there is a parabola, y=x(4-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 4) II. (2, 3) III. (4, 1)
options: A)I only B)II only C)III only D)I and II E)I, II, and III
SOLUTION:Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 1, y = 3 lies on the parabola, so (1, 4) will not be enclosed by the parabola and x axis.
When x = 2, y = 4 lies on the parabola, so (2, 3) will lie below it and this point will be enclosed by the parabola and x axis.
When x = 4, y = 0 lies on the parabola, so (4, 1) will not be enclosed by the parabola and x axis.
The answer is B. #### B
QUESTION:A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
options: A)A)300 B)B)350 C)C)450 D)D)470 E)E)500
SOLUTION:Explanation:
10 * 150 = 1500
4 * 100 + 5 * 150 = 1150
1500 – 1150 =350
B #### B
QUESTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, is
options: A)131 B)176 C)274 D)405 E)495
SOLUTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}.
6 times 40 something is approx north of 240
Hence the answer is (C) 274 #### C
QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am
SOLUTION:In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours.
Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am.
Answer: D #### D
QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?
options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31
SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 2/7 + 2/5 * 5/7
= 16/35
Answer:A #### A
QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have?
options: A)27 B)32 C)43 D)54 E)77
SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys
49 - 5 = 44 for Tom and Bob
If distributed equally, each one will have
44 / 2 = 22 toys
Bob has 5 more toys than Tom, so Bob has
22 + 5 = 27 toys
correct answer A #### A
QUESTION:How many diagonals does a 62-sided convex polygon have?
options: A)1829 B)2356 C)3458 D)3843 E)4820
SOLUTION:A 62-sided convex polygon has 62 vertices.
If we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829.
The answer is A. #### A
<<<Examples ends
QUESTION:A train 440 meters long is running with a speed of 65 kmph. The time taken by it to cross a tunnel 180 meters long is?
options: A)40.338 sec B)41.338 sec C)42.338 sec D)40 sec E)34.338 sec
SOLUTION:D = 440 + 180 =620
S = 65 * 5/18 = 18.05556 mps
T = 620/18.05556 =34.33846
E #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%?
options: A)41 B)48 C)49 D)44 E)43
SOLUTION:96% ---- 72
144% ---- ?
96/144 * 72 = 48
Answer: B #### B
QUESTION:A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 10% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
options: A)$22.68 B)$23.94 C)$24 D)$25.20 E)$30
SOLUTION:A. #### A
QUESTION:How much is 80% of 60 is greater than 4/5 of 25?
options: A)15 B)28 C)16 D)12 E)73
SOLUTION:(80/100) * 60 – (4/5) * 25
48 - 20 = 28
Answer: B #### B
QUESTION:Jenna rode her bike to school at 5 kph, but rode home at 15 kph. What was her average speed traveling to and from school?
options: A)5 kph B)7 kph C)10 kph D)13 kph E)15 kph
SOLUTION:(5 kph +15 kph)/2 =10 kph
Correct answer is: C #### C
QUESTION:A shopkeeper sold an article for 240 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’?
options: A)25% B)50% C)23% D)28% E)None of these
SOLUTION:Cost price = 240×100/120= 200
S.P. at no discount = 240×100/80 = 300
∴ % profit = 100×100/200 = 50 %
Answer B #### B
QUESTION:4, 6, 12, 14, 28, 30, ?
options: A)32 B)64 C)62 D)60 E)52
SOLUTION:The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60
Answer : D. #### D
QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
options: A)20 B)15 C)25 D)18 E)12
SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
ANSWER B #### B
QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm
SOLUTION:33 + 43 + 53 = a3 => a = 6
ANSWER:D #### D
QUESTION:During a certain two-week period, 75 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 2/3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
options: A)5 A B)10 A C)15 A D)18 A E)25 A
SOLUTION:Movies: 75 % comedies. 25 % remaining genre.
Now in this 25 %, there are only 2 categories. Action movies and Drama Movies.
If Action = x; Drama movies = 2x/3. Total 5x/3.
5x/3 = 25; x = 15
Action movies: 15 %
Drama movies: 10 %
we can say that out of 100 z,:
comedies: 75 z
action: 15 z
drama: 10 z
Now action movies were A
This means:
A = 15 z.
z = A/ 15
Comedies: 75 z = 75 * (A/15)
5 A
A is the answer. #### A
QUESTION:What percent is 2 gm of 1 kg?
options: A)0.5 % B)0.2% C)1.5% D)2% E)3%
SOLUTION:1 kg = 1000 gm
2/1000 × 100 = 200/1000
=1/5 = 0.2 %
B) #### B
QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is
options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above
SOLUTION:Let distance be D
10 = D/4 + D/6 Answer : D #### D
QUESTION:If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x?
I. 1/2x
II. -5/x
III. 4/x
options: A)II B)II and III C)I &II D)III E)IV
SOLUTION:x2y2 - xy = 20
x2y2-xy-20 = 0
(xy-4)(xy+5)=0
xy = 4 or xy=-5
y = 4/x or y = -5/x
II and III only
B #### B
QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
options: A)3999 B)7799 C)2500 D)2772 E)2912
SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500.Answer: C #### C
QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten?
options: A)15 B)18 C)21 D)23 E)29
SOLUTION:There are two conditions:
1. Angel got at least one score of each of 1, 2, 3, and 4.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18.
Answer: B. #### B
QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually?
options: A)4.5 B)3.5 C)3 D)2 E)1
SOLUTION:We can form equations as following:
Initial amount = P, Total amount after interest = T, Interest per year = I
T = P+I
Given T1 = P+2I = 1400
T2 = P+ 5I = 2000
From this we get, P = 1000I = 200 $
Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually)
consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$.
To get a 440 $ compound interest the duration have to be > 1 year and < 3 years.
Only option fitting : Option D. #### D
QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale?
options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these
SOLUTION:Let the original price be x and sale be of y units.
Then, the revenue collected initially = x × y
Now, new price = 0.8x, new sale = 1.8y
Then, new revenue collected = 1.44xy
% increase in revenue = 0.44xy/xy×100
= 44% increase
Answer A #### A
QUESTION:There are 8 people and 5 chairs. In how many different ways people can occupy the chairs?
options: A)1640 B)1650 C)1660 D)1670 E)1680
SOLUTION:number of ways = 8*7*6*5 = 1680
Answer is E #### E
QUESTION:If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
options: A)4 B)8 C)12 D)9 E)18
SOLUTION:Let length of rectangle = L
6^2 = L*4
=> L = 36/4 = 9
Answer D #### D
QUESTION:The salary of a person was reduced by 20%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
options: A)50% B)32% C)25% D)43% E)29%
SOLUTION:Let the original salary be $100
New salary = $80
Increase on 80 = 20
increase on 100 = 20/80 *100 = 25%
Answer is C #### C
QUESTION:Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm.
options: A)221 cm2 B)211 cm2 C)231 cm2 D)236 cm2 E)241 cm2
SOLUTION:Given: length = 17 cm, breadth = 13 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (17 + 13) cm
= 2 × 30 cm
= 60 cm
We know that the area of rectangle = length × breadth
= (17 × 13) cm22
= 221 cm2 ANSWER :A #### A
QUESTION:A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
options: A)675 B)680 C)685 D)690 E)695
SOLUTION:Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec.
Length of the train = 75 * 9 = 675 m.
Answer: Option A #### A
QUESTION:A sum of money when distributed among friends is in the ratio of 3:4:5, if the amount is the larger 3digit number divisible by 24, what is the share of 3rd person?
options: A)400 B)410 C)420 D)430 E)440
SOLUTION:Largest 3 digit number divisible by 24= 984
So their shares are (984*3/12=246) , (984*4/12=328) , (984*5/12=410)
ANSWER:B #### B
QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23?
options: A)4 B)3 C)2 D)1 E)0
SOLUTION:Explanation :
1056 ÷ 23 = 45 with remainder = 21
Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be
divisible by 23. Answer : Option C #### C
QUESTION:850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
options: A)a) 162 B)b) 138 C)c) 60 D)d) 17 E)e) 12
SOLUTION:Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 850 = 17
Answer: D #### D
QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840
SOLUTION:11+6=17%, therefore 17/100*6000= 1020, now add 1020 + 580= 1600. (B) #### B
QUESTION:City X has a population 5 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
options: A)1:8 B)1:4 C)2:1 D)4:1 E)10:1
SOLUTION:x= 5y, y= 2*z
X : Y , Y : Z
5 : 1 , 2 : 1
10 : 2 , 2 : 1
So, X : Z = 10 : 1
(E) #### E
QUESTION:On a two-dimensional coordinate plane, the line s = x^2 - x^3 touches the x-axis in how many places?
options: A) 0 B) 1 C) 2 D) 3 E) 4
SOLUTION:Apparently it's s = x^2 - x^3 instead of s = x^2 - s^3.
In this case: the x-intercept is the value(s) of x for s = 0.
0 = x^2 - x^3;
0 = x^2(1 - x);
x = 0 or x = 1.
Answer: C. #### C
QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons?
options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20
SOLUTION:5p3 =5 x4= 20
Option 'E' #### E
QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
options: A)6 B)5 C)8 D)9 E)4
SOLUTION:S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8.Answer: C #### C
QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
options: A)10 B)12 C)15 D)20 E)25
SOLUTION:Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
ANSWER:B #### B
QUESTION:A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?
options: A)21% B)25% C)69% D)31% E)12%
SOLUTION:Let the price be 100.
The price becomes 140 after a 40% markup.
Now a discount of 20% on 140.
Profit=112-100
12%
answer E #### E
QUESTION:If x^2+(1/x^2)=7, x^4+(1/x^4)=?
options: A)10 B)11 C)12 D)14 E)47
SOLUTION:-> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47.
Thus, the answer is E. #### E
QUESTION:Which of the following is a pair of co–primes?
options: A)(16, 62) B)(18, 25) C)(21, 35) D)(23, 92) E)none
SOLUTION:Solution
H.C.F. of 18 and 25 is 1. So, they are co-primes.
Answer B #### B
QUESTION:What inequality represents the condition 1<x<13?
options: A)|x|<3 B)|x+5|<4 C)|x-7|<6 D)|-5+x|<4 E)|3+x|<5
SOLUTION:1<x<13 represents segment with
length: 13-1 = 12
center: (13+1)/2 = 7
For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer C) #### C
QUESTION:Which of the following is non-negative number?
options: A)(a-0.9)(a-1) B)(a+1)(a-1) C)(a+0.9)(a+1) D)(a-0.6)(a-0.6) E)a(a+1)
SOLUTION:5-sec approach:
D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative.
Answer: D. #### D
QUESTION:I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price?
options: A)$2000 B)$2500 C)$2400 D)$3120 E)$1540
SOLUTION:115% of cost - 110% of cost = $120
5% of cost = $120
cost = 120*100/5 = $2400
Answer is C #### C
QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5
SOLUTION:We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.
# of different approximations are possible.
Approach #1:
2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);
2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107
Answer: C.
Approach #2:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107.
Answer: C. #### C
QUESTION:How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
options: A)20 B)40 C)80 D)140 E)60
SOLUTION:Explanation:
The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
Answer:E #### E
QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her
options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger
SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1997 has to be the ring finger
Answer is (D) #### D
QUESTION:Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 4 = f(3x – 6)
options: A)3 B)4 C)6 D)7 E)13
SOLUTION:Answer = A = 3
f(x) = 3x – 5
2*[f(x)] – 4 = f(3x – 6)
2(3x-5) -4 = 3 (3x-6) - 5
6x - 14 = 9x - 23
x = 3 #### A
QUESTION:Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together?
options: A)6 B)7 C)7.5 D)8 E)9
SOLUTION:Each day, Molly can do 1/15 of the task.
Each day, Sandy can do 1/10 of the task.
Each day, they can do 1/15 + 1/10 = 1/6 of the task.
The task will be completed in 6 days.
The answer is A. #### A
QUESTION:A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income?
options: A)Rs.900 B)Rs.800 C)Rs.500 D)Rs.1000 E)Rs.1200
SOLUTION:X * 4/5 * 80/100 = 576
X = 14400/16
X = 900
ANSWER:A #### A
QUESTION:A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is?
options: A)72 kmph B)88 kmph C)54 kmph D)18 kmph E)19 kmph
SOLUTION:S = 120/6 * 18/5
= 72 kmph
Answer: A #### A
QUESTION:For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?
options: A)None B)One C)Two D)Three E)Four
SOLUTION:$ is basically a factorial of a number.
So, we are asked to find the number of primes between 7!+2 and 7!+10, inclusive.
From each number 7!+k were 2≤k≤102≤k≤10 we can factor out k, thus there are no pries in the given range.
For example:
7!+2=2(3*4*5*6*7+1) --> a multiple of 2, thus not a prime;
7!+3=3(2*4*5*6*7+1) --> a multiple of 3, thus not a prime;
...
7!+10=10(3*4*6*7+1) --> a multiple of 10, thus not a prime.
Answer: A. #### A
QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 15 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
options: A)25 pounds B)46 pounds C)150 pounds D)100 pounds E)146 pounds
SOLUTION:Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*15 --> x = 150.
Answer: C. #### C
QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him?
options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7
SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E
QUESTION:A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
options: A)621 B)276 C)236 D)600 E)211
SOLUTION:Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer: D #### D
QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n?
options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years
SOLUTION:Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $700.
Therefore, the Simple Interest earned = 700 - 100 = $600.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 600 = (100 * n * 8) / 100
Or 8n = 600
Or n = 75 years.
correct choice is (E) #### E
QUESTION:What is the area of a square with perimeter 8P ?
options: A) 16p^2 B) 4P^2 C) P^2/4 D) P/16 E) P^2/16
SOLUTION:Each side is 2p
A = (2p)^2 = 4(p^2)
Answer B #### B
QUESTION:In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?
options: A)2 people B)6 C)14 D)16 E)24
SOLUTION:FIRST OFFUnderstand what you are trying to find - In this case, you are trying to find how many people rank Vanilla first. For someone to rank Vanilla first, they have to rank them before Chocolate or Strawberry. This should be the very first hint that the correct answer cannot be bigger than 1/10 * 60 = 6.
So if you are time pressured on the real test, at least you narrowed down the selections to two choices - not bad. But what now?
Solve the easier problem. From 60 people, we are already told that 3/5 of them rank Vanilla last, leaving us with 2/5 of the people not ranking vanilla last - 24 people. So what are those combinations that vanilla are not last?
A) C, V, S
B) S, V, C
C) C, S, V (vanilla first)
D) S, C, V (vanilla first)
What are we ultimately hunting for here? The number of people that rank vanilla first:C+D
Now let's represent the given info into three equations
1) A+B+C+D = 24(2/5 of the people do not rank vanilla last)
2) A+C+D = 6(1/10 rank vanilla before chocolate)
3) B+C+D = 20(1/3 rank vanilla before strawberry)
Subtract equation 1 from 2, leaving us with
B = 24 - 6 = 18
Sub in B into equation 3 and solve for C+D
18 + C + D = 20
C+D = 20 - 18 = 2
There you go! 2 people out of the 60 ranked Vanilla as first A #### A
QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is:
options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2
SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2
= 134 m2.
answer :E #### E
QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y
SOLUTION:The answer is B.
She runs x yards in 10x/y seconds =10x/60y minutes. #### B
QUESTION:Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 550. The income of the deceased was?
options: A)Rs. 692.80 B)Rs. 820 C)Rs. 990 D)Rs. 1385 E)None
SOLUTION:Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 735 x 4 - 550 x 3 Rs.
= 1290 Rs.
Correct Option: E #### E
QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:Solution
Radius = Area / Semi perimeter
= [Area x 2 / Area]
= 2.
Answer B #### B
QUESTION:Which of the following fractions is the largest?
options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6
SOLUTION:L.C.M of 8, 16, 40 and 80 = 80.
7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80
Since, 70/80 > 63/80 > 65/80 > 62/80,
So, 7/8 > 63/80 > 13/16 > 31/40
So, 7/8 is the largest.
Answer: A #### A
QUESTION:The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
options: A)10º B)75º C)90º D)130º E)180º
SOLUTION:Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º.
Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º.
Required angle = (130 - 120)º = 10º.
Answer A #### A
QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded?
options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these
SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :-
letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..)
Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get
IDAATRE
ANSWER:D #### D
QUESTION:If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses?
options: A)1/8 B)1/3 C)1/4 D)1/2 E)1
SOLUTION:P(THH) = 1/2*1/2*1/2=1/8
The answer is A. #### A
QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3
SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D #### D
QUESTION:The present population of a town is 240. Population increase rate is 10% p.a. Find the population of town after 1 years?
options: A)100 B)120 C)200 D)220 E)264
SOLUTION:P = 240
R = 10%
Required population of town = P*(1 + R/100)^T
= 240*(1 + 10/100)
= 240*(11/10)
= 264
Answer is E #### E
QUESTION:How many diagonals does a 62-sided convex polygon have?
options: A)1829 B)2356 C)3458 D)3843 E)4820
SOLUTION:A 62-sided convex polygon has 62 vertices.
If we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829.
The answer is A. #### A
QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins
SOLUTION:The pool was 1/5 full initially.
In 6/5 hrs, it was filled to 8/9 of its capacity.
Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled.
So, 6/5 hrs = 8/9 - 1/5 = 31/45
Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins.
Hence D #### D
QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie?
options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9
SOLUTION:There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9
Answer: E #### E
QUESTION:A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen?
options: A)119 B)1,200 C)3,240 D)3,600 E)14,400
SOLUTION:To meet the conditions we can have only 2 cases:
2 officers and 3 civilians: C25∗C39=840
3 officers and 2 civilians: C35∗C29=360
Total: 840+360=1,200.
Answer: B. #### B
<<<Examples ends
QUESTION:If 5^10 x 2^10 = 10^n what is the value of n?
options: A)16 B)14 C)12 D)10 E)18
SOLUTION:5^10*2^10 = 10^n
or 10^10 =10^n
n=10
D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:power windows: 60%
anti-lock brakes: 25%
CD player: 45%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
options: A)25 B)8 C)11 D)3 E)0
SOLUTION:Answer: B
Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.
If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation:
45=15+22+x
x=8, choice B. #### B
QUESTION:P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
options: A)8/15 B)7/15 C)6/15 D)5/15 E)4/15
SOLUTION:Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
Answer is A. #### A
QUESTION:On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1?
options: A) 8 B) 12 C) 24 D) 32 E) 36
SOLUTION:Jan 1 = C
Feb 1 = C - 3
March 1 = C - 6
April 1 = C - 9
May 1 = C - 12
June 1 = C - 15
July 1 = C - 18
Aug 1 = C - 21
Sept 1 = C - 24
Difference between stock on September 1 than were in stock on January 1 will be -
C - ( C - 24 )= 24
Hence answer will be (C) #### C
QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed.
options: A)32 B)15 C)18 D)20 E)25
SOLUTION:Relative speed = (420/18)m/s = (420/18)*(18/5) = 84 kmph
speed of goods train = 84-64 = 20 kmph
Answer is D #### D
QUESTION:The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is ?
options: A)96 litres B)98 litres C)100 litres D)102 litres E)None
SOLUTION:Answer
Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12
Average = ( 110 x 7 + 86 x 5 ) / 12
=(1200 / 12 = 100 liters
Correct Option: C #### C
QUESTION:If one cat eats 1.5 rats in 1.5 days, then in howmany days 3 cats will eat 3 rats??
options: A)1 Day B)2 Days C)3 Days D)4 Days E)5 Days
SOLUTION:1Cat ------ 3/2 Rat --------- 3/2 Days
1 Cat ------(3/2)*2 Rat -----(3/2)*2 Days (Rat doubled, days doubled)
1*3 Cat----- 3 Rat -----------3/3=1 Day (Cat*3 , Same rat , Days/3 )
ANSWER:A #### A
QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
options: A)4 B)8 C)6 D)2 E)1
SOLUTION:Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer:A #### A
QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have?
options: A)9 B)12 C)18 D)28 E)36
SOLUTION:Lets take an example: find the number of factors of 100
try to represent 100 in least possible prime numbers
100= 2^2 * 5^2=p^a*q^b
no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9
similarly find the number of factors of p^3 * q^6--->a=3,b=6
(3+1)(6+1)=28 Ans D. #### D
QUESTION:One woman and one man can build a wall together in four hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them eight hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
options: A)5/7 B)1 C)10/7 D)12/7 E)24/7
SOLUTION:Solution:Let work done by man, women and girl per hour be m,w,g respectively.
Then, m+w = 1/4-->(1) , w + 2g = 1/4-->(2) and m + g =1/8-->(3).
No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g
From (1) and (2), m=2g and from (3) g=1/24,m=1/12 and w=1/6.
So, n = 1/(7/24) = 24/7
Option, E #### E
QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling?
options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr
SOLUTION:Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*50 = 2500m = 2.5km
Speed = 60*2.5=150km/hr
Answer is D #### D
QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n?
options: A)10 B)12 C)16 D)22 E)24
SOLUTION:The average of the numbers in set S is 10.
If we increase the mean by 10%, the new mean is 11.
Thus, on average, 5 numbers increase by 1.
Therefore n = 11+5 = 16
The answer is C. #### C
QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow?
options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt
SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10%
So 8100+15100⋅x+10100⋅(8100−x)=9100
Therefore 8100+320x+110(8100−x)=9100
120x=190
x=3800
Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres
correct answer is D)4370 lt #### D
QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
options: A)180 B)128 C)276 D)297 E)236
SOLUTION:Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer:A #### A
QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle?
options: A)16 B)25 C)33 D)46 E)58
SOLUTION:The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*9 + 2*9 which is about 46.
The answer is D. #### D
QUESTION:If the probability W of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?
options: A)8/125 B)2/25 C)5/16 D)8/25 E)3/4
SOLUTION:5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
W= 5/16
Answer - C #### C
QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him?
options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7
SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E
QUESTION:The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams T?
options: A)T=16 B)T=32 C)T=64 D)128 E)512
SOLUTION:Weight directly proportional to 4 pi r^2
Now, 4pi is constant, so, weight is directly proportional to r^2.
When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8;
(0.15)^2 * 4 proportional to 8*4, solving further
(0.15)^2 * 2 ^2 = (0.15*2)^2 = 0.3 ^ 2; so answer = 32 (B) #### B
QUESTION:The ratio of cats to dogs to birds to fish is 3:4:5:6. There are no other types of animals in the pet store. which of the following cannot be the total number of animals in the store?
options: A)36 B)54 C)72 D)90 E)101
SOLUTION:The parts add up to 3 + 4 + 5 + 6 = 18, so we know that any possible number of total answers must be a multiple of 18. All five answer choices are multiples of 18:
(A) 36 = 18*2
(B) 54 = 18*3
(C) 72 = 18*4
(D) 90 = 18*5
(E) 101 = not a multiple of 18
ans is E #### E
QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 14 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
options: A)13 B)13.5 C)14 D)14.5 E)15
SOLUTION:Ans is E
Given d_ab = 2*d_bc
let d_ab = d and d_bc = x so d=2x
for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time) #### E
QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min
SOLUTION:A
20 hours 30 min
1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours #### A
QUESTION:Which of the following equations has a root in common with x^2−3x+2=0 ?
options: A)x^2-2x+1=0 B)x^2-2x-1=0 C)x^2-x+1=0 D)x^2-3x+3=0 E)x^2-7x=0
SOLUTION:If we carefully look at the given equation we can arrange it in the following manner:
(x-1)(x-2)= 0
so the two roots are 1 and 2.
Now put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 1: we get 0. This is the equation.
We are lucky. No need to check other options.
A is the answer. #### A
QUESTION:The H.C.F. of two numbers is 59 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is:
options: A)678 B)944 C)456 D)323 E)899
SOLUTION:: Explanation:
Clearly, the numbers are (59 x 13) and (59 x 16).
{\color{Blue} \therefore } Larger number = (59 x 16) = 944.
Answer: B)944 #### B
QUESTION:A man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water?
options: A)11 B)77 C)30 D)88 E)35
SOLUTION:US = 25
DS = 45
M = (45 + 25)/2 = 35
Answer:E #### E
QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142
options: A)23 B)25 C)46 D)49 E)50
SOLUTION:(C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 . #### C
QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was
options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000
SOLUTION:A+B=20000
total profit=5000
5000-2000=3000
3000;2000=3:2
then 3*20000/5=12000
ANSWER:E #### E
QUESTION:A store reported total sales of $400 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
options: A)2% B)17% C)25% D)65% E)83%
SOLUTION:New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 400 million
February sales last year = 320 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 400 million and the old value = 320 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(400 – 320)/320] x 100
= 25%.
The answer is C. #### C
QUESTION:A small college reduced its faculty by approximately 15 percent to 195 professors. What was the original number of faculty members?
options: A)182 B)208 C)224 D)229 E)302
SOLUTION:If x is the original number of faculty members, then after 15% reduction in faculty members number is .85x
but we are given .85x = 195
x = 229
So the original number of faculty members is 229
Correct Answer - D #### D
QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm?
options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km
SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM.
It travels at 500 kmph.
Hence, the plane flying north would have covered 1000 kms from the city at 2 PM.
The plane flying east would have traveled for 1.5 hours at 2 PM.
It travels at 400 kmph.
Hence, the plane flying east would have covered 1.5*400 = 600 kms from the city at 2 PM.
The two planes are flying at right angles to each other.
The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes.
Hence, distance = 1000square + 200 square = 1166 km
The nearest 100 km distance between the two planes = 1200 kms.
Answer D #### D
QUESTION:16, 23, 19, 19, 22, 15, 25, ?
What number should replace the question mark?
options: A)13 B)11 C)16 D)18 E)19
SOLUTION:B
11
There are two alternate sequences: +3 and –4; #### B
QUESTION:One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ?
options: A)Rs. 130,000 B)Rs. 150,000 C)Rs. 160,000 D)Rs. 140,000 E)None
SOLUTION:EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then,
1/3x=1/2(350000-x)
=> x/3 + x/2 = 175000
=> 5x/6 = 175000
=> x= 175000 x 6 /5= 210000
Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000
Answer D #### D
QUESTION:A sequence contains y numbers of alternating positive and negative numbers, If the first number is postive and y is an even number, how many negative numbers are in it?
options: A)(y+1)/2 B)(y-1)/2 C)y/(2+1) D)y/(2-1) E)y/2
SOLUTION:Lets put values for y, say y=8 since it's even
and first number is positive so sequence will be {pos,neg,pos,neg,pos,neg,pos,neg} we can see that it has 4 negative terms
so putting y=8 in the options,
option E = y/2 => 8/2 = 4 , the number of negative integers
So, E is the answer #### E
QUESTION:A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?
options: A)22 B)23 C)25 D)35 E)30
SOLUTION:Explanation:
Clearly, we have :
B-3 = E ...(i)
B + 3 = D ...(ii)
A+B = D + E+10 ...(iii)
B = C + 2 ...(iv)
A+B + C + D + E= 133 ...(v)
From (i) and (ii), we have : 2 B = D + E ...(vi)
From (iii) and (vi), we have : A = B + 10 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(B + 10) + B + (B - 2) + 2B = 133 => 5B = 125=> B = 25.
ANSWER IS C #### C
QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours.
Working together how long will it take both pipes to fill the tank ?
options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes.
SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour.
Pipe B has a rate of 400 liters per hour.
400 + 600 (A+B) = Together they have a rate of 1000 liters per hour.
1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes
Answer -E #### E
QUESTION:What is the different between the place value and face value of 6 in the numeral 5468?
options: A)45 B)54 C)60 D)36 E)44
SOLUTION:place value of 6 = 6 * 10 = 60
face value of 6 = 6
60 - 6 = 54
Answer is B #### B
QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre?
options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6
SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8 Ratio of water and milk = 4 : 8 = 1 : 2
Answer:B #### B
QUESTION:The mean of (54,825)^2 and (54,827)^2 =
options: A)(54,821)^2 B)(54,821.5)^2 C)(54,820.5)^2 D)(54,826)^2 + 1 E)(54,821)^2 – 1
SOLUTION:54825^2 = (54826-1)^2 = 54826^2 + 1^2 - 2*54826*1
54827^2 = (54826+1)^2 = 54826^2 +1^2 + 2*54826*1
Taking the average of above 2 , we get (54826)^2 +1
hence the answer is D #### D
QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer?
options: A)55 B)25 C)85 D)45 E)35
SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer.
Therefore 0+1+3+4+5+6+7+9=35
Answer is E #### E
QUESTION:Find the middle one when The sum of three consecutive even numbers is 36?
options: A)10 B)12 C)15 D)16 E)20
SOLUTION:3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B #### B
QUESTION:P and Q entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by:
options: A)Rs.2400 B)Rs.3000 C)Rs.3600 D)Rs.4800 E)Rs.3800
SOLUTION:A : B : C = (16000 x 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)
= 147 : 189 : 126 = 7 : 9 : 6.
Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22
= Rs.3600
ANSWER:C #### C
QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals?
options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6
SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15
ANSWER:D #### D
QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
options: A)11 B)77 C)12 D)99 E)887
SOLUTION:x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C #### C
QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches
were made?
options: A)15 B)30 C)38 D)42 E)48
SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts
and we should calculate how many sandwiches holds 1 part:
120 / 20 = 6 sandwiches in one part
For bologna we have 7 parts so:
5* 6 = 30
Answer is B #### B
QUESTION:number of ways by which 4digit no made where aless than b,bless than c,c less than d where all lies between 1 to 9
options: A)1290 B)1296 C)1380 D)1480 E)1580
SOLUTION:we have to make 4 digit number
in which the format is d> c > b > a
__ __ __ __
1st position can be filled by 6 digits(9, 8, 7, 6, 5, 4)
2nd position can be filled by 6 digits(8, 7, 6, 5, 4, 3)
3rd position can be filled by 6 digits(7, 6, 5, 4, 3, 2)
4th position can be filled by 6 digits(6, 5, 4, 3, 2, 1)
hence every place can be filled by 6 digits,
6* 6* 6* 6 = 1296
ANSWER:B #### B
QUESTION:I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there?
options: A)12 B)44 C)56 D)120 E)200
SOLUTION:6C3*4C2
=120=D #### D
QUESTION:A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ?
options: A)7.5km/hr B)3.5km/hr C)9km/hr D)4km/hr E)5km/hr
SOLUTION:given upstream(u) =5km/hr
down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C) #### C
QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
options: A)Rs. 1(2/9) B)Rs. 2(2/9) C)Rs. 2(1/9) D)Rs. 4(2/9) E)Rs. 3(1/9)
SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B #### B
QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with two children, what is the probability that all the children are of the same gender?
options: A)1/2 B)1/16 C)1/9 D)1/4 E)1/25
SOLUTION:There are two cases. All boys and all girls.
case 1. all boys.
1/2*1/2= 1/4
case 2 .all girls.
1/2*1/2=1/4
We will add the cases to get 1/2 #### A
QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true.
options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7
SOLUTION:Since all the answers include S4, let's start from there.
S4=S2^2-S3
S3=S1^2-S2
Substituting S3 into the first equation we get:
S4=S2^2-(S1^2-S2)
Since S2=1
S4=1-(S1^2-1)
S4=2-S1^2
We need S1^2 in order to calculate S4.
E) provides S1 and from there we can calculate S4:
S4=2-(-3)^2
S4=-7
Correct.
As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.
For example:
If S4=-7 then S1=3 :
if we substitute S4 with - 7 we get:
-7=2-S1^2
S1^2=9
now S1 can be +/-3 !!
E #### E
QUESTION:There are 8 magazines lying on a table; 4 are movie magazines and the other 4 are education magzines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the movie magazine will be selected?
options: A)9/14 B)11/14 C)13/14 D)1/14 E)3/14
SOLUTION:1- (4c3/8c3) = 13/14
Answer : C #### C
QUESTION:The diameter of a garden roller is 1.4 m and it is 4 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7)
options: A)80 m2 B)84 m2 C)88 m2 D)86 m2 E)None of these
SOLUTION:Required area covered in 5 revolutions
= 5 × 2Ï€rh = 5 × 2 × 22â„7 × 0.7 × 4 = 88 m2
Answer C #### C
QUESTION:A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
options: A)30 B)60 C)75 D)90 E)105
SOLUTION:Answer : A
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 160
16x = 160
x = 10.
Hence, total number of notes = 3x = 30. #### A
QUESTION:A can give B 70 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
options: A)139.78 B)139.13 C)139.22 D)111.0 E)111.12
SOLUTION:A runs 1000 m while B runs 930 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/930
= 860.21 m.
B can give C = 1000 - 860.21
=139.78m.
Answer:A #### A
QUESTION:A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
options: A)15 kmph B)36 kmph C)21 kmph D)17 kmph E)19 kmph
SOLUTION:Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph.
Ans: B #### B
QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25%
SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D
QUESTION:The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
options: A)4329 B)2799 C)4312 D)2799 E)2712
SOLUTION:Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer: C #### C
QUESTION:There are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
options: A)120. B)132. C)141 D)154. E)166.
SOLUTION:Let the foam generators capacity be -
A = 12 lit/hr
B = 12 lit/hr
C = 18 lit/hr
Total foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate 42 + 21 => 63 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 12 lit/hr
C = 18 lit/hr
Total foam generation in 2 hour will be 60 litres {2 (12+18)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 12 => 18 litres
So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C) #### C
QUESTION:Let B represent a set of four distinct prime numbers. If the sum of the numbers in B is even and x is a member of B, then what is the least possible value that x can be?
options: A)1 B)2 C)3 D)5 E)7
SOLUTION:We are told that B is a set of four distinct prime numbers, and the sum of the numbers in B is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of B must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number. #### C
QUESTION:The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
options: A)52 minutes B)45 minutes C)30 minutes D)48 minutes E)44 minutes
SOLUTION:Explanation:
Total time a student spends in college = 4 hours 20 minutes = 260 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (260 – 20)/5
= 48 minutes
ANSWER D #### D
QUESTION:The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer?
options: A)1500 B)1600 C)1750 D)1900 E)2000
SOLUTION:Let the price of basic computer be C and the price of the printer be P: C+P=$2,500.
The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750.
Plug this value in the first equation: C+750=$2,500 --> C=$1,750
Answer: C. #### C
QUESTION:A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work?
options: A)10 B)12 C)22 D)28 E)20
SOLUTION:A can do the work in 60/4 i.e., 15 days.
A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12
So A and B together can do the work in 12 days.
Answer: B #### B
QUESTION:Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
options: A)11 B)32 C)24 D)48 E)50
SOLUTION:The product of two integers is equal to the product of their LCM and GCF. Hence.
16 * N = 48 * 8
N = 48 * 8 / 16 = 24
correct answer C #### C
QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next?
options: A)3 B)3.3 C)3.5 D)3.6 E)None
SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4.
Answer: Option D #### D
QUESTION:1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10
what is....?
options: A)7 B)8 C)9 D)6 E)10
SOLUTION:Equation 28 + 8 + 92 = 10 can be derived from
twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10
Similarly for equation,
1 + 9 + 8
One (o) + nine (n) + eight (e) => one (1)
correct answer is E)10 #### E
QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu?
options: A)10 B)20 C)40 D)80 E)100
SOLUTION:Q=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C #### C
<<<Examples ends
QUESTION:A train is 360 meter long is running at a speed of 75 km/hour. In what time will it pass a bridge of 140 meter length?
options: A)87 B)69 C)40 D)72 E)24
SOLUTION:Speed = 75 Km/hr = 75*(5/18) m/sec = 125/6 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (6/125) = 24 seconds
Answer: E #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1200 employees, then the no. of female employees who are computer literate ?
options: A)504 B)674 C)672 D)960 E)None
SOLUTION:Solution: Total employees,
= 1200
Female employees, 60% of 1200.
= (60 *1200) /100 = 720.
Then male employees,
= 480
50 % of male are computer literate,
= 240 male computer literate.
62 % of total employees are computer literate,
= (62 *1200) /100 = 744 computer literate.
Thus, Female computer literate = 744 - 240
= 504.
Answer: Option A #### A
QUESTION:In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent W of her bushes have only yellow roses?
options: A)20 B)30 C)50 D)70 E)80
SOLUTION:let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so, W=0.8T+x=T
x=0.2T
so, 1.5x=0.3T
30% flowers are yellow flowers
OA B #### B
QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least?
options: A)John B)Susan C)Sam D)Mark E)Lynn
SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 160% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.6*J)=0.8*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John.
Answer: B. #### B
QUESTION:3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
options: A)45% B)48% C)57% D)59% E)61%
SOLUTION:Total number of votes polled = (5136 + 7636 + 11628) = 24400
So, Required percentage = 11628/24400 * 100 = 48%
B #### B
QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
options: A)8 years B)10 years C)12 years D)14 years E)15 years
SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C #### C
QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m?
options: A)1350 B)1357 C)2025 D)2052 E)2122
SOLUTION:Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 3 = Rs.2025
Answer:C #### C
QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)285 m B)240 m C)277 m D)765 m E)176 m
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/39 = 15 ==> x + 300 = 585 ==> x
= 285 m.
Answer: A #### A
QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race?
options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m
SOLUTION:C
111.12 m
X runs 1000 m while Y runs 900 m and Z runs 800 m.
The number of meters that Z runs when Y runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
Y can give Z = 1000 - 888.88 = 111.12 m. #### C
QUESTION:Twenty four men can do a work in 32 days. How many men are required to complete the work in 12 days?
options: A)32 B)10 C)64 D)40 E)60
SOLUTION:C
64
We have M1 D1 = M2 D2
So, 24 * 32 = M2 * 12 => M2 = 64.
Answer is C #### C
QUESTION:How many 5-digit positive integers exist the sum of whose digits are odd?
options: A)36000 B)38000 C)45000 D)90000 E)None
SOLUTION:Solution:
There are 9�104 = 90000, 5-digit positive integers.
Out of these 90000 positive integers, the sum of the digits of half of the numbers will add up to an odd number and the remaining half will add up to an even number.
Hence, there are 90000 /2= 45000, 5-digit positive integers whose sum add up to an odd number.
Answer: Option C #### C
QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is?
options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400
SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4
Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C
QUESTION:Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 70, the three numbers in order are?
options: A)60, 120, and 30 B)60, 30, and 120 C)30, 60, and 120 D)30, 120, and 60 E)120, 30, and 60
SOLUTION:Let the numbers be 2x, x and 4x
(2x + x + 4x)/3 = 70
7x/3 = 70
x = 30
The numbers in order are 60, 30, and 120
The answer is B. #### B
QUESTION:In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/6.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
options: A)25. B)24. C)23. D)20. E)16.
SOLUTION:We need to get some number which is less than 50 and exactly divisible by 6,5 and 10
Lets take LCM of three balls 6,5 and 10 = 30.
The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls.
The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls.
The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS.
Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls.
IMO option E is correct. #### E
QUESTION:Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
options: A) 22 hours B) 30 hours C) 44 hours D) 60 hours E) It cannot be determined from the information above.
SOLUTION:Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours.
Answer: C. #### C
QUESTION:Find the product of the localvalue and absolutevalue of 4 in 20468?
options: A)1000 B)1100 C)1200 D)1300 E)1600
SOLUTION:Local value of 4 = 4 x 100 = 400
Place value of 4 = 4
There fore = 4 x 400 = 1600
E #### E
QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3?
options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10
SOLUTION:arrangement = 5!/3!=20
Probability of getting all 3 balls=
3 from 5=5c3
1 from 3 red ball,1 green,1 yellow
(3c1*1c1*1c1)/5c3 =3/10
ANSWER:A #### A
QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the
rest at 5 kmph. Find the total distance.
options: A)4 km B)5 km C)6 km D)7 km E)8 km
SOLUTION:time=distance/speed
let total distance travelled be x in 84/60 hrs
2/3 rd of x travelled in 4 km/hr
1/3 rd of distance travelled in 5 km/hr
2x/(3*4)+x/(3*5)=84/60
x=6 km
ANSWER:C #### C
QUESTION:It will take 16 days for Mary to complete a certain task alone. She worked for 8 days before she was joined by her sister. both of them completed the remaining task in 2 and half days. if her sister had joined her when she started the task, how many days would it have taken?
options: A)6 B)8 C)2 D)5 E)4
SOLUTION:Explanation:
Mary and her sister complete half work in 2.5 days
=> they can complete whole work in 5 days
Answer: Option D #### D
QUESTION:In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate?
options: A)69 B)70 C)71 D)72 E)73
SOLUTION:number of ways = 2*3!*3! = 72
Answer is D #### D
QUESTION:A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
options: A)17% B)25% C)69% D)31% E)19%
SOLUTION:Let the price be 100.
The price becomes 130 after a 30% markup.
Now a discount of 10% on 130.
Profit=117-100
17%
answer A #### A
QUESTION:If a^2+b^2=177and ab=54 then find the value of a+b/a-b?
options: A)1 B)3 C)5 D)7 E)9
SOLUTION:(a+b)^2=a^2+b^2+2ab=117+2*24=225
a+b=15
(a-b)^2=a^2+b^2-2ab=117-2*54
a-b=3
a+b/a-b=15/3=5
Answer is C. #### C
QUESTION:A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share?
options: A)Rs.12 B)Rs.18 C)Rs.15 D)Rs.21 E)Rs.25
SOLUTION:Explanation :
Face value of each share = Rs.20
Dividend per share = 9% of 20 = 9×20/100=9/5
He needs to have an interest of 12% on his money
ie, Money Paid for a share 9×12/100=9/5
Money Paid for a share=9/5×100/12=15
ie, Market Value of the share = Rs.15
Answer : Option C #### C
QUESTION:The prices of tea and coffee per kg were the same in june. In August the price of coffee shot up by 20% and that of tea dropped by 20%. if in August , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?
options: A)45 B)50 C)40 D)35 E)30
SOLUTION:Let the price of tea and coffee be x per kg in June.
Price of tea in August = 1.2x
Price of coffee in August = 0.8x .
In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50
1.2x(1/2) + 0.8x(1/2) = 50
=> x =50
B #### B
QUESTION:If a > 0 and x is m percent of y, then, in terms of a, y is what percent of x?
options: A)a) 100a B)b) 1/100a C)c) 1/a D)d) 10/a E)e) 10,000/a
SOLUTION:x= a/100 * y
So y= 100/a * x
So y= (10000/a)/100 * x
E #### E
QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $18,000 to $28,000, by how much will the property tax increase?
options: A) $320 B) $800 C) $320 D) $600 E) $850
SOLUTION:Increase in house value = $28,000 - $18,000 =$10000
So, tax increase = 8% of$10000=$800
Answer: B #### B
QUESTION:5.005/4.004 =
options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25
SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25
The answer is E. #### E
QUESTION:For how many integers n is 1^n+2 = (n+2)^1?
options: A)0 B)1 C)2 D)None of these E)3
SOLUTION:If n=0
1^0+2 = (0+2)^1
1^2 = 1 ; 2^1 =2 not ok
If n=1
1^1+2 =1 ; (1+2)^1=3^1=3 not OK
So, Answer : D #### D
QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?
options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280
SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet.
The number of revolutions = distance/circumference = 5,280z/y.
Answer: A. #### A
QUESTION:Jackson invested $500,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
options: A)$115,384 B)$120,000 C)$121,072 D)$124,129 E)$130,000
SOLUTION:x be the amount invested in account P
0.12*x +(500000-x)*0.25=60,000
15000/.13=x
x=1500000/13=11...=$121,072
hence answer is C #### C
QUESTION:A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):
m------M---------------W
w
In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 3*15/60 =15/20 miles and the man walks the distance mM, which is 3*9/60 = 9/20 mile.
The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes.
Answer B. #### B
QUESTION:12 times a number gives 156. The number is
options: A)11 B)12 C)13 D)None E)Cannot be determined
SOLUTION:Explanation:
Let the number be 'N'
12×N=156⇒N=13
Correct Option: C #### C
QUESTION:Find the simple interest on Rs. 73,000 at 16 2/3% per year for 9 months.
options: A)7500 B)6500 C)8125 D)9125 E)None of them
SOLUTION:P = Rs.73000,R = 50/3% p.a and T = 9/12 years = 3/4years.
Simple Interest = (P*R*T)/100 = Rs.(73,000*(50/3)*(3/4)*(1/100))= Rs.9125
Answer is D. #### D
QUESTION:On return from a business trip Mr. Chidambaram was to be picked up from the railway station by
his coachman. Someone he managed a train connection earlier and thus arrived two hours too early.
Immediately on arrived he rang up home for the coach and was told that it had just left in order to be
exactly in time for the train by which he was scheduled to come. To save the time he started walking
homeward at 3kmph. On the way he met the coachman who brought him home an hour before
schedule. How far is the Mr. Chidambaram’s house from the railway station?
options: A)22 B)18 C)99 D)27 E)11
SOLUTION:Very good questions. Appeared in Puzzles book of Ravi Nirula.
Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am.
But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance.
So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km.
We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km.
Answer:B #### B
QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
options: A)4 B)16 C)25 D)36 E)100
SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number.
The answer is C. #### C
QUESTION:There are 9 people in the room. There are two pairs of siblings within that group. If we choose two people, what is the probability that they will not be siblings?
options: A)12/18 B)17/18 C)2/9 D)1/18 E)4/18
SOLUTION:we have XXXXXBBCC
We have to take into the account when we have XX, XB, XC
So 5/9*4/8 5/9*2/8 and 5/9*2/8 note we need to multiply these by 2 (except the first) b/c we can have BX and CX.
20+20+20 --> 60/72 --> 30/36 --> 15/18
then next is
BC 2/9*2/8 --> 4/72 2/36 1/18 --> multiply this by 2 b/c of CB
so 2/18+15/18 --> 17/18
ANSWER:B #### B
QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa?
options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71
SOLUTION:Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002
Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792
Hence,Probability=792/2002=36/91
Answer: Option B #### B
QUESTION:A man had to make 3 trips to the store because he kept forgetting items his wife had requested. The store was 500 meters from his home. It took the man 45 minutes to complete the store run. What was the man's speed in kilometers per hour.
options: A)2 B)1.5 C)2.25 D)3 E)1.75
SOLUTION:The distance between the man's home and the store is 500 meters.
3 times means that the man made the 500 meter trip 6 times in total.
6 * 500 = 3000 meters or 3 km.
Since the man's total time was 45 min, we need to multiply 3000 by 3/4 or .075.
Correct answer is 2.25 km per hour #### C
QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period?
options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3
SOLUTION:600 dollars in 2 years means 300 dollars in 1 year.
To get 2400 dollars' it will take 8 years.
To get 2400 in 3 years, we need 8/3 times money.
Answer is E. #### E
QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740
SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All two
2. One symmetry and other two non
4. All the two letters can be arranged in 2 ways
( 11c2+ 11c1 * 15c2) *2
( 11*10/ 2 + 11 * 15 * 14 / 2 ) * 2
2420
IMO option D is the correct answer..
OA please...will correct if I missed anything..D #### D
QUESTION:There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ?
options: A)120ways B)220ways C)420ways D)720ways E)520ways
SOLUTION:By kept 3boys together(1) and arranging 4 girls with them
5! = 5*4*3*2*1 = 120ways. (i.e., 4+1 =5)
Possible arrangements of 3 boys in following ways
3! = 3*2*1 = 6ways
Now, arrange all with the boys together
120*6 = 720ways
ANSWER:D #### D
QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
options: A)10 m B)16 m C)245 m D)19 m E)235 m
SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30
= 25/2 => 2(140 + x) = 750 => x
= 235 m.
Answer: E #### E
QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
options: A)25 B)30 C)50 D)55 E)70
SOLUTION:I came up with (E) 70
Think of 100 people total:
From the first fact, 28 of these are women with fair hair.
From the second fact, these 20 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*28 equals the number of fair haired men, which is 42 men with fair hair.
Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women.
70%E #### E
QUESTION:If a is a positive integer, which of the following could NOT be the square of a?
options: A) 5,008,644 B) 5,004,169 C) 4,999,696 D) 4,995,225 E) 4,990,752
SOLUTION:A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E) #### E
QUESTION:A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 10% lemonade syrup?
options: A)1.5 B)1.75 C)2.14 D)2.34 E)2.64
SOLUTION:Let the total solution is 150 L with 80 L water70 L syrup.
To make 10% syrup solution, the result solution must have 135 L syrup and 15 L syrup.
Therefore we are taking 55 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
55 L syrup in 117.9 L solution
We started by multiplying 10
Now to get to the result we need to divide by 55 => amount of solution to be replaced with water = (117.9/55) = 2.14.
Correct option : C #### C
QUESTION:Express of the following as a fraction:
25%
options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them
SOLUTION:25% = 25/100= 1/4.
Answer is A. #### A
QUESTION:A 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
options: A)6%. B)7.5%. C)9.2%. D)10.5%. E)14%.
SOLUTION:Denominator:
340+10+3.2+6.8=360
Numerator:
340(1-.80-.06)+3.2
340(0.14)+3.2
47.6+3.2
50.8
Ratio:
50.8/360=0.14
Answer: E #### E
QUESTION:A coin is weighted so that the probability of heads on any flip is 0.2, while the probability of tails is 0.8. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?
options: A)(0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 B)(0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2 C)(0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2 D)(0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2
SOLUTION:Probability of Head, P(H) = 0.2
Probability of Tail, P(T) = 0.8
Tail will appear NO more than twice
i.e. favourable cases
2 Tails and 3 Heads, Probability = 5C2*(0.2)^3*(0.8)^2
1 Tail and 4 Heads, Probability = 5C1*(0.2)^4*(0.8)^2
0 Tail and 5 Heads, Probability = (0.2)^5
Required Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2
Answer: option A #### A
QUESTION:Which of the following CANNOT be the median of the 3 positive integers a, b, and c?
options: A)a B)c C)a+c D)(a+c)/2 E)(a+c)/3
SOLUTION:The median of a set with odd number of terms is justa middle term, so it's a, b or c. Eliminate A and B right away. Now, the median can also be (a+c)/2 and (a+c)/3 (for example: {1, 2, 3} and {1, 2, 5}).
But since a, b, and c are positive integers then it no way can be a+c . Why? Because a middle term (the median) cannot possibly be greater than two terms (a and c) in a set with 3 terms.
Answer: C. #### C
QUESTION:A ship sails 4 degrees north, then 14 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?
options: A)0 B)1 C)2 D)3 E)None of these
SOLUTION:Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 14 + 17 - 19 = -11
And x = 1.
Answer B #### B
QUESTION:The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
options: A)42.85 B)44 C)46 D)48 E)50
SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours.
Dan needs to take less than 3.5 hours for the trip.
Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour.
The answer is A. #### A
QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class?
options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm
SOLUTION:The total height was 45 cm too much.
The average height should be reduced by 45 cm/30 = 1.5 cm
The answer is B. #### B
QUESTION:What is the smallest positive integer x such that 108x is the cube of a positive integer?
options: A)2 B)4 C)8 D)10 E)7
SOLUTION:Given 108x is a perfect cube
so we will take 216 = 6*6*6
108x = 216
x = 216/108 = 2
correct option is A #### A
QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is:
options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these
SOLUTION:Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (45 x 2) = 90 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv)
Subtracting (i) from (iv), we get : B = 35.
B’s weight = 35 kg.
Answer: D #### D
QUESTION:In how many ways can the letters of the word REPORT be arranged?
options: A)1206 B)360 C)2520 D)3000 E)3478
SOLUTION:REPORT has 6 words, but R is repeated two times. Thus ways = 6! / 2! = 360 ways
B #### B
QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her
options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger
SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1996 has to be the ring finger
Answer is (D) #### D
QUESTION:At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.)
options: A)96 B)240 C)E=256 D)E=384 E)E=480
SOLUTION:Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E #### E
QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ?
options: A)87 B)95 C)99 D)100 E)103
SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.
Answer: C. #### C
QUESTION:The ratio 25:50 expressed as percent equals to
options: A)50 % B)85 % C)25 % D)75 % E)None of above
SOLUTION:Explanation:
Actually it means 25 is what percent of 50, which can be calculated as,
(25/50)*100 = 25 * 2 = 50
Answer: Option A #### A
QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
options: A)23 days B)16 days C)11 days D)24 days E)35 days
SOLUTION:D
24 days
2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days #### D
QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n?
options: A)-200 B)-130 C)-104 D)51 E)305
SOLUTION:2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:
-51 < c < 151
-51 < n < 151
-102 < c+n < 302.
Only option D is in this range.
Answer: D. #### D
QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4?
options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1
SOLUTION:Solving for y/x gives, 1/17 (C) #### C
QUESTION:The 323rd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
options: A)u B)v C)w D)y E)z
SOLUTION:a is one time, b,2 times so on...
so 323=n(n+1)/2..
0r n(n+1)= 646... now 25*26=650...24*25<646 so n= 25. and 25th alphabet is Y. ans D #### D
QUESTION:Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R?
options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5
SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C
QUESTION:Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
options: A)300 B)368 C)375 D)337 E)639
SOLUTION:A+B+C = 1200
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1200 => 300
Answer:A #### A
<<<Examples ends
QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
options: A)14years B)26 years C)17 years D)18 years E)22 years
SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 20) + 2 = 2(x + 2)
x + 22 = 2x + 4
x = 18.
answer :D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A boat goes 100 km downstream in 10 hours, and 80 km upstream in 20 hours. The speed of the stream is?
options: A)4km/h B)3km/h C)2km/h D)(1/2) km/h E)E)None
SOLUTION:100 --- 10 DS = 10
? ---- 1
80 ---- 20 US = 4
? ----- 1 S = (10 - 4)/2
= 3 kmph
ANSWER:B #### B
QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
options: A)1236 B)1345 C)1358 D)1321 E)1365
SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E #### E
QUESTION:In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 6 metres then what will be the area of the square so formed?
options: A)Cannot be determined B)2600 cm2 C)5184 cm2 D)3025 cm2 E)None of these
SOLUTION:Let the side of the square be x m.
∴ Perimeter of the square = 48 × 6 = 4x ∴ x = 72 m
∴ Area = (72)2 = 5184 m2
Answer C #### C
QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300
SOLUTION:Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 616
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 616
⇒ y[12/10 + 1] = 616
⇒ 22y/10 = 616
⇒ 22y = 6160
⇒ y = 6160/22 = 560/2 = Rs.280
B #### B
QUESTION:1/2+[(2/3*3/8)+4]-7/16=
options: A)29/16 B)19/16 C)69/16 D)9/13 E)0
SOLUTION:1/2+[(2/3*3/8)+4]-7/16=
1/2+[(1/4)+4]-7/16=
1/2+[17/4]-7/16=
8/16 + 68/16 - 7/16 = 69/16
C #### C
QUESTION:If log10 2 = 0.3010, the value of log10 80 is:
options: A)1.5252 B)1.903 C)3.9252 D)3.903 E)2.5252
SOLUTION:= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
ANSWER B #### B
QUESTION:Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
options: A)A)35 B)B)28 C)C)45 D)D)25 E)E)26
SOLUTION:Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Eight years ago, P was half of Q in age
=> 2(3x – 8) = (4x – 8)
=> 6x – 16 = 4x – 8
=> 2x = 8
=> x = 4
7x=7*4=28
Answer: Option B #### B
QUESTION:The ratio of the two natural numbers is 6 : 5. If a certain number is subtracted to both the numbers, the ratio becomes 5 : 4. If the larger number exceeds the smaller number by 5, find the number subtracted?
options: A)8 B)5 C)15 D)22 E)6
SOLUTION:Let the two numbers be 6x and 5x.
Let the numbers subtracted to both so that their ratio becomes 5 : 4 be k.
(6x - k) / (5x - k) = 5/4
=> 24x - 4k = 25x - 5k => k = x.
6x - 5x = 5 => x = 5
k = x = 5.
Answer:B #### B
QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n?
options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years
SOLUTION:Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $700.
Therefore, the Simple Interest earned = 700 - 100 = $600.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 600 = (100 * n * 8) / 100
Or 8n = 600
Or n = 75 years.
correct choice is (E) #### E
QUESTION:Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 3.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn?
options: A)1/3 B)1/30 C)1/42 D)2 E)30
SOLUTION:Pete covered 3.5*60=210 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/210=1/42.
Answer: C. #### C
QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is?
options: A)40m2 B)45m2 C)49m2 D)51m2 E)55m2
SOLUTION:39/360 * 22/7 * 12 * 12
= 49m2
Answer:C #### C
QUESTION:If w and t are positive integers, wt + w + t cannot be
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Let wt + t + w = x
Add 1 on both sides:
wt + t + w + 1 = x + 1
t(w + 1) + w + 1 = x + 1
(w + 1)(t + 1) = x + 1
Minimum value of (w + 1) = 2
Minimum value of (t + 1) = 2
Hence x + 1 cannot be prime
Substitute x from the given options: 6 + 1 = 7 --> prime --> wt + t + s cannot be 6
Answer: B #### B
QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:Solution
Start with 11 coins.
Sharon takes 3 coins from you: 11 - 3 = 8 coins.
Steven takes 4 coins from you: 8 - 4 = 4 coins.
So you have 4 at the end.
Correct answer : C #### C
QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.
options: A)124 B)241 C)394 D)421 E)842
SOLUTION:Ratio of a:b:c= 2:4:1
Two possible greatest single digit values for b are 8 and 4
if b is 8, then x= 482
if b is 4, then x= 241
difference= 482-241= 241
B is the answer #### B
QUESTION:In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y =
options: A)6 B)7 C)5 D)8 E)3
SOLUTION:Line k passes through the origin and has slope 1/7 means that its equation is y=1/7*x.
Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6.
Answer: A #### A
QUESTION:There are 3 people and 3 chairs. In how many different ways people can occupy the chairs?
options: A)6 B)15 C)24 D)36 E)120
SOLUTION:number of ways =3! = 6
Answer is A #### A
QUESTION:The average of two numbers is P. If one number is Q, then the other number is
options: A)2Q B)2P C)P - Q D)2P-Q E)None of these
SOLUTION:Explanation :
Let the other number be x,
According to the question,
=> ( x + Q ) / 2 = P.
=> x + Q = 2P.
=> x = 2P - Q.
Hence, the required number is 2P - Q.
Answer : D #### D
QUESTION:A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days B will the work get over?
options: A)60 B)70 C)B=75 D)B=80 E)100
SOLUTION:We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75
Ans: C (75 days) #### C
QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is :
options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7
SOLUTION:Explanation:
We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.
Now. .
Answer: B) 3 M^2 #### B
QUESTION:If C.P. of 28 books is equal to S.P of 30 books , then your gain or loss is ?
options: A)23 1/3 gain % B)30 10/23 loss % C)6.67 loss % D)30 1/3 loss % E)40 1/3 loss %
SOLUTION:Say the cost price of 28 books is $28 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 28$, hence the loss = ($30 - $28)/$30 = ~6.67%.
Answer: C. #### C
QUESTION:A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 7. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.
The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
options: A)7000 B)1000 C)1011 D)1101 E)1110
SOLUTION:The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 7*10*10*10=9*10^3
The difference = 10^4 - 7*10^3 = 10^3(10-7) = 7*10^3.
Answer: A.
Similar questions to practice:
Hope it helps. #### A
QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?
options: A)767 km B)975 km C)678 km D)900 km E)546 km
SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.
x/40 = (x + 100)/50
50x = 40x + 4000 => x = 400
So, distance between P and Q = (x + x + 100)km =900 km.
Answer: D #### D
QUESTION:If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x?
I. 1/2x
II. -5/x
III. 4/x
options: A)II B)II and III C)I &II D)III E)IV
SOLUTION:x2y2 - xy = 20
x2y2-xy-20 = 0
(xy-4)(xy+5)=0
xy = 4 or xy=-5
y = 4/x or y = -5/x
II and III only
B #### B
QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females?
options: A)16% B)45% C)32% D)40% E)28%
SOLUTION:answer b
male-employed - 64%
female-employed-19%
Total employed 64%
means total unemployed = 36%
therefore d and e are not correct because female unemployed has to be less than 36%
female-unemployed = 32% male unemployed = 4%
48% + 4% = 52%
16% + 32% = 48%
plug in a and b in place of 32% and the sum is not 100%
19/64 =28 E #### E
QUESTION:A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every three leaps of the hare, the jackal takes five leaps. Find the ratio of the speed of the hare to the speed of the jackal.
options: A)6:7 B)4:5 C)5:8 D)25:64 E)3:5
SOLUTION:The hare takes 3 leaps and the jackal takes 5 leaps.
1 hare leap = 4/3 jackal leaps
Thus the hare's 3 leaps = 3*(4/3) = 4 jackal leaps.
The ratio of their speeds is 4:5.
The answer is B. #### B
QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
options: A)38 B)41 C)30 D)31 E)29
SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: C #### C
QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58?
options: A)2784 B)2287 C)2977 D)2668 E)1298
SOLUTION:Let the side of the square plot be a ft.
a2 = 144=> a = 12
Length of the fence = Perimeter of the plot = 4a = 48 ft.
Cost of building the fence = 48 * 58 = Rs. 2784.
Answer:A #### A
QUESTION:The C.P of 20 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
options: A)10% B)20% C)30% D)40% E)50%
SOLUTION:20 CP = 12 SP
20 --- 8 CPgain
100 --- ? => 40%
Answer: D #### D
QUESTION:A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is
options: A)83.33 ml B)83.03 ml C)93.33 ml D)63.03 ml E)82.33 ml
SOLUTION:Explanation:
Profit (%) = 9.09 % = \inline \frac{1}{11}
Since the ratio of water and milk is 1 : 11,
Therefore the ratio of water is to mixture = 1:12
Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml]
Answer: A) 83.33 ml #### A
QUESTION:45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours?
options: A)50 B)55 C)60 D)65 E)70
SOLUTION:45 workers * 8 hours / 30 meters = x * 6 / 55
x = 110 total workers
110 - 45 = 65 new workers
The answer is D. #### D
QUESTION:The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books?
options: A)7 B)12 C)13 D)5 E)26
SOLUTION:Surface area of each shelf= 2ab + 2ac + 2bc
848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c
848 = 32 + 2c + 32c
816 = 34c
c = 24 in. (i.e. the length of each shelf)
Each book is 4 in thick
24/4 = 6 books per shelf
26/6 = 4.333=5 shelves
Answer is D #### D
QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct?
options: A)120 B)130 C)110 D)150 E)180
SOLUTION:let x be the correct answer and y be the wrong answer
so the total number of questions is (x+y)=150
=>4x-2y=480
=>6x=780
hence x=130
ANSWER:B #### B
QUESTION:simplify : 3x - 5 + 23x - 9
options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7)
SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9
= 26x - 14, = 2(13x - 7). correct answer : (B) #### B
QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
options: A)1350 B)2997 C)2087 D)2697 E)9824
SOLUTION:Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5
=> 675
675 * 2
= Rs.1350
Answer:A #### A
QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.)
Can somebody explain?
options: A)6720 B)7720 C)7820 D)7950 E)8120
SOLUTION:First ring can be worn in 4 ways (on any of the four fingers);
Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1);
Third ring can be worn in 6 ways (the same logic as for the second ring);
Fourth ring can be worn in 7 ways;
Fifth ring can be worn in 8 ways;
Total: 4*5*6*7*8=6720. ANS:A #### A
QUESTION:How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/6!?
options: A)2 B)3 C)5 D)6 E)9
SOLUTION:7! = 720
1/1000 < 1/720< 1/100
0.001 < 1/720 < 0.01
So 1/720 has 2 leading zeros
Answer: A #### A
QUESTION:What is the largest integer n such that 2^n is a factor of 20^8 ?
options: A)1 B)2 C)4 D)8 E)16
SOLUTION:20^8=(2^2∗5)^8=2^16 5^8 Therefore the largest integer n such that 2^n is a factor of 2^165^8 is 16.
Answer: E. #### E
QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D?
options: A) 1 B) 8 C) 19 D) 20 E) 27
SOLUTION:I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.
C #### C
QUESTION:A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
options: A)16 km B)87 km C)89 km D)67 km E)20 km
SOLUTION:Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 3.5
=> x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x
= 16 km.
Answer:A #### A
QUESTION:A shopkeeper cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 20% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.
options: A)20% B)32% C)23.365% D)22.109% E)2%
SOLUTION:Anyways, one can infer that he 'steals' 20% from suppliers and then charges 10% extra to customers
So basically 1.2 * 1.1 = 1.32
Given that 1 is start point, we get 32% more
Hence answer is B #### B
QUESTION:What is the difference between local value & face value of 9 in the numeral 65793?
options: A)8453 B)8956 C)8991 D)9890 E)10000
SOLUTION:(Local value of 9) - (Face value of 9)
= (9000 - 9) = 8991
C #### C
QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
options: A)4/8 B)9/2 C)7/6 D)9 E)2/21
SOLUTION:Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³Câ‚‚/¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²Câ‚‚/¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³Câ‚ * ²Câ‚)/¹âµCâ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: E #### E
QUESTION:14,24,54,34,44,56,53, ?
options: A)44 B)55 C)66 D)77 E)88
SOLUTION:14-24...dif -10
54-34..dif -20
44-56..dif-12
53-77...dif-24
ANSWER:D #### D
QUESTION:The product of all the prime numbers less than 25 is closest to which of the following powers of 10?
options: A)10^9 B)10^8 C)10^7 D)10^8 E)10^5
SOLUTION:Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19,23
=2.2 *10^8
D #### D
QUESTION:The contents of a certain box consist of 24 carrots and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be carrrots?
options: A) 24 B) 26 C) 30 D) 46 E) 50
SOLUTION:carrrots = (carrrots + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B. #### B
QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents?
options: A)24 B)18 C)32 D)16 E)20
SOLUTION:0.10(x)+0.35(20-x)=2.5
0.10x+7-0.35x=2.5
so x=18
ans is B #### B
QUESTION:There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?
options: A)36 B)77 C)88 D)99 E)22
SOLUTION:Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1)
Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get
=> 2r = 72 => r = 36.
Answer: A #### A
QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None
SOLUTION:Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1250 x 2/5) = Sterling 500.
Answer: Option C #### C
QUESTION:When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y?
options: A)560 B)616 C)672 D)728 E)784
SOLUTION:ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
W=8(2+3+4....+12)=616 #### B
QUESTION:8^100 is divisible by 17. Find the remainder?
options: A)8 B)12 C)16 D)18 E)20
SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 = (816)6×8417
Now this problem simply boils down to (1)6×8417 = 8417
84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.
C #### C
QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
options: A)4 B)6 C)8 D)9 E)1
SOLUTION:There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B #### B
QUESTION:The list price of a watch is 160. A retailer bought the same watch 122.40. He got two successive discounts one at 10% and the other at a rate which was not legible. What is the second discount rate?
options: A)12% B)14% C)15% D)18% E)None of these
SOLUTION:Retailer price = list price (1−d1/100)(1−d2/100)
⇒ 122.40 = 160(1−10/100)(1−d2/100)
⇒ 1−d2/100=122.40×100/160×90=0.85
⇒ d2 = (1 - 0.85) × 100 = 15%
Answer C #### C
QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere?
options: A) 6/π B) 9/π C) 6 D) 9 E) 12
SOLUTION:Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4*PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !! #### D
QUESTION:A monkey ascends a greased pole 12 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?
options: A)21st B)22nd C)23rd D)24th E)None of these
SOLUTION:In 2 minutes, he ascends = 1 metre
∴ 10 metres, he ascends in 20 minutes.
∴ He reaches the top in 21st minute.
Answer B #### B
QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct?
options: A)9 B)10 C)11 D)12 E)13
SOLUTION:let no. of right ques be x,
then no. of wrong ques will be= 26 - x
now, according to ques
8x - (26-x)5 = 0,
hence x=10...no. of right ques is 10
ANSWER:B #### B
QUESTION:A word is defined as a sequence of five dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed?
options: A)124 B)150 C)212 D)243 E)316
SOLUTION:3^5 = 243
The answer is D. #### D
QUESTION:The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?
options: A)55 B)44 C)66 D)60 E)12
SOLUTION:H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60.
Answer:D #### D
QUESTION:If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?
options: A)41 B)42 C)43 D)44 E)45
SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d.
The sum of A + B = (10c+d)+(10d+c)=11(c+d).
The only answer that is a multiple of 11 is 44.
The answer is D. #### D
QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic?
options: A)240 B)65 C)110 D)130 E)200
SOLUTION:Adult + Children = 200
Let, Children = y
then, Adult = y+20
i.e. y+(y+20) = 200
i.e. y = 900
i.e. Adult = 90+20 = 110
Adults include only Men and Women
i.e. Men + Women = 110
Let women, W = x
then Men, M = x+20
i.e. x+(x+20) = 2x+20 = 110
i.e. x = 45
i.e. Men, M = 45+20 = 65
Answer: Option B #### B
QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number?
options: A)10 B)60 C)30 D)40 E)50
SOLUTION:Explanation:
6:7
6x + 10 : 7x + 10 = 7 : 8
8[6x + 10] = 7[7x + 10]
48x + 80 = 49x + 70
49x - 48x = 80 - 70
x = 10
Then smallest number is = 6
6x = 60
Answer: Option B #### B
QUESTION:210 school students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
options: A)25 B)40 C)50 D)60 E)75
SOLUTION:We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.
So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40. #### B
QUESTION:A jogger running at 9 km/hr along side a railway track is 180 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
options: A)89 B)20 C)36 D)88 E)30
SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 180 + 120 = 300 m.
Time taken = 300/10 = 30 sec.
Answer: Option E #### E
QUESTION:If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10?
options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5
SOLUTION:92p × 5p+r + 11r × 6pr--1=B #### B
QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination.
options: A)15 B)21 C)17 D)19 E)21
SOLUTION:Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 36 - X
Now,
50*X + 500 * (36 - X) = 10350
50X + 18000 - 500X = 10350
- 450X = - 7650
X = 17.
No. of 50 rupees note = 17.
Answer: Option C #### C
<<<Examples ends
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train?
options: A)500 m B)620 m C)872 m D)150 m E)765 m
SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 30) m
= 500 m.
Answer: A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers?
options: A)7 and 12 B)8 and 12 C)9 and 12 D)10 and 12 E)None of these
SOLUTION:Let x and y be the two numbers such that x is larger than y. The statement "the larger number is four less than twice the smaller number" may be formulated by
x = 2y - 4
We use the sum of the two numbers to write a second equation.
x + y = 20
Substitute x by 2y - 4 in x + y = 20 to obtain
2y - 4 + y = 20
Solve for y to find
y = 8 and x = 2y - 4 = 12
Answer B #### B
QUESTION:In an election contested by two parties, Party ADMK secured 24% of the total votes more than Party DMK. If party DMK got 266,000 votes, by how many votes did it lose the election?
options: A)34,000 B)56,000 C)164,000 D)168,000 E)200,000
SOLUTION:ADMK + DMK = 100 ---- (1)
ADMK - DMK = 24 ---- (2)
Solving (1) and (2) ADMK = 62% and DMK = 38%
38% of Total = 266000
Total = 700000
ADMK = 434000
Difference = 434000 - 266000 = 168000
Answer: D #### D
QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 26th of September 1990?
options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday
SOLUTION:19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 26th September was a Wednesday.
The answer is C. #### C
QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 72 kmph?
options: A)22 sec B)77 sec C)25 sec D)18 sec E)12.5 sec
SOLUTION:D = 100 + 150 = 250
S = 72 * 5/18 = 20 mps
T = 250/20 = 12.5 sec
Answer:E #### E
QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n?
options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years
SOLUTION:Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $700.
Therefore, the Simple Interest earned = 700 - 100 = $600.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 600 = (100 * n * 8) / 100
Or 8n = 600
Or n = 75 years.
correct choice is (E) #### E
QUESTION:Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ?
options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1
SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4.
Actually B is the right answer. #### B
QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove?
options: A)$240 B)$260 C)$280 D)$300 E)$320
SOLUTION:J+K=700 so K=700-J
2J=K+80
2J=(700-J)+80
3J=780
J=260
The answer is B. #### B
QUESTION:Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
options: A)126 B)120 C)101 D)112 E)115
SOLUTION:8 shirts
9 pants
we can combine 2 shirts with (12-3) pants
2*9=18
we can combine the other shirts (6) with any pants (9)
9*12=54
Thus total :108+18=126 ANS:A #### A
QUESTION:The H.C.F. of two numbers is 18 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
options: A)270 B)300 C)299 D)322 E)345
SOLUTION:the numbers are (18 x 11) and (18 x 15).
Larger number = (18 x 15) = 270.
ANSWER :A #### A
QUESTION:If x and y are integers and x + y = 3, which of the following must be true?
options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5.
SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option A is right could you explain #### A
QUESTION:Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week?
options: A)$0.00 B)$133.00 C)$250.05 D)$66.74 E)$10000.00
SOLUTION:Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be
n/4, n/8, n/16, n/32
So, answer will be D #### D
QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
options: A)400 B)991 C)881 D)771 E)551
SOLUTION:2000 ---- 50
2000 ---- 40
x ----- 50
x*50 = 2000*40
x=1600
2000
-------
400
Answer: A #### A
QUESTION:There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
options: A)320 B)345 C)375 D)380 E)400
SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 × 75 = 225
Number of girls
5x = 5 × 75 = 375
C #### C
QUESTION:Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
options: A)2 B)4 C)6 D)8 E)10
SOLUTION:P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
880/x = 880/1.1x + 10
1.1(880) = 880 + 11x
11x = 88
x = 8
The answer is D. #### D
QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec
SOLUTION:D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer: C #### C
QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?
options: A)42 years B)41 years C)43 years D)40 years E)45 years
SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years
Answer C #### C
QUESTION:A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
options: A)621 B)276 C)236 D)600 E)211
SOLUTION:Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer: D #### D
QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity?
options: A)7/18 B)9/18 C)2 D)18/7 E)18/5
SOLUTION:Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D
QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5
options: A)18 B)20 C)24 D)30 E)40
SOLUTION:Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30
Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20
Answer:B #### B
QUESTION:How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:The numbers should be of the form 6c+3.
The minimum is 3 when c=0.
The maximum is 45 when c=7.
There are 8 such numbers.
The answer is D. #### D
QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate?
options: A)100 B)50 C)Cannot be determined D)105 E)25
SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position.
Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C
QUESTION:Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?
options: A)2 B)3 C)4 D)5 E)7
SOLUTION:2 + 3 + 5 + 7 + 11= 28 ( sum is even)
Least number = 2
A #### A
QUESTION:The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January?
options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500
SOLUTION:Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8600
= 34400 ----(2)
(2)-(1) i.e. May - Jan = 2400
Salary of May is Rs.6500
Salary of January = Rs.4100
Answer:A #### A
QUESTION:Which of the following numbers is divisible by 4?
options: A)27767 B)10224 C)26778 D)26679 E)26711
SOLUTION:10224. This is the only option with last two digits divisible by 4
Answer:B #### B
QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?
options: A) 4 B) 2 C) 2 D) 10 E) 12
SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8.
Answer A #### A
QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%?
options: A)41 B)48 C)49 D)44 E)43
SOLUTION:96% ---- 72
144% ---- ?
96/144 * 72 = 48
Answer: B #### B
QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ?
options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None
SOLUTION:Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.9 - 19 x 15) kg
= 13 kg.
Correct Option: D #### D
QUESTION:In your classes you counted 120 hands. How many students were at the class?
options: A)60 B)61 C)85 D)86 E)88
SOLUTION:Total number of hands = 120
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 120 by 2
220 ÷ 2 = 60
Therefore, there were 60 students at the class.
ANSWER IS A #### A
QUESTION:If -2/(a - 6) = 4/(a + 4), then a = ?
options: A)2/3 B)1/2 C)5/3 D)8/3 E)7/3
SOLUTION:Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve
(a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ]
- 2 (a + 4) = 4 (a - 6)
a = 8/3
correct answer D #### D
QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
options: A)4 B)8 C)6 D)2 E)1
SOLUTION:Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer:A #### A
QUESTION:Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?
options: A)2 B)5 C)15 D)20 E)25
SOLUTION:Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12
Collective work Time = 12/7 = 1.7 Hrs
Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 6 breaks
=.3/6=.06 hrs = 5 m
so Answer is B) 10 mins #### B
QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
options: A)256 B)512 C)4096 D)1024 E)1536
SOLUTION:0.4*2^10=0.4*1024=409.6
The answer is C. #### C
QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x?
options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1
SOLUTION:x^2 > x^3 > x^1
1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x.
This can be possible only if the base is negative; therefore, the variable, x, must be a negative number.
2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1.
With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B
QUESTION:A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the difference of the numerator and denominator of the original fraction?
options: A) 49 B) 9 C) 28 D) 26 E) 21
SOLUTION:x/y = 2/5 -> 1
(x+4)/2y = 1/3 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 6/5
=> 5x = 3x + 12
=> x = 6
=> y = 5/2 * 6 = 15
so x - y = 9
The answer is B #### B
QUESTION:A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy
options: A)s. 600 B)s. 800 C)s.500 D)s.900 E)s. 1300
SOLUTION:Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 27300.
Gain = SP – CP
3X = 27300 – 18X
21X = 27300
X = Rs. 1300.
ANSWER : OPTION E #### E
QUESTION:If d is the mean of x, y, and z, what is the mean of x + 5, y + 5, z + 5 ?
options: A)d B)3d C)15d D)d + 5 E)d + 15
SOLUTION:If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case mean will increase by 5 as we are adding 5 to each term in a set --> Mean =d + 5.
Answer: D. #### D
QUESTION:You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.
options: A)180 B)181 C)182 D)183 E)184
SOLUTION:52+50+78 = 180
Answer: A #### A
QUESTION:A polling company reports that there is a 50% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?
options: A)11 B)10 C)6 D)4 E)5
SOLUTION:50% - Candidate Elected
100%-60% = 40% - Candidate doesnotsigh Bill X
50% - Candidate randomly chooses between two bills.
These are multiplicative:
50% x 40% x 50%
0.5 x 0.4 x 0.5 = 0.10 = 10%
Answer (B) #### B
QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle?
options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE
SOLUTION:Solution
S.P = 85% of Rs.1200
= Rs.(85/100×1200)
Rs.1020.
Answer B #### B
QUESTION:A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
options: A)15 sec B)16 sec C)18 sec D)20 sec E)25 sec
SOLUTION:Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec
ANSWER: D #### D
QUESTION:The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?
options: A)3 B)1 C)0 D)19 E)20
SOLUTION:Average of 20 numbers = 0
Sum of 20 numbers / 20=0
=> Sum of 20 numbers = 0
Hence at the most, there can be 19 positive numbers.
(Such that if the sum of these 19 positive numbers is x, 20th number will be -X)
ANSWER:C #### C
QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these
SOLUTION:Explanation:
Let the cost of one pen is ‘5x’ and pencil is ‘x’
3 X 5x + 5x = Rs.150
15x + 5x = Rs.150
X = 150/20 = 7.50
:. Cost of 1 pen = 5x = 5 x 7.50 = 37.50
:. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450
Answer: Option D #### D
QUESTION:Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is
options: A)360 B)240 C)2520 D)480 E)None of these
SOLUTION:Solution
Order of vowels of fixed
∴ required number of ways are 7!/2!.
Answer C #### C
QUESTION:The total age of A and B is 18 years more than the total age of B and C. C is how many years younger than A ?
options: A)12 B)27 C)21 D)18 E)11
SOLUTION:(A+B) - (B+C) = 18
A - C = 18.
C is younger than A by 18 years.
Answer: D #### D
QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots?
options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M
SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours.
The answer is A. #### A
QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 35 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
options: A)33 1/3% B)51 23/27% C)50% D)62 1/2% E)75%
SOLUTION:P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
35% of (70-x) = x => 24.5 - 0.35x = x => x = 18 4/27% so only P = 70 -x = 51 23/27%
Answer B #### B
QUESTION:If log303 = a, log305 = b, then log308 =?
options: A)3(1 - a - b) B)(a - b + 1) C)(1 - a - b) D)(a - b + 1) E)none of these
SOLUTION:a + b = log3015 = log30(30/2) = 1- log302
=> log302 = (1 - a - b)
Therefore, log308 = 3(1 - a - b).
ANSWER:A #### A
QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2
options: A)I only B)I,II only C)II only D)I,III only E)III only
SOLUTION:12=2*2*3
16=2*2*2*2
GCF =2*2=4
Answer : C #### C
QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India.
Action:
I. Pollution committee should immediately take certain measures to control the pollution levels in India.
II. Licenses of polluting industries should be cancelled and owners should be put behind the bars.
options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow
SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided.
ANSWER IS A #### A
QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 14 adults have their meal, find the total number of children that can be catered with the remaining food.
options: A)33 B)54 C)18 D)17 E)72
SOLUTION:Explanation:
As there is meal for 70 adults and 14 have their meal, the meal left can be catered to 56 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 56 adults = 72 children
Hence, the meal can be catered to 72 children.
ANSWER: E #### E
QUESTION:A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers?
options: A)330 B)650 C)729 D)800 E)890
SOLUTION:Choose 4 starters from a team of 11 players. Order is not important.
\inline {\color{Black} 11C_{4}}= 330
A #### A
QUESTION:There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division?
options: A)22 B)35 C)37 D)20 E)75
SOLUTION:D
20
29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30 = 20. #### D
QUESTION:Which of the following equations represents a line that is perpendicular to y=1/2*x+3?
options: A)y−2x=8 B)2x+4y=10 C)3y+6x=12 D)4y−8x=16 E)5x−10y=20
SOLUTION:For two lines to be perpendicular, the product of slopes should be equal to -1.
Slope of line 1 = 1/2
Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2
Answer: E #### E
QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58?
options: A)2784 B)2287 C)2977 D)2668 E)1298
SOLUTION:Let the side of the square plot be a ft.
a2 = 144=> a = 12
Length of the fence = Perimeter of the plot = 4a = 48 ft.
Cost of building the fence = 48 * 58 = Rs. 2784.
Answer:A #### A
QUESTION:John and Jacob set out together on bicycle traveling at 12 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
options: A)3 B)2 1/3 C)3 1/2 D)4 E)4 1/2
SOLUTION:John's speed - 12 miles/hr
Jacob's speed - 9 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles.
Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr.
Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours
Answer B #### B
QUESTION:Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
options: A)15:8 B)15:5 C)15:9 D)15:2 E)15:3
SOLUTION:Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8
Answer:A #### A
QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3
SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D #### D
QUESTION:Insert the missing number. 34, 7, 37, 14, 40, 28, 43, (...)
options: A)31 B)42 C)46 D)56 E)68
SOLUTION:Explanation :
We have two series here
34, 37, 40, 43, ... (Increase by 3)
7, 14, 28, ... (Multiply by 2)
Hence, next term is 28 × 2 = 56
Answer : Option D #### D
QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use?
options: A)14 B)47 C)54 D)180 E)64
SOLUTION:Area = Length x Breadth
480 = 40 x Breadth
So, Breadth = 12 Units
Fencing required is -
Breadth + Breadth + Length
12 + 12 + 40 => 64 feet
Answer must be (E) 64 #### E
QUESTION:Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/10 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?
options: A)$110 B)$152.3 C)$180 D)$220 E)$260
SOLUTION:Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/10*(A+E) ==> 9A = 11E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2)
Substituting (1) in (2):
11E/9*11 = 220+12E or (121/9-12) E = 220 or 13/9 E =220 E = 220*9/13 =152.3
B #### B
QUESTION:If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle.
options: A)127 cm^2 B)125 cm^2 C)120 cm^2 D)102 cm^2 E)None of them
SOLUTION:Let length = x and breadth = y. Then,
2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289.
Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120
Area = xy = 120 cm^2
Answer is C. #### C
QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680?
options: A)1500 B)2777 C)2889 D)27670 E)2771
SOLUTION:1680 = P [1 + (5*12/5)/100]
P= 1500.Answer:A #### A
QUESTION:In 6 years, A will be thrice as old as B was 4 years ago. If A is now 6 years older than B, find the present age of B.
options: A)16 years B)24 years C)8 years D)12 years E)18 years
SOLUTION:let present age of A be A
let presennt age of B be B
in 6 yrs
A+6:B+6=3(B-4):B=6
ie A+6=3(B-4)
but given A=B+6
so B+6+6=3(B-4)
B=12
ANSWER:D #### D
QUESTION:From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
options: A)16 B)24 C)60 D)120 E)150
SOLUTION:Answer=E=150
No of 4 person committees that can be formed=5C2*6C2=150
Answer E #### E
<<<Examples ends
QUESTION:If 10 litres of an oil of Rs.55 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?
options: A)Rs.49.17 B)Rs.51.03 C)Rs.58.66 D)Rs.55.33 E)None of the above
SOLUTION:55*10 = 550
66*5 = 330
880/15 = 58.66
ANSWER:C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60?
options: A)10 B)15 C)8 D)12 E)20
SOLUTION:4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 60
4n< 53
n < 13. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13)
Combining the two
-1.5 < n<13.25
n = 1 to 13 (48 integers)
and n = -1 and 0
so 15 integers.
B #### B
QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers?
options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2!
SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 8 is 8!.
2. # of arrangements when 3 boys are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!6!.
# of arrangements when 3 boys do not sit together would be: 8!-3!6!.
Answer: B). #### B
QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper?
options: A)30 B)40 C)42 D)44 E)46
SOLUTION:here two cases are possible.
case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3
case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2
thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30
ANS:A #### A
QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
options: A)1200 B)1723 C)1129 D)2613 E)1372
SOLUTION:A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 150= 3k + 150 => 2k = 300 => k = 150
The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A
QUESTION:Find the average of all numbers between 2 and 63 which are divisible by 5
options: A)15 B)20 C)25 D)32.5 E)35
SOLUTION:Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60)/12=390/12=32.5
Answer: Option D #### D
QUESTION:One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
options: A)5:4 B)9:4 C)5:6 D)5:0 E)2:4
SOLUTION:Explanation:
45 * 5/18 = 10
25:20 => 5:4
Answer: Option A #### A
QUESTION:The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a quarter of its new value. What is the stock's value at the end of Monday?
options: A)X. B)3X/8. C)2X/3. D)X/3. E)X/4.
SOLUTION:Stock value= X
AT sunday end= x+.5X= 1.5 X
On monday the value drop to 1/4rd of its value on sunday
1.5x/4= 3X/8
B is the answer #### B
QUESTION:5 - [5 - {5 - 5(5 + 5)}] = ?
options: A)5 B)-45 C)45 D)50 E)60
SOLUTION:Explanation:
=> ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)]
= 5 - (50) = - 45
Answer: Option B #### B
QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?
options: A)767 km B)975 km C)678 km D)900 km E)546 km
SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.
x/40 = (x + 100)/50
50x = 40x + 4000 => x = 400
So, distance between P and Q = (x + x + 100)km =900 km.
Answer: D #### D
QUESTION:If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 5.
II. x is an integer multiple of 3
III. x is an integer multiple of 6
options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only
SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6.
Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.
Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even
Answer E #### E
QUESTION:A present value of a machine is $2000. Its value depletiation rate is 20% per annum then find the machine value before 2 years?
options: A)$3125 B)$2945 C)$3012 D)$2545 E)$3150
SOLUTION:P= $2000
R = 20%
T = 2 years
Machine value before 2 years = P/[(1-R/100)^T]
=2000*5/4 * 5/4
=$3125
Answer is A #### A
QUESTION:A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
options: A) 81 B) 83 C) 85 D) 86 E) 89
SOLUTION:Overall, there can be 81 minuses. Tus, it is A. #### A
QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter?
options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm
SOLUTION:Perimeter of the sector = length of the arc + 2(radius)
= (130/360 * 2 * 22/7 * 21) + 2(21)
= 47.6 + 42
= 89.6 cm
Answer:B #### B
QUESTION:Two persons A and B can complete a piece of work in 30 days and 60 days respectively. If they work together, what part of the work will be completed in 10 days?
options: A)1/8 B)1/3 C)1/6 D)1/2 E)5/3
SOLUTION:A's one day's work = 1/30
B's one day's work = 1/60
(A + B)'s one day's work = 1/30 + 1/60 = 1/20
The part of the work completed in 10 days = 10 (1/20) = 1/2.
Answer:D #### D
QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
options: A)19 B)19.7 C)19.9 D)21.7 E)22.8
SOLUTION:Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B) #### B
QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
options: A)5.79 B)5.73 C)5.76 D)5.75 E)5.71
SOLUTION:M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
\Answer:C #### C
QUESTION:The price for a loaf of bread in April was $1.20, in May the price was $1.27, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period?
options: A)$1.18 B)$1.17 C)$1.16 D)$1.15 E)$1.14
SOLUTION:Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(120) + 127x + (4x/3)(108) / (2x/3 + x + 4x/3) =
(80 + 127 + 144) / (3) = 351/3 = $1.17
The answer is B. #### B
QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job?
options: A)6 B)13 1â„2 C)17 D)Data inadequate E)None of these
SOLUTION:12 M × 18 = 12 W × 18 × 3/1
\ w = 1/3 M
10M + 8W = 10M + 8 × 1/3M = 12 2/3 M
\12 2/3 men can complete the same work
in 12×18/12 2/3=17days
Answer C #### C
QUESTION:For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is?
options: A)between 2 and 20 B)between 10 and 20 C)between 20 and 30 D)between 30 and 40 E)greater than 40
SOLUTION:SOL:
Lets consider h(100):
=> 2*4*6*8.........*98*100
=> (2*1) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50)
=> (2^50) * (1*2*3*4........*49*50)
=> h(100) = (2^50) * (50!)
We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100).
But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50;
ANSWER:E #### E
QUESTION:A man buys Rs. 60 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
options: A)s. 12 B)s. 15 C)s. 18 D)s. 21 E)s. 45
SOLUTION:Dividend on Rs. 60 = Rs. 9/100 x 60 =Rs. 5.4 .
Rs. 12 is an income on Rs. 100.
Rs. 5.4 is an income on Rs.100/12 x 5.4 = Rs. 45.
Answer: Option E #### E
QUESTION:When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8?
options: A)3 B)4 C)5 D)6 E)2
SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 24)
3n = 3(6) =18, which leaves a remainder of 2 when divided by 8.
Answer E #### E
QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is:
options: A)4 B)5 C)6 D)8 E)9
SOLUTION:Explanation :
Let the required number of men be x.
Less days, More men (Indirect Proportion)
More working hrs per day, Less men (Indirect Proportion)
Days 8 : 10
Working Hrs 20 : 8 :: 12 : x
=> 8 x 20 x x = 10 x 8 x 12
=> x = 10 x 8 x 12 / (8 x 20)
=> x = 6
Answer : C #### C
QUESTION:Six cards numbered from 1 to 6 are placed in a cardboard box . First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 5 ?
options: A)1/2 B)1/4 C)1/5 D)1/6 E)1/3
SOLUTION:(6,4) (4,6) (5,5) – only 3 possible scenarios for sum to be 10. One from this 5 has already happened.
From this three cases, only in one we have 5. So, the probability is 1 chances out of 3 that the one that occurred had 5: P=1/3.
Answer: E. #### E
QUESTION:Two coins are tossed, find the probability that two Tails are obtained
options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3
SOLUTION:The sample space S is given by.
S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two heads are obtained".
E = {(T,T)}
P(E) = n(E) / n(S) = 1/4
B #### B
QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the
rest at 5 kmph. Find the total distance.
options: A)4 km B)5 km C)6 km D)7 km E)8 km
SOLUTION:time=distance/speed
let total distance travelled be x in 84/60 hrs
2/3 rd of x travelled in 4 km/hr
1/3 rd of distance travelled in 5 km/hr
2x/(3*4)+x/(3*5)=84/60
x=6 km
ANSWER:C #### C
QUESTION:By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph
SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km
He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x
=30 kmph.
Answer: A #### A
QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet?
options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am
SOLUTION:meet x hrs after 8 a.m.
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
==>60x+75(x-1) = 330
x=3.
So,they meet at (8+3). i.e 11a.m.
ANSWER A #### A
QUESTION:hat should come in place of question mark (?) in the following equation ?
197 × ? + 16(2) = 2620
options: A)22 B)12 C)14 D)16 E)None of these
SOLUTION:? = 2620−256 /197=12
Answer B #### B
QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
options: A)200 B)300 C)500 D)600 E)700
SOLUTION:Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: Option C #### C
QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2012) = ?
options: A)2013 B)2088 C)270 D)1881 E)1781
SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2012) = 2013
Ans: A #### A
QUESTION:A person travels equal distances with speeds of 8 km/hr, 9 km/hr and 10 km/hr and takes a total time of 47 minutes. The total distance is?
options: A)6 km B)3 km C)7 km D)5 km E)2 km
SOLUTION:Let the total distance be 3x km.
Then, x/8 + x/9 + x/10 = 47/60
x/3 = 47/60 => x = 2.33.
Total distance = 3 * 2.33 = 6.99 km.
Answer:C #### C
QUESTION:If c is 14% of a and 40% of b, what percent of a is b?
options: A) 2.5% B) 15% C) 25% D) 35% E) 250%
SOLUTION:Answer = D
14a/100 = 40b/100
b = 14a/40 = 35a/100 = 35% #### D
QUESTION:What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
options: A)20(2/3)% B)20% C)21% D)22(2/3)% E)None of these
SOLUTION:Explanation :
Total numbers = 70
Total numbers in 1 to 70 which has 1 in the unit digit = 7
Total numbers in 1 to 70 which has 9 in the unit digit = 7
Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14
Required percentage = (14/70) × 100 = 140/7 = 20%
Answer : Option B #### B
QUESTION:The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
options: A)2:6 B)2:3 C)4:5 D)2:1 E)2:4
SOLUTION:Let the ratio be k : 1. Then,
k * 16.3 + 1 * 15.4 = (k + 1) * 15.8
= (16.3 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.5 = 4/5
Required ratio = 4/5 : 1 = 4:5.
Answer:C #### C
QUESTION:Can you find next number in tricky mathematical series below?
111 , 113 , 117 , 119 , 123 , 137 ?
options: A)151 B)161 C)171 D)131 E)121
SOLUTION:Solution:
151 (131+20)
Explanation:
1st 7 prime numbers post 100 are
101 , 103 , 107 , 109 , 113 , 127 , 131
...Adding 20 to numbers
121 , 123 , 127 , 129 , 133 , 147 , 151
Answer A #### A
QUESTION:What least number must be subtracted from 9679 so that the remaining number is divisible by 15?
options: A)3 B)1 C)16 D)4 E)15
SOLUTION:On dividing 9679 by 15, we get remainder = 4.
Required number be subtracted = 4
ANSWER:D #### D
QUESTION:A student committee on academic integrity has 42 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
options: A)7 B)8 C)9 D)10 E)11
SOLUTION:xC1 * (x-1)C1=42
x^2 -x -42 =0
(X-7 (X+6) = 0
X= 7 , -6
-6 can't possible.
Hence 7 should be the answer
A #### A
QUESTION:A car covers a distance of 1080 km in10 hrs. What is its speed in mps.
options: A)40 m/s B)25 m/s C)20 m/s D)15 m/s E)30 m/s
SOLUTION:Explanation:
Distance = Speed x Time
Speed = (1080/10) = 108 kmph
Spees in mps = 108 x 5/18 = 6 x 5 = 30 mps.
Answer: Option E #### E
QUESTION:Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail?
options: A)3/4 B)1/4 C)3/8 D)1/2 E)1/8
SOLUTION:Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting 3 heads
Then E = {HHH,HTH,THH,HHT}
P(E) = n(E)/n(S) =4/8 = 1/2
Answer is D #### D
QUESTION:If 9x^2-16y^2=3x+4y,then what will give the answer?
options: A)3x-4y=0 B)3x-4y=2 C)3x-4y=1 D)3x+4y=0 E)3x+4y=1
SOLUTION:9x^2-16y^2=3x+4y
(3x+4y)(3x-4y)=3x+4y
3x-4y=(3x+4y)/(3x+4y)
3x-4y=1
Answer is option C #### C
QUESTION:In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows.
options: A)12 B)14 C)16 D)18 E)20
SOLUTION:Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 32 more than twice the number of heads
=> 2(d + 2c) = 32 + 2(c + d)
=> d + 2c = 16 + c + d
=> 2c = 16 + c
=> c = 16
i.e., total number of cows = 16
Answer is C. #### C
QUESTION:If 3^x = 2, then 3^(4x+3) =
options: A)429 B)454 C)432 D)438 E)108
SOLUTION:3^x=2
3^4x=2^4
3^4x=16
3^(4x+3)
=3^4x*3^3
=16*27
=432
Answer: C #### C
QUESTION:How many two digit numbers of distinct digits can be formed by using digits 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases
Answer: option E #### E
QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was
options: A)14 B)17 C)11 D)19 E)26
SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31.
Son's age 5 years back = (31 - 5) = 26 years
Answer: E #### E
QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is?
options: A)33 B)60 C)88 D)27 E)26
SOLUTION:Explanation:
length of the diagonal = 52*(15/60) =13m
sum of length and breadth = 68*(15/60) = 17m
\inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 }
area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169]
=1/2*120 = 60 sq meter
Answer: B) 60 #### B
QUESTION:The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
options: A)3:5 B)3:9 C)3:2 D)2:2 E)3:8
SOLUTION:The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r1^2 . h1/r2^2. h2 => 1/15
= (1)^2h1/(2)^2h2
=> h1/h2 = 3/5
i.e. h1 : h2 = 3:5
Answer: A #### A
QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats?
options: A)12 B)302 C)1 D)250 E)286
SOLUTION:Total number of hats = 13
Possible number of formations = 13C3 = 286
Correct answer is E #### E
QUESTION:Calculate the % profit or loss, if the cost price of 9 balls is equal to the selling price of 14 balls.
options: A)35.7% B)25.7% C)15.7% D)55.7% E)45.7%
SOLUTION:Let the cost price of 1 balls be Rs 1
Cost of 14 balls= Rs 14
Selling price of 14 balls = 9
Gain/loss = 14 - 9 = 5
%=5/14∗100= 35.7
Answer: A #### A
QUESTION:A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
options: A)1.4 B)1.5 C)1.6 D)1.8 E)1.0
SOLUTION:Let the speed be 's' and let the distance between rose and poppy be 'x'
The problem boils down to:
Rose to Poppy: s+3=x/6 ------- 1
Daisy to Rose: s=(x+18)/10------ 2
so from 1 we can re write x as x=6s+18
substitute the value of x in 2 gives us s=1.8 m/s
D #### D
QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work?
options: A)3 B)5 C)4 D)2 E)6
SOLUTION:A rate = 1/8
B rate = 1/24
(A+B) rate = (1/8)+(1/24) = 1/6
A & B finish the work in 6days
correct option is E #### E
QUESTION:A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
options: A)5 B)7 C)3 D)1/2 E)4
SOLUTION:Explanation:
M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: C #### C
QUESTION:A brick measures 20cm*10cm*7.5cm how many bricks will be required
for a wall 25m*2m*0.75m ?
options: A)24000 B)23000 C)22000 D)25000 E)27000
SOLUTION:25*2*0.75=20/100*10/100*0.75/100*X
25=1/100*X
X=25000
Answer :D #### D
QUESTION:A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?
options: A)(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 B)(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2 C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D)(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2
SOLUTION:Probability of Head, P(H) = 0.1
Probability of Tail, P(T) = 0.9
Tail will appear NO more than twice
i.e. favourable cases
2 Tails and 3 Heads, Probability = 5C2*(0.1)^3*(0.9)^2
1 Tail and 4 Heads, Probability = 5C1*(0.1)^4*(0.9)^2
0 Tail and 5 Heads, Probability = (0.1)^5
Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2
Answer: option A #### A
QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
options: A)121km B)242km C)224km D)112km E)115km
SOLUTION:Explanation:
Average Speed =2×21×24/21+24=22.4 km/hr
Total distance =22.4×10=224 km
ANSWER IS C #### C
QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255
options: A)11 B)8 C)27 D)63 E)127
SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong.
B #### B
QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true?
options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6
SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) .
ans B #### B
QUESTION:.05% of cans of beans that go down a conveyor belt are sealed improperly and must be disposed of. How many cans of beans must pass down a conveyor belt for 5 cans to be sealed improperly?
options: A)500 B)5000 C)4000 D)2500 E)10000
SOLUTION:Let the number of total cans of beans be x
Then, .05% of x=5
(5/100)*(1/100)*x=5
x=10000
Answer is E #### E
QUESTION:There are 9 books on a shelf that consist of 3 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book?
options: A)95 B)103 C)111 D)119 E)127
SOLUTION:The total number of ways to select 4 books is 9C4 = 126
The number of ways which do not include any paperbacks is 6C4 = 15
The number of combinations with at least one paperback is 126-15 = 111
The answer is C. #### C
QUESTION:Four persons enter the lift of a six storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
options: A)625 B)1296 C)1540 D)1478 E)360
SOLUTION:Each person out of 4 has 5 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 5*5*5*5=5^4=625.
Answer: A. #### A
QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
options: A)18% B)20% C)25% D)23% E)Cannot be determined
SOLUTION:Answer: C. #### C
QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches
were made?
options: A)84 B)30 C)38 D)42 E)48
SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
240 / 20 = 12 sandwiches in one part
For bologna we have 7 parts so:
7 *12 = 84
Answer is A #### A
QUESTION:In your classes you counted 120 hands. How many students were at the class?
options: A)60 B)61 C)85 D)86 E)88
SOLUTION:Total number of hands = 120
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 120 by 2
220 ÷ 2 = 60
Therefore, there were 60 students at the class.
ANSWER IS A #### A
QUESTION:If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates?
options: A) 4 B) 8 C) 12 D) 15 E) 20
SOLUTION:I understand this might not be required but I used the equation of a circle.
Since the origin is at 0, x^2+y^2=5^2.
X,Y could be +/- (0,5 or 5,0) - 4 possibilities.
X,Y could be +/- (3,4 or 4,3) - 8 possibilities.
Ans: J=C #### C
QUESTION:Remainder of (6^17+17^6)/7= ?
options: A)2 B)1 C)0 D)3 E)4
SOLUTION:6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7
17^6/7 = (2*7+3)^6/7 = 3^6/7 = 27^2/7 =(4*7-1)^2/7 =(-1)^2/7 = 1/7
so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0
ANSWER:C #### C
<<<Examples ends
QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
options: A)212 km B)214 km C)224 km D)216 km E)204 km
SOLUTION:50(x + 1) = 64x
X = 3.57
60 * 3.57 = 214 km
ANSWER:B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book.
options: A)23777 B)69667 C)26976 D)2697 E)1079
SOLUTION:Explanation:
Number of digits used in 1 digit numbers = 1*9 = 9
Number of digits used in 2 digit numbers = 2*90 = 180
Number of digits used in 3 digit numbers = 3*900 = 2700
Number of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320
Hence, number of pages with 4 digit number = 320/4 = 80
Total number of pages = 1079
ANSWER: E #### E
QUESTION:N, a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is
options: A)(a) 61250 B)(b) 65525 C)(c) 42455 D)(d) 62525 E)(e) 55425
SOLUTION:The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question.
To start, we're given information on the sub-sets of numbers:
-The 1st set has 1 number
-The 2nd set has 2 numbers
-The 3rd set has 3 numbers
Etc.
So the 50th set will have 50 numbers in it.
Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching...
The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers
The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers
Etc.
This pattern will continue all the way down to...
The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers
Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'...
So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive...
Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)...
25(1226+1275) =
25(2501) =
62525
D #### D
QUESTION:14 times a number gives 210. The number is
options: A)11 B)12 C)15 D)None E)Cannot be determined
SOLUTION:Explanation:
Let the number be 'N'
14×N=210⇒N=15
Correct Option: C #### C
QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
options: A)153550 m^2 B)153600 m^2 C)153700 m^2 D)153800 m^2 E)153900 m^2
SOLUTION:Explanation:
Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
Option B #### B
QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
options: A)6 B)9 C)36 D)120 E)144
SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways
Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places
Second Place, Physics Book - in 4 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.
Total no of ways = 4*3*3*2*2*1*1 = 144 ways
E #### E
QUESTION:If the cost price of 60 boxes is equal to the selling price of 50 boxes, the gain percent is
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:Let C.P. of each box be Re. 1.
Then, C.P. of 50 boxes = Rs. 50; S.P. of 50 boxes = Rs. 60.
Gain % = 10/50 * 100 = 20%
Answer:D #### D
QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase?
options: A)80% B)90% C)70% D)60% E)50%
SOLUTION:Ans. Let previous income = Rs. 100
Previous savings = 10% of Rs. 100 = Rs. 10
Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120
Increased savings = 15% of Rs. 120 = Rs. 18
Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8
Therefore, Percent increase in savings = 8/10 x 100 = 80%
Answer A #### A
QUESTION:Eight children — A, B, C, D, E, F, G and H — are going to sit in eight chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
options: A)600 B)720 C)10080 D)14320 E)14800
SOLUTION:for such questions , we can treat both as one then total person=7..
these 7 can be arranged in 7! ways.. but within these 7 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080
ans C #### C
QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price
options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/-
SOLUTION:100 % ------> 200 (100 * 2 = 200)
120 % ------> 240 (120 * 2 = 240)
Selling price = Rs.240/-
Answer : D #### D
QUESTION:If after 700 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
options: A)180 grams B)220 grams C)250 grams D)350 grams E)1400 grams
SOLUTION:I too think 1400 grams should be the answer.
My reasoning is
The h20 content in 700 gms of water is 1
h20 content in 24% solution is 0.76
Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84
Let amount of solution be X
Then the equation can be set up
700*1 + 0.76X = 0.84 (X+700)
0.08X = 112
8X = 11200
X = 1400 (ANS E) #### E
QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
options: A)300 km B)320 km C)360 km D)390 km E)400 km
SOLUTION:Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C) #### C
QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.
options: A)20% B)21% C)21.33% D)22.109% E)23%
SOLUTION:Lets say the indicated weight is x for $10
but the trader actually get 1.1x for $10
now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1
so profit % = (12.1-10)/ 10 = 0.21 = 21%
ANSWER:B #### B
QUESTION:A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
options: A)59020 B)59299 C)59020 D)59300 E)59008
SOLUTION:Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer: D #### D
QUESTION:The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this triangle.
options: A)15° ,45° ,110° B)15° ,45° ,130° C)15° ,45° ,110° D)15° ,35° ,110° E)25° ,45° ,110°
SOLUTION:Solution
If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
x = 15
The measures of the three angles are
x = 15°
3x = 3 × 15 = 45°
8x = 8 × 15 = 120°
ANSWER IS C #### C
QUESTION:A rocket soars for 12 seconds at 150 meters per second. It then plummets 600 meters in 3 seconds. What is the average speed of the rocket in meters per second?
options: A)140 B)150 C)155 D)160 E)175
SOLUTION:When soaring, the rocket travels a total distance of 1800m(150m/s for 12s)
While plummeting the rockets travel distance of 600m in 3s
The total distance traveled is 2400m(1800 + 600)
The time taken to travel this distance is 15s(12 + 3)
Average speed = 2400/15 = 160
ANS: (Option D) #### D
QUESTION:10^(600) ÷ 10^(580) = ?
options: A)10^10 B)10^20 C)10^22 D)10^23 E)10^24
SOLUTION:10^(600) ÷ 10^(580) = 10^ (600-580) = 10^20
Answer : B #### B
QUESTION:Two mechanics were working on your car. One can complete the given job in 5 hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
options: A)7/4 B)4/3 C)14/5 D)10/3 E)17/5
SOLUTION:Rate(1)=1/5
Rate(2)=1/8
Combined = 13/40
Work done in 2 days=13/20
Work left = 7/20
Rate * Time = Work left
1/8 * Time = 7/20
Time=14/5
C #### C
QUESTION:If 20m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
options: A)2m −1 B)4m C)6m D)7m E)6m/5
SOLUTION:20m - n = p
Add n to both sides:
20m = n + p
Add m to both sides:
21m = n + p + m
Now, divide both sides by 3
7m = (n + p + m)/3 = the average of n, p, and m
D #### D
QUESTION:Mr. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck
options: A)$145 B)$250 C)$300 D)$175 E)$150
SOLUTION:Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A) #### A
QUESTION:If 75 percent of 600 is 50 percent of x, then x=?
options: A)800 B)900 C)1000 D)1100 E)1200
SOLUTION:0.75 * 600 = 0.5 * x
x = 7.5/5 * 600 = 900 #### B
QUESTION:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?
options: A)30 B)44 C)42 D)46 E)50
SOLUTION:Total # of students 20+28+18-(9+7+10)+4=44.
Answer: B. #### B
QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball?
options: A)12 cm B)16 cm C)18 cm D)20 cm E)none of the these
SOLUTION:similar triangle properties..
2/r+6 = 6/r-6
giving r = 12.
Answer: A #### A
QUESTION:At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 30 other employees of Company K, how many employees does Company K have?
options: A) 160 B) 120 C) 190 D) 200 E) 400
SOLUTION:Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 30
so 25% of x = 30
x = 120
Therefore there a total of 120 employees in the company K
Correct answer - B #### B
QUESTION:Which one the following fractions has the biggest value?
options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711
SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D
QUESTION:A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
options: A)109 ways B)908 ways C)128 ways D)108 ways E)104 ways
SOLUTION:The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer:D #### D
QUESTION:When n is divided by 24, the remainder is 3. Find thee difference between previous remainder and the remainder when 9n is divided by 7 ?
options: A)2 B)7 C)5 D)3 E)6
SOLUTION:Let n=3 (leaves a remainder of 3 when divided by 24)
9n = 9(3) =27, which leaves a remainder of 6 when divided by 7.
difference = 6 - 3 = 3.
Answer D #### D
QUESTION:A cylinder of height h is 7/8 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
options: A)25% B)50% C)69% D)80% E)100%
SOLUTION:Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 7/8
New cylinder 3/5
So 3/5/7/8 = 3/5*8/7 = 0.69 or 69%.
Answer C #### C
QUESTION:What is the principal sum?
I. The sum amounts to Rs. 720 in 4 years at S.I.
II. The sum amounts to Rs. 810 in 7 years at S.I.
III. The rate of interest is 10% p.a.
options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above
SOLUTION:Explanation:
Clearly, any of the three will give us the answer
Answer: E #### E
QUESTION:John and Jacob set out together on bicycle traveling at 12 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
options: A)3 B)2 1/3 C)3 1/2 D)4 E)4 1/2
SOLUTION:John's speed - 12 miles/hr
Jacob's speed - 9 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles.
Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr.
Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours
Answer B #### B
QUESTION:A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office?
options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h
SOLUTION:u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27
\inline \Rightarrow 1.5k = 27
\inline \Rightarrow k=18km/h
E #### E
QUESTION:Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
options: A)A)35 B)B)28 C)C)45 D)D)25 E)E)26
SOLUTION:Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Eight years ago, P was half of Q in age
=> 2(3x – 8) = (4x – 8)
=> 6x – 16 = 4x – 8
=> 2x = 8
=> x = 4
7x=7*4=28
Answer: Option B #### B
QUESTION:A data set with a mean of 60 has a standard deviation of 1.5. Which of the following is the smallest number that falls within one standard deviation of the mean?
options: A)53 B)56 C)58 D)63.5 E)65
SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=60-1.5=58.5 to{mean}+{deviation}=60+1.5=61.5. The smallest number within this range from the options is 58.
Answer: C.
Hope this helps. #### C
QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E?
options: A)60 B)80 C)40 D)120 E)160
SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30
(9/8)x - (3/4)x = 30
x = 80=E
Answer: B #### B
QUESTION:The average of first ten prime numbers which are odd is?
options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5
SOLUTION:Sum of first 10 prime no. which are odd = 158
Average = 158/10
= 15.8
Answer:D #### D
QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches?
options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0
SOLUTION:Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.2
x = 3.2
Alternate solution: Try to backsolve.
Initial volume = 3.2
After one hour --> (1/4)3.2 = 0.8
After two hours --> (1/4)0.8 = 0.2
Answer: B #### B
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)123 B)166 C)240 D)157 E)198
SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C #### C
QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0
SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100%
=> The required ratio = 100%/25% = 4.0
Answer : B #### B
QUESTION:Of 55 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
options: A)49 B)55 C)59 D)71 E)92
SOLUTION:Total = 55
Thrower = 37
Rest = 55 - 37 = 18
Left Handed = 18/3 = 6
Right handed = 12
If all Thrower are right handed then total right handed is 37 + 12 = 49
so A. 49 is the right answer #### A
QUESTION:The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$430 per month. The salary of the new supervisor is:
options: A)870 B)600 C)287 D)771 E)191
SOLUTION:Explanation:
Total salary of 8 workers and supervisor together = 9 × 430 = 3870
Now total salary of 8 workers = 3870 − 870 = 3000
Total salary of 9 workers including the new supervisor = 9 × 430 = 3870
Salary of the new supervisor = 3870 − 3000 = 870
Answer: A #### A
QUESTION:One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish.
options: A)10 B)11 C)12 D)13 E)14
SOLUTION:Fast's 1 hr work = 1/2
slow's 1 hr work = 1/3
1/2 + 1/3 = 5/6
they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins
ANSWER:C #### C
QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
options: A)33 1/7% B)33 2/3% C)33 1/3% D)37 1/3% E)23 1/3%
SOLUTION:675 ---- 225
100 ---- ? =>
=33 1/3%
Answer:C #### C
QUESTION:A certain fraction has the same ratio to 1/18, as 2/5 does to 7/9. What is this certain fraction?
options: A)1/20 B)1/25 C)1/30 D)1/35 E)1/40
SOLUTION:x / (1/18) = (2/5) / (7/9)
x = 2*9*1 / 18*5*7 = 1/35
The answer is D. #### D
QUESTION:Machine T can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
options: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33
SOLUTION:Let the following be true:
T makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C #### C
QUESTION:The fourth proportional to 14, 22 and 28 is?
options: A)21 B)66 C)88 D)99 E)44
SOLUTION:(22*28)/14 = 44
Answer: E #### E
QUESTION:A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5760. What is the average monthly balance maintained by John in his
account during the year?
options: A) 2840 B) 28800 C) 6840 D) 7540 E) 28400
SOLUTION:bank balance is doubled with accumulation of interest tp 5760..
this means INTEREST is 5760/2=2880 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 28800..
B #### B
QUESTION:If a + b = y and a - b = z , then 3ab =
can someone explain!
options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2
SOLUTION:plugging numbers is quite fast in this case:
Let
a=1
b=2
Then; y= 1+2=> 3 and z= 1-2=> -1
Question asks 3ab=.........
As our number 3ab= 3*1*2=6
now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need.
Hence: Ans is A. #### A
QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following?
options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2
SOLUTION:initially - did x= 1/y^2
But this yielded the wrong answer,
I then re examined the question and tried y^2/x =1
Which I then got y = SQR(X)
subbing into y/6a I got answer E) #### E
QUESTION:Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat?
options: A)3! B)8! C)11! D)12! E)14!
SOLUTION:Ans.(A)
Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways #### A
QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college?
options: A)13680 B)13885 C)14005 D)14280 E)14680
SOLUTION:dana borrows 6000 and returns 2% per month.
so returns 120 per month. and 1440 per year.
so dana owes 6000-1440=4560 per year.
after 3 years she will owe 13680.
Ans (A) #### A
QUESTION:What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x
options: A)2450 B)2560 C)3200 D)3400 E)3158
SOLUTION:12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
E #### E
QUESTION:A man divides $8600 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
options: A)A)$200 B)B)$1000 C)C)$800 D)D)$1011.76 E)E)$400
SOLUTION:Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 4*4X+4*4X+2*X=8600
16X+16X+2X=8600
34X=8600, X=252.94.
Daughter receives four times of nephew so 4 * 252.94 = 1011.76.
So Each Daughter receives $800. answer is option D) $1011.76. #### D
QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his
original salary?
options: A)25% B)50% C)75% D)85% E)95%
SOLUTION:Salary he get after reduced 20% = 100-20% = 80%
So,percentage should be added to get back his salary = (20/80)*100 = 25%
ANSWER:A #### A
QUESTION:Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of
Rs. 13,800. Deepak's share is
options: A)Rs 9600 B)Rs 8500 C)Rs 8450 D)Rs 8400 E)None of these
SOLUTION:Explanation:
Ratio of their shares = 22500 : 35000
=9 : 14
Deepak's share = Rs.(13800×14/23)
= Rs. 8400
Option D #### D
QUESTION:The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?
options: A)Rs.32 B)Rs.28 C)Rs.36 D)Rs.25 E)None of these
SOLUTION:Let the cost of each pen and pencil be 'p' and 'q' respectively.
16p + 8q = 352 --- (1)
4p + 4q = 96
8p + 8q = 192 --- (2)
(1) - (2) => 8p = 160
=> p = 20
ANSWER:E #### E
QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘POWER’, using each letter exactly once?
options: A)700 B)720 C)750 D)800 E)120
SOLUTION:The word ‘POWER’ contains 5 different letters.
Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time
=5P5
= 5!
= 5*4*3*2*1
= 120
ANSWER:E #### E
QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place.
options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours
SOLUTION:1/5+2/8 + 3/x = 1
x =20 hours. ANSWER =D #### D
QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing?
options: A)191 B)400 C)737 D)840 E)1,560
SOLUTION:Let weight of side of beef before processing = x
(60/100)*x = 240
=> x = (240 * 100)/60 = 400
Answer B #### B
QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is?
options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C
SOLUTION:Let temperature on 4th day be X°C
Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1
=> X = 41.9
Therefore, temperature on 4th day = 41.9°C.
ANSWER:D #### D
QUESTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 4y) is odd
II. xy^2 is an even negative integer
III. (y^2 - x) is an odd negative integer
options: A)(3X-4Y) IS ODD TRUE B)II only C)I and II D)I and III E)II and III
SOLUTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 4y) is odd
3x - is always negative and odd
2y - can be 0, when y=0, or always even integer (positivie or negative)
odd integer +/- even integer = always odd
I statement is always true
II. xy^2 is an even negative integer
y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true
III. (y^2 - x) is an odd negative integer
y can be 0 => -x will be positive => III statement is not true
basing on above, only I statement will always be true
answer is A #### A
QUESTION:A man buys an article and sells it at a profit of 5%. If he had bought it at 5% less and sold it for Rs.25 less, he could have gained 5%. What is the cost price?
options: A)197 B)476 C)279 D)278 E)268
SOLUTION:CP1 = 100 SP1 = 105
CP2 = 95 SP2 = 95 * (105/100) = 99.75
5.25 ----- 100
25 ----- ? => 476
Answer:B #### B
QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?
options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000
SOLUTION:1% is quite small and hence the answer is A) #### A
QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13?
options: A)6 B)7 C)8 D)9 E)3
SOLUTION:We have to include 3 also.As 13*0 + 3 =3
If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3.
Answer is E #### E
QUESTION:John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend?
options: A)$2,125 B)$1,320 C)$2,000 D)$1,580 E)$2,000.75
SOLUTION:Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125. #### A
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)210m B)240m C)963m D)874m E)578m
SOLUTION:Explanation:
Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer: B)240m #### B
<<<Examples ends
QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
options: A)40% B)45% C)57% D)58% E)60%
SOLUTION:tot no of votes = (1136+7636+11628) = 20400
req = > (11628/20400 * 100) = > 57%
ANSWER C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
options: A)9.30 a.m B)10 a.m C)10.40 a.m D)11 a.m E)11.40 am
SOLUTION:Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
answer B #### B
QUESTION:A man can row his boat with the stream at 16 km/h and against the stream in 6 km/h. The man's rate is?
options: A)5 kmph B)6 kmph C)7 kmph D)4 kmph E)9 kmph
SOLUTION:Explanation:
DS = 16
US = 6
S = ?
S = (16 - 6)/2 =5 kmph
Answer: A #### A
QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600
SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.
Let p be the population of the least populated district.
Then 160,080 = p + 7(1.1)p
8.7p=160,080
p = 18,400
The answer is C. #### C
QUESTION:calendar=52097083 november=538=8651
march=2*308 blue=7154 december=?
options: A)9535&153 B)9585&153 C)9525&153 D)9525&*53 E)9525&*54
SOLUTION:from above in formation
d=9
e=5
c=2
e=5
m=3
b=1
e=5
r=8
95253158( Order doesnot matter i guess!)
another thing is &=8 for mathcing above ans
ANSWER:C #### C
QUESTION:Combine terms: 15a + 26b -4b – 16a.
options: A)4a + 22b B)-28a + 30b C)-a + 22b D)28a + 30b E)5a + 30b
SOLUTION:Solution:
15a + 26b -4b – 16a.
= 15a – 16a + 26b – 4b.
= -a + 22b.
Answer: (C) #### C
QUESTION:In an examination, 34% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
options: A)975 B)1150 C)1175 D)1243 E)1525
SOLUTION:Failed in 1st subject = 34*2500/100 = 850
Failed in 2nd subject = 42*2500/100 = 1050
Failed in both = 15*2500/100 = 375
Failed in 1st subject only = 850-375 = 475
Failed in 2nd subject only = 1050-375 = 675
Passed in either subject but not in both = 675+475 = 1150
Answer is B #### B
QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
options: A)17% B)19% C)18% D)14% E)16%
SOLUTION:Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer: C #### C
QUESTION:Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
options: A)87 B)89 C)90 D)93 E)95
SOLUTION:Total score on 3 tests = 81*3 = 243
Jerry wants the average to be = 83
Hence total score on 4 tests should be = 83*4 = 332
Score required on the fourth test = 332 - 243 = 89
Option B #### B
QUESTION:he average of 30 numbers is zero. Of them, at the most, how many may be greater than zero?
options: A)29 B)1 C)10 D)30 E)8
SOLUTION:Average of 30 numbers = 0.
Sum of 30 numbers (0 x 30) = 0.
It is quite possible that 29 of these numbers may be positive and if their sum is a the 30th number is (-a).
Answer: Option A #### A
QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
options: A)3377 B)2997 C)3600 D)2799 E)7719
SOLUTION:P = 144(100/5)2 => P
= 3600
Answer:C #### C
QUESTION:If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above?
A.
B.
C.
D.
E.
options: A)(−8,8) B)(4,−4) C)(5,−5) D)(2,−2) E)(−4,4)
SOLUTION:Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A)
Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B)
Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C)
Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D)
Answer: Option C #### C
QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
options: A)69 B)78 C)96 D)56 E)48
SOLUTION:let the digits be x,y
x + y = 15
x - y = 3
2x = 18, x = 9 so y = 6
hence the number is 96
so the correct answer is option C) 96. #### C
QUESTION:Two numbers are in the ratio of 7:6. If 18 be subtracted from each, they are in the ratio of 6:5. Find the numbers?
options: A)5,9 B)7,9 C)4,7 D)7,6 E)6,9
SOLUTION:(7x-18):(6x-18) = 6:5
x = 1 => 7,6
Answer: D #### D
QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced?
options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None
SOLUTION:Explanation :
Time = 80*4 / 60 = 5 hours 33 mins
Answer – B #### B
QUESTION:What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each?
options: A)$3.36 B)$6.85 C)$8.46 D)$10.08 E)$12.46
SOLUTION:Answer = E
2 * 2.49 + 4 * 1.87
= 2 (2.50 - 0.01) + 4 (2.00 - 0.13)
= 5 + 8 - 0.02 - 0.52
= 13 - 0.54
= 12.46 #### E
QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive?
options: A)–5040 B)–3600 C)–720 D)–600 E)–120
SOLUTION:Maximize the total product with a -ve sign
so -1 * 10 * 9 * 8 = 720 * -1 = -720
Answer is C. #### C
QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases?
options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc
SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips
The answer is C. #### C
QUESTION:Venus travels around the sun at a speed of approximately 21.9 miles per second. The approximate speed is how many miles per hour?
options: A)64,420 B)78,840 C)83,160 D)88,970 E)94,320
SOLUTION:21.9 * 3600 = 78,840
The answer is B. #### B
QUESTION:It will take 16 days for Mary to complete a certain task alone. She worked for 8 days before she was joined by her sister. both of them completed the remaining task in 2 and half days. if her sister had joined her when she started the task, how many days would it have taken?
options: A)6 B)8 C)2 D)5 E)4
SOLUTION:Explanation:
Mary and her sister complete half work in 2.5 days
=> they can complete whole work in 5 days
Answer: Option D #### D
QUESTION:Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)
options: A)Rs. 8167 B)Rs. 4261 C)Rs. 4269 D)Rs. 4266 E)Rs. 4262
SOLUTION:Explanation:
CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266
Answer:D #### D
QUESTION:What is the sum of the local values of the digits 2, 3, 4, 5 in the number 2345?
options: A)2345 B)4500 C)5000 D)6000 E)7000
SOLUTION:2000 + 300 + 40 + 5 = 2345
ANSWER A #### A
QUESTION:A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
options: A)2.5 min B)3 min C)3.2 min D)3.5 min E)4 min
SOLUTION:Total distance = (7/2 + 1/4) miles
= 15/4 miles
time taken = 15/4*75 hrs
=1/20 hrs = 3 min
ANSWER B #### B
QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142
options: A)23 B)25 C)46 D)49 E)50
SOLUTION:(C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 . #### C
QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?
options: A)36 B)66 C)132 D)264 E)152
SOLUTION:12 * 396 = 36 * x
x = 132
ANSWER:C #### C
QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
options: A)56 B)28 C)45 D)24 E)45
SOLUTION:D
24
Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x <-> 27 x x = 36 x 18
x = (36 x 18)/27
x = 24 #### D
QUESTION:All of the citizens of a country have a four-character or five-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes?
options: A)37(36^4) B)36^9 C)35(36^5) D)37(36^5) E)35(36^9)
SOLUTION:The number of possible 4-digit codes is 36^4.
The number of possible 5-digit codes is 36^5.
The total sum is 36^4 + 36^5 = 36^4(1+36) = 37(36^4)
The answer is A. #### A
QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream?
options: A)30/18 hours B)37/13 hours C)80/13 hours D)20/9 hours E)30/43 hours
SOLUTION:Speed downstream = 20 + 7 = 27 kmph.
Time required to cover 60 km downstream
= d/s = 60/27
= 20/9 hours.
Answer: D #### D
QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is?
options: A)39 B)28 C)27 D)69 E)71
SOLUTION:1/2 * d (12 + 8) = 690
d = 69
Answer: D #### D
QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is:
options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these
SOLUTION:Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (45 x 2) = 90 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv)
Subtracting (i) from (iv), we get : B = 35.
B’s weight = 35 kg.
Answer: D #### D
QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
options: A)228 B)200 C)279 D)480 E)221
SOLUTION:SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480.Answer:D #### D
QUESTION:A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
options: A)42.3 B)560.45m C)79m D)26m E)111.12m
SOLUTION:Explanation:
A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
ANSWER E #### E
QUESTION:What is the difference between the local value of 1 and 2 in the number 2124?
options: A)70 B)75 C)20 D)80 E)60
SOLUTION:Explanation:
100 – 20 = 80
Answer: D #### D
QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ?
options: A)87 B)95 C)99 D)100 E)103
SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.
Answer: C. #### C
QUESTION:A card is drawn at random from a pack of 52 cards. What is the probability that it is neither a spade nor a jack?
options: A)9/13 B)4/13 C)2/13 D)6/13 E)5/13
SOLUTION:There are 13 spades including a jack and 3 more jacks of other suits.
Probability of getting spade or a jack:
= (13 + 3)/52
= 16/52
= 4/13
Therefore, the probability of getting neither a spade nor a jack:
= 1 − 4/13
= 9/13
ANSWER:A #### A
QUESTION:9, 16, 18, 25, 36,49
options: A)9 B)16 C)18 D)25 E)36
SOLUTION:Each of the numbers except 18, is perfect square.
Answer: Option C #### C
QUESTION:If 0 < m < 1 < n< 7, which of the following must be less than 1? I.m/n II. mn III. n - m
options: A)II,III only B)I,III only C)I only D)III only E)II only
SOLUTION:n > 1. So, option II, III is not possible.
So, Option I is correct.
Answer : C #### C
QUESTION:9log9(5) = ?
options: A)1 B)2 C)3 D)5 E)8
SOLUTION:Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
9log9(5) = 5
correct answer D #### D
QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
options: A)227 B)350 C)881 D)277 E)271
SOLUTION:Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: B #### B
QUESTION:The average of two numbers is P. If one number is Q, then the other number is
options: A)2Q B)2P C)P - Q D)2P-Q E)None of these
SOLUTION:Explanation :
Let the other number be x,
According to the question,
=> ( x + Q ) / 2 = P.
=> x + Q = 2P.
=> x = 2P - Q.
Hence, the required number is 2P - Q.
Answer : D #### D
QUESTION:in base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 1*72+3*7+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7?
options: A)11101 B)11110 C)10111 D)11011 E)11010
SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0)
3+4 + 1 carry from above step= 1 and 1 carry to next digit
2+5 + 1 carry to next digit= 1 and 1 carry
1+6= 11
so ans=11110
ANSWER:B #### B
QUESTION:Yesterday, a pie shop sold 6 apple pies, 5 peach pies, and 6 pumpkin pies. How many pies did the shop sell in all?
options: A)21 B)37 C)13 D)17 E)32
SOLUTION:Add the number of pies
6+5+6 =17.
Answer is D. #### D
QUESTION:Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid?
options: A)D + 40 B)D + H – 1 C)D + 2H D)6.93H E)1.21D
SOLUTION:before Discount price was: 1.4D+1.5H
After Discount: 1.4D +1.5H-.42D-.45H
substitute D=6H
final value: 6.93H
Ans Is D #### D
QUESTION:A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work?
options: A)20days B)15days C)30days D)45days E)50days
SOLUTION:10days work of A = 10/40 = 1/4
remaining work = 1-1/4 = 3/4
B can finish 3/4 work = 60*3/4 = 45days
Answer is D #### D
QUESTION:If the a radio is sold for Rs 490 and sold for Rs 465.50.find loss%.
options: A)4% B)5% C)6% D)3% E)5.5%
SOLUTION:sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Answer is B. #### B
QUESTION:A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
options: A)45 kmph B)50 kmph C)85 kmph D)60 kmph E)70 kmph
SOLUTION:Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 150/((x+5)×5/18)=6 <=> 30 (x + 5) = 2700 <=> x = 85
Speed of the train is 85 kmph.
Answer: Option C #### C
QUESTION:Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
options: A)a) 66.67-x B)b) 40-x C)c) 80-2x D)d) 120-x E)e) 40-x/2
SOLUTION:Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of:
R = (100 mi)/(1.5) = 66.67 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is x, and let's call the other y. We want y.
x + y = 66.67
y = 66.67 - x
Answer =(A) #### A
QUESTION:A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?
options: A)160 B)180 C)200 D)220 E)None
SOLUTION:Answer
Let the number be N.
Then, (N/5) + 4 = (N/4) - 4
⇒ (N/4) - (N/5) = 8
⇒ (5N - 4N)/20 = 8
∴ N = 160
Option: A #### A
QUESTION:a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase?
options: A)50 % B)60 % C)70 % D)80 % E)40 %
SOLUTION:let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit.
Nw he adds 10% milk ie total milk z 110 lit.
Now he will get 132 rs. by selling 110 lit f milk (120*110/100)
total profit = 32 rs
increased profit =12 rs
%age increase= 12/20= 60 %
ANSWER:B #### B
QUESTION:For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/8 + 8^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
options: A)1/3 B)1/5 C)1/6 D)1/7 E)1/8
SOLUTION:For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/3
Answer A #### A
QUESTION:Jimmy has a pot of soup, and he ate 1/5 of the soup for lunch. If Jimmy ate 1/6 of the remaining soup for dinner, what fraction of the soup was left after dinner?
options: A)1/2 B)2/3 C)3/4 D)4/5 E)5/6
SOLUTION:Let x be the amount of soup at the beginning.
After lunch, the remaining soup was (4/5)x.
After dinner, the remaining soup was (5/6)(4/5)x = (2/3)x.
The answer is B. #### B
QUESTION:Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
options: A)2 : 3 B)4 : 3 C)6 : 7 D)9 : 16 E)None
SOLUTION:Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √16 : √9
= 4 : 3.
Answer B #### B
QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5
SOLUTION:Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8
ANSWER:B #### B
QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 24th of September 1990?
options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday
SOLUTION:19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 24th September was a Monday.
The answer is A. #### A
QUESTION:The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home?
options: A)60% B)50% C)55% D)40% E)33.3%
SOLUTION:Increase = 168000-120000 = 48000
% increase = 48000*100/120000 = 40%
Answer: option D #### D
QUESTION:A tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
options: A) 1.25% B) 3.75% C) 9.33% D) 10.67% E) 11.7%
SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 700 gallons (7% of initial solution of 10,000 gallons) then sodium chloride is 700/7,500*100=~9.33% of the remaining solution of 7,500 gallons.
Answer: C. #### C
QUESTION:A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
options: A)2400 B)2880 C)2787 D)3087 E)0728
SOLUTION:1200 * 12: x * 9 = 2:3
x = 2400
Answer: A #### A
QUESTION:Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 35 as remainder
options: A)1235 B)1456 C)1567 D)1678 E)1631
SOLUTION:Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 35
5x = 1330
x = 266
Large number = 266+1365 = 1631
E #### E
QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?
options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours
SOLUTION:Explanation:
We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as
Work done for 1 hour without leak = 1/3
Work done with leak = 3 1/2=7/2
Work done with leak in 1 hr=2/7
Work done by leak in 1 hr=1/3=2/7=1/21
So tank will be empty by the leak in 21 hours.
ANSWER IS D #### D
QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble?
options: A)134 B)167 C)125 D)113 E)111
SOLUTION:C
lb : reverse the calculations:
So 48.75 ÷ 0.75 = 65,
65 ÷ 0.8 = 81.25 and
81.25 ÷ 0.65 = 125. #### C
QUESTION:A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?
options: A)126 Kmph B)136 Kmph C)172 Kmph D)128 Kmph E)19 Kmph
SOLUTION:Length = Speed * time
Speed = L/T
S = 700/20
S = 35 M/Sec
Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 126 Kmph
Answer: A #### A
QUESTION:A hall 36m long and 15m broad is to be paved with stones, each measuring 8dm by 5 dm. The number of stones required is:
options: A)180 B)1800 C)18 D)18000 E)1350
SOLUTION:Area of the hall= 3600*1500
Area of each stone= (80*50)
Therefore, number of stones= (3600*1500/ 80*50)= 1350
ANSWER:E #### E
QUESTION:The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:8, the price of the cheapest item is?
options: A)2379 B)2889 C)5625 D)9000 E)28311
SOLUTION:Let their prices be 3x, 5x and 7x.
Then, 2x + 6x + 8x = (15000 * 3) or x = 2812.5.
Cost of cheapest item = 2x = Rs. 5625.
Answer: C #### C
QUESTION:If five chimpanzee can eat five mangoes in five minutes.
How many minutes would it take for four chimpanzee to eat four mangoes ?
options: A)5 minutes B)10 minutes C)8 minutes D)14 minutes E)20 minutes
SOLUTION:A
5 minutes #### A
QUESTION:If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many C such committees are possible?
options: A)20 B)40 C)C=50 D)C=80 E)C=120
SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D. #### D
<<<Examples ends
QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z?
options: A)50% B)40% C)37.5% D)331⁄3% E)25%
SOLUTION:Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) Q= 3/8 = 37.5%
Answer (C) #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4
options: A)II,III only B)I only C)I,III only D)II only E)III only
SOLUTION:question is asking for must be there elements.
According to the question if t is there t+4 must be there.
if -3 is the starting element the sequence is as follows.
S ={-3,1,5,9....}
if -3 is not the starting element the sequence is as follows
S = {...-7,-3,1,5,9...}
By observing the above two sequences we can say that 9 must be there in set S.
Answer : B #### B
QUESTION:The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
options: A)1752 B)1799 C)1719 D)1750 E)1800
SOLUTION:Speed = [216 * 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 60 è x = 60 * 60 / 2 = 1800
Answer: E #### E
QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit
SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1
[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1
[(5.4 + 2.4 + 1.8)/8] - [8/8]
+1.6/8
+20%
answer is D #### D
QUESTION:How many 3 digit positive integers T exist that when divided by 7 leave a remainder of 5?
options: A)128 B)142 C)143 D)141 E)129
SOLUTION:Minimum three digit number is 100 and maximum three digit number is 999.
The first three digit number that leaves remainder 5 when divided by 7 is 103.
14 * 7 = 98 +5 = 103
The second three digit number that leaves remainder 5 when divided by 7 is 110.
15 * 7 = 105 +5 =110
The third three digit number that leaves remainder 5 when divided by 7 is 117
and so on
The last three digit number that leaves remainder 5 when divided by 7 is 999
142 * 7 = 994 + 5 = 999
Therefore, we identify the sequence
103,110,117.....999
use the formula of last term
Last term = first term + (n - 1) * common difference
you will get the answer 129 that is definitely E. #### E
QUESTION:The 7th grade French and Spanish classes each have 26 students in them, and there are nine students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
options: A)26 B)28 C)30 D)32 E)34
SOLUTION:French class + Spanish class = 52 students.
Nine students are in both classes so they were counted twice.
The number of students taking just one class is 52 - 2(9) = 34.
The answer is E. #### E
QUESTION:In how many ways can 4 men & 3 women can be made from a gang of 6 men & 7 women ?
options: A)10 hr B)50 C)20 D)250 E)260
SOLUTION:Explanation:
6C4 * 7C3 = 50
B #### B
QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour?
options: A)181 B)211 C)241 D)271 E)301
SOLUTION:In 2/5 of an hour there are 24*60 = 1440 seconds
The number of 6-second intervals = 1440/6 = 240
After the first flash, there will be 240 more flashes for a total of 241.
The answer is C. #### C
QUESTION:A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
options: A)25 B)37 C)36 D)29 E)21
SOLUTION:Explanation:
From the information provided we know that,
Principal + 8% p.a. interest on principal for n years = 180 …….. (1)
Principal + 4% p.a. interest on principal for n years = 120 ……… (2)
Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60.
Now, we can substitute this value in equation (2),
i.e Principal + 60 = 120
= Principal = Rs.60.
We know that SI = , where p is the principal, n the number of years and r the rate percent of interest.
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 =(60*n*4)/100
=> n = 100/4 = 25 years.
Answer: A) 25years #### A
QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage
options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain
SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100
= (750 ~ 1020)/1020 = 26% Loss
A #### A
QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is:
options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62
SOLUTION:(3x-9):(5x-9) = 3:2
x = 1 => 3x = 3
Answer:A #### A
QUESTION:Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
options: A)1/19 B)1/20 C)1/23 D)2/17 E)1/17
SOLUTION:(2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
B) #### B
QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years?
options: A)587 × 108 miles B)587 × 10-12 miles C)587 × 1010 miles D)587 × 10-10 miles E)587 × 1012 miles
SOLUTION:The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
Answer is B. #### B
QUESTION:If x is divisible by 2 and 7, which of the following must divide evenly into x? I. 60 II. 32 III. 14
options: A)I,II only B)I,III only C)I only D)III only E)II only
SOLUTION:If x is divisible by 2,7 means it will be = or > 14, 28,42 etc...
That are not divisible by 60, 32.
So, the answer is D #### D
QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:Solution
Radius = Area / Semi perimeter
= [Area x 2 / Area]
= 2.
Answer B #### B
QUESTION:If f is a function defined for all k by f(k) = k^3 /16, what is f(2 k) in terms of f(k)?
options: A)1/8 f(k) B)8 f(k) C)2 f(k) D)10 f(k) E)32 f(k)
SOLUTION:f(k) = k^3 /16
f(2k) = (2k)^3 /16 =8 * k^3/16 = 8 x (k^3 /16) = 8 f(k).
So answer is B. #### B
QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.
options: A)7/18 B)7/19 C)7/11 D)7/12 E)7/15
SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ways.
7/15
Answer: E #### E
QUESTION:A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers?
options: A)330 B)650 C)729 D)800 E)890
SOLUTION:Choose 4 starters from a team of 11 players. Order is not important.
\inline {\color{Black} 11C_{4}}= 330
A #### A
QUESTION:Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 60 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
options: A)2hrs, 48mins B)7hrs, C)7hrs, 12mins D)13hrs, 4mins E)14hrs, 24mins
SOLUTION:The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/60 --> x=1/420--> (time) = (reciprocal of rate) = 392 minutes = 7 hours
Answer: B. #### B
QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have?
options: A)27 B)32 C)43 D)54 E)77
SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys
49 - 5 = 44 for Tom and Bob
If distributed equally, each one will have
44 / 2 = 22 toys
Bob has 5 more toys than Tom, so Bob has
22 + 5 = 27 toys
correct answer A #### A
QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed?
options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5!
SOLUTION:Explanation:
Total number of letters = 5
Using these letters the number of 5 letters words formed is 5!.
Answer: Option E #### E
QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square?
options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5)
SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square?
I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means
Vertex #1 = (c, d) is in QII (that is, negative x and positive y)
Vertex #2 = (c, -d) is in QIII (that is, both xy negative)
Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)
That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E
QUESTION:If x ≠ 1 and if yx/(y - x) = 1, what is the value of y in terms of x?
options: A)(1-x)/x B)(x - 1)/x C)x/(x + 1) D)(x + 1)/x E)x/(1-x)
SOLUTION:This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
E #### E
QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P?
options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36
SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house.
J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs
Answer:B #### B
QUESTION:If -1 < x < 0, which of the following must be true?
I. x^4 < x^3
II. x^6 < 1 – x
III. x^5 < x^2
options: A)I only B)II only C)III only D)II,III only E)I,II,III only
SOLUTION:Answer : E #### E
QUESTION:There are different 15 circles. What is the number of the greatest possible points with which the circles intersect?
options: A)390 B)100 C)110 D)180 E)210
SOLUTION:Maximum points of intersection between n different circles = n*(n - 1) = 15*14 = 210
Answer: E #### E
QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h?
options: A)6 B)12 C)24 D)36 E)48
SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24.
ANS :C #### C
QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C?
options: A)2250 B)3000 C)3018 D)3019 E)3012
SOLUTION:60*5:36*6:75*3
100: 72: 75
75/247 * 7410 = 2250
Answer: A #### A
QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms?
options: A)6 1â„7 hours B)6 2â„7 hours C)8 2â„7 hours D)Cannot be determined E)None of these
SOLUTION:Distance covered in first two hours = 8 × 2 = 16 km
Distance covered in next two hours = 10 × 2 = 20 km
Distance covered in next two hours = 12 × 2 = 24 km
Distance covered in first six hours
16 + 20 + 24 = 60 km
Remaining distance = 64 – 60 = 4 km.
Now, this distance will be covered at the speed of 12 km/hr.
∴ Time taken = 4â„12 = 1â„3 hour.
Total time= 6 + 1â„3 = 6 1â„3 hour
Answer E #### E
QUESTION:35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
options: A)87 B)18 C)42 D)16 E)10
SOLUTION:Binders Books Days
35 1400 21
x 1600 20
x/35 = (1600/1400) * (21/20) => x = 42
Answer:C #### C
QUESTION:What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, x
options: A)214 B)215 C)213 D)320 E)216
SOLUTION:Go on dividing by 6 to the next number
Answer : E #### E
QUESTION:An old priest fell on a bottom of the well of a church.
The well is 16 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
options: A)12-days B)14-days C)11-days D)19-days E)10-days
SOLUTION:A
12-days
In 11-days, he will climb 11-inch and when he climbs 5 inch more, he will be out of the well :-) #### A
QUESTION:Sandy can do a job in 12 days and Molly can do the same job in 24 days. If they work together, in how many days will they complete the job?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:Sandy can do 1/12 of the job each day.
Molly can do 1/24 of the job each day.
The combined rate is 1/12 + 1/24 = 1/8 of the job each day.
The job will take 8 days.
The answer is C. #### C
QUESTION:One type of liquid contains 10% of water and the second type of liquid contains 15% of water. A glass is filled with 5 parts of 1st liquid and 2 parts of 2nd liquid. The percentage of water in the new mixture in the glass is?
options: A)5.6% B)11.4% C)15.6% D)21.3% E)18.9%
SOLUTION:Required percentage = (10% of 5 + 15% of 2)/5+2 *100
= 0.8/7 * 100 = 11.4%
Answer is B #### B
QUESTION:Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
8 minutes more to walk to work than to ride his bicycle, then x equals
options: A)4 B)7 C)12 D)15 E)20
SOLUTION:The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 8 mins or 8*60 secs in 8*60/40 =12 km
ANSWER:C #### C
QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0
options: A)-1 B)1 C)-2 D)2 E)-3
SOLUTION:a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A #### A
QUESTION:If watches bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425. What is the greatest possible profit that might be made in selling eight watches?
options: A)Rs 900 B)Rs 800 C)Rs 1,800 D)Rs 2,800 E)None of these
SOLUTION:Profit would be maximum if watches are brought for Rs 200 and sold for Rs 425
Profit = Rs (425 - 200) = Rs 225
Profit of 8 watches = Rs 225 x 8 = Rs 1,800
ANSWER:B #### B
QUESTION:A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum?
options: A)337 B)268 C)198 D)697 E)168
SOLUTION:1200 = P [1 + (12*6)/100]
P = 697'
Answer:D #### D
QUESTION:If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b?
options: A)35 B)42 C)45 D)49 E)54
SOLUTION:First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
35 = 7 * 5
45 = 3 * 3 * 5
so, (105)^3 = 3 * 7 * 7 * 5 * 3 *3 *5 *b
Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2
b = 5*7 = 35
Correct answer A. #### A
QUESTION:After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B?
options: A)N/15 B)7N/8 C)14N/15 D)N/5 E)4N/5
SOLUTION:1/4 of tested had infection A, thus N/4 had infection A;
Of those with infection A, 1/2 also had infection B, thus 1/2*N/4 = N/8 had both infections A and B.
Therefore, N - N/8 = 7N/8 did not have both infection A and B.
Answer: B. #### B
QUESTION:If n is an integer greater than 8, which of the following must be divisible by 3?
options: A)1. n (n+1) (n-4) B)2. n (n+2) (n-1) C)3. n (n+3) (n-5) D)4. n (n+4) (n-2) E)5. n (n+5) (n-6)
SOLUTION:We need to find out the number which is divisible by three,
In every 3 consecutive integers, there must contain 1 multiple of 3.
So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three
1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)
2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)
3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)
4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)
5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)
from the above onlyoption Ais product of consecutive three numbers.
C #### C
QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740
SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All two
2. One symmetry and other two non
4. All the two letters can be arranged in 2 ways
( 11c2+ 11c1 * 15c2) *2
( 11*10/ 2 + 11 * 15 * 14 / 2 ) * 2
2420
IMO option D is the correct answer..
OA please...will correct if I missed anything..D #### D
QUESTION:R campers fished for 2 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour?
options: A)2m + n(R-m) B)(2m + n(R-m))/3 C)(2m + n(m-R))/3 D)(2m + n)/2 E)(2m + n)/R
SOLUTION:m of the campers caught 2 fish apiece in 2 hours --> total fish caught by m campers = 2m;
The rest caught a combined total of n fish.
Total fish caught in 2 hours = 2m+n --> per hour (2m+n)/2.
Answer: D. #### D
QUESTION:The diameter of a garden roller is 1.4 m and it is 3 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7)
options: A)60 m2 B)64 m2 C)68 m2 D)66 m2 E)None of these
SOLUTION:Required area covered in 5 revolutions
= 5 × 2Ï€rh = 5 × 2 × 22â„7 × 0.7 × 3 = 66 m2
Answer D #### D
QUESTION:A train 480 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
options: A)22 kmph B)108 kmph C)54 kmph D)71 kmph E)88 kmph
SOLUTION:S = 480/16 * 18/5 = 108 kmph
Answer:B #### B
QUESTION:A Cone, a hemisphere and a cylinder stand on equal bases and have the same height .Find ratio of their volumes.
options: A)2:1:3 B)2:1:4 C)1:2:3 D)4:1:7 E)5:1:8
SOLUTION:Let R be the radius of each
Height of the hemisphere = Its radius = R.
Height of each = R.
Ratio of volumes = (1/3)∏ R2 x R : (2/3)∏R3 : ∏ R2 x R = 1:2:3
ANSWER C 1:2:3 #### C
QUESTION:Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
options: A)12 to 1 B)6 to 1 C)5 to 1 D)20 to 7 E)1 to 5
SOLUTION:The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job;
The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 3*7=21
The ratio thus is 60 to 21, or 20 to 7.
Answer: D. #### D
QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers?
options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr
SOLUTION:speed of man = 20km/hr
number of rests = (120/30)-1 = 3
time taken for the man = (120/20)+3*(20/60) = 7 hr
Answer is D #### D
QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
options: A)1 B)2 C)8 D)7 E)0
SOLUTION:S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C #### C
QUESTION:A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?
options: A)124 sq.ft. B)120 sq.ft. C)126 sq.ft. D)129 sq.ft. E)132 sq.ft.
SOLUTION:Let l = 9 ft.
Then l + 2b = 37
=> 2b = 37 - l = 37 - 9 = 28
=> b = 28/2 = 14 ft
Area = lb = 9 × 14 = 126 sq. ft.
Answer is C. #### C
QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies
options: A)231 B)150 C)200 D)450 E)451
SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
Ans: C #### C
QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females?
options: A)16% B)25% C)30% D)40% E)52%
SOLUTION:We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 45 are employed males, hence 19% are employed females.
(employed females)/(total employed people)=19/64=30%
Answer: C. #### C
QUESTION:A gold mine has 5% depletion rate. i.e. after each year of mining, the miners extract 5/100 of the mine's ore. If the current quantity of the gold reserves of the mine is currently estimated at 2 tons, how much gold would the miners be able extract over the next 4 years?
options: A)0.400 tons B)0.200 tons C)0.175 tons D)0.160 tons E)0.185 tons
SOLUTION:X is the quantity of gold reserves of the mine
After a year of mining the quantity of gold left would be X1=X-5/100X i.e. X1=95/100X
Same thing for X2, X3, X4, respectively representing the quantity of gold left after 2, 3, 4 years of mining.
So we have:
X1=95/100 X
X2=95/100 X1
X3=95/100 X2
X4=95/100 X3
By multiplying both ends of the equations we get:
X1*X2*X3*X4 = (95/100)^4 X*X1*X2*X3
Simplification leaves us with:
X4 = (95/100)^4 X
X4 is the quantity of gold left after four years of mining. So the cumulative quantity of gold (Q4) which has been extracted after 4 years is: Q4= X-X4=X-(95/100)^4X i.e. Q4 = X (1-(95/100)^4)
In this case, given X was: X=2 tons
So Q4 = 2 * (1-(95/100)^4) = 2 * (1-81450625/10^8) =2 * 18549375/10^8 = 0.1854 tons round to Q4=0.185 ton
Answer E. #### E
QUESTION:Evaluate combination
100C100
options: A)10000 B)1000 C)10 D)1 E)0
SOLUTION:Explanation:
nCn=1
100C100=1
Option D #### D
QUESTION:Denise is trying to open a safe whose combination she does not know. IF the safe has 3000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one correct combination.
options: A)1 B)159/160 C)157/160 D)0.875 E)0.975
SOLUTION:If Denise does not pick the correct combination in first 75 try, then the correct combination is one of remaining 2925. So Probability = 2925/3000 = 0.975.
answer is E #### E
QUESTION:The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices.
options: A)220. B)205. C)250 D)105 E)225
SOLUTION:different ways..
1) EASIEST approach..
lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220...
Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15..
total = 220-15 = 205
ANSWER:B #### B
QUESTION:The factorial expression 10!/2! is not divisible by which of the following integers?
options: A)3 B)5 C)6 D)7 E)None of these
SOLUTION:10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3
(A) 3 Can divide 12 or 9
(B) 5 Can divide 10
(C) 6 Can divide 12
(D) 7 can divide 7,21,28
Hence answer will be (E) #### E
QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease
SOLUTION:100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B #### B
QUESTION:In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can?
options: A)52 B)56 C)60 D)64 E)68
SOLUTION:Let C be the capacity of the can.
(5/8)*(C-20)+20=(3/4)*C
5C-100+160=6C
C=60
The answer is C. #### C
QUESTION:In a friendship gang Angel has 3 gang, in how many ways can he invite one or more of the gang to his house?
options: A)58 B)5 C)12 D)9 E)7
SOLUTION:Angel can select one or more than one of his 8 gang.
=> Required number of ways = 2^3 – 1= 7.
E #### E
QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :
options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 5
SOLUTION:Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 495
99c - 99a = 99(c - a) = 495
495 = 99*5 = 99(c - a)
So c - a = 5
Answer (E) #### E
QUESTION:If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number?
options: A)20 B)22 C)27 D)28 E)30
SOLUTION:Given Ratio => 2:3
2x - 10 : 3x - 10 = 2 : 4
4[2x - 10] = 2[3x - 10]
8x - 40 = 6x - 20
8x - 6x = 40 - 20
x = 10
Then biggest number is = 3x
3x = 30
Ans = E #### E
QUESTION:Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?
options: A)14 mph B)20 mph C)70/3 mph D)80/3 mph E)30 mph
SOLUTION:Average speed for first two hours, S1 = 30 mph
Distance travelled in these two hours, D1 = 60 miles
Average speed for the entire 5 hour ride, S = 30 mph
Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90
Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30
Hence, the correct answer is E #### E
QUESTION:The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ?
options: A)6 years B)7 years C)8 years D)9 years E)None
SOLUTION:Answer
Let the age of youngest child be y.
so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12
⇒ 4y + 24= 48
∴ y = 6 years
Correct Option: A #### A
QUESTION:A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday
SOLUTION:This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.
To show the correct time, it has to gain 5 min.
So the correct time will be shown on wednesday at 7:20 PM
Answer: B #### B
<<<Examples ends
QUESTION:A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 117 pounds?
options: A)8 B)7 C)12 D)9 E)none of the above
SOLUTION:Ans is C:
39 pounds --> 6 days
117 pounds --> x days
x = 117*6/39 = 18
the animal has already consumed food in 6 days so the the number of days
for it's total consumption be 117 pounds is 18-6 = 12 #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
options: A)$140 B)$141 C)$142 D)$147 E)$145
SOLUTION:Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 147.
So after completing the 1st week she will get $ (x+147).
Similarly after completing the 2nd week she will get $ (x + 147) + $ 147.
= $ (x + 147 + 147)
= $ (x + 294)
So in this way end of every week her salary will increase by $ 147.
correct answer D)$147 #### D
QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?
options: A)409 B)1636 C)16360 D)16000 E)15360
SOLUTION:terms in this sequence are 7,12,17----402
now since this is an a.p. with a common difference of 5. therefore its sum can be given as
a(f+l)/2----------------1)
a= total no. of terms =80
f= first term=7
l= last term=402
subsituting values in the expression 1 we have
80(7+402)/2
= 40(409)
=16360=C #### C
QUESTION:A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is
options: A)3 B)7 C)21 D)189 E)267
SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be D #### D
QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0
SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100%
=> The required ratio = 100%/25% = 4.0
Answer : B #### B
QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
options: A)3% B)4% C)5% D)6% E)7%
SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate =(100 x 3000)/(12500 x 4)% = 6%
answer :D #### D
QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours?
options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44)
SOLUTION:Explanation:
Here clock-wise and anti-clockwise arrangements are same.
Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}}
Answer: C) 18!(6 x 24) #### C
QUESTION:At what rate percent per annum will a sum of money double in 8 years.
options: A)12.5% B)13.5% C)11.5% D)14.5% E)21.5%
SOLUTION:Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum. Answer: A #### A
QUESTION:Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol.
What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol?
options: A)32 B)21 C)27 D)None of these E)18
SOLUTION:Explanation:
Let t be the time after Kajol starts, when she meets Ajay, then
\inline t=\frac{300}{(x+y)}
This should be less than 2.5 or (x+y)>120
Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72
This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol.
Answer: D #### D
QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:Solution
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
Tens place can be filled by any of the remaining 5 numbers.
So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it.
So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D
QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
options: A)320 B)350 C)340 D)360 E)400
SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(912-9-90*2)/3=340
Answer : C #### C
QUESTION:A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
options: A)1/10 B)1/8 C)1/6 D)1/5 E)1/4
SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 5*3*2=30.
P(dispensing one of each color)=30/120=1/4.
The answer is E. #### E
QUESTION:A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
options: A)Rs.3178 B)Rs.3120 C)Rs.3127 D)Rs.3121 E)Rs.3122
SOLUTION:Explanation:
Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B #### B
QUESTION:Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 249 marks in the second test and failed by 66 marks in that test. Find the pass mark in the first test?
options: A)768 B)243 C)246 D)280 E)224
SOLUTION:Let the maximum mark in each test be M.
The candidate failed by 66 marks in the second test.
pass mark in the second test = 249 + 66 = 315
45/100 M = 315
Pass mark in the first test = 40/100 M = 40/45 * 315 = 280.
Answer:D #### D
QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350
SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C #### C
QUESTION:Two trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ?
options: A)10.7 Seconds B)10.8 Seconds C)10.9 Seconds D)11.8 Seconds E)None of these
SOLUTION:Explanation:
Relative Speed = 60+40 = 100 Kmph
= 100*(5/18) = 250/9 m/sec
Distance to be covered = 140 + 160 = 300 metres
Time = Distance/Speed
Time=300∗9/250=54/5=10.8 seconds
Option B #### B
QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?
options: A)767 km B)975 km C)678 km D)900 km E)546 km
SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.
x/40 = (x + 100)/50
50x = 40x + 4000 => x = 400
So, distance between P and Q = (x + x + 100)km =900 km.
Answer: D #### D
QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly?
options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20
SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/5*1/4 = 9/10.
Answer: D. #### D
QUESTION:What percent of a day is 15 hours?
options: A)37×1/2% B)16×1/2% C)18×2/3% D)22×1/2% E)None
SOLUTION:Solution
Required percentage = (15/24×100)%
= (75 / 2)%.
= 37×1/2%.
Answer A #### A
QUESTION:The two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?
options: A)16 B)3/√2 C)8 D)2√2 E)(√2)/3
SOLUTION:800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(3 × 3) = 9/2; so z = 9/2.
The next step requires us to find the length of a side of a cube that has a face area equal to 9/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 9/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 9/2. Clearly s = √9/2 = 3/√2 , oranswer choice (B). #### B
QUESTION:A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work ?
options: A)30 days B)15 days C)45 days D)24 days E)None of these
SOLUTION:Let C completes the work in x days.
Work done by (A + B) in 1 day = 1⁄10
Work done by (B + C) in 1 day = 1⁄18
A’s 5 days’ work + B’s 10 days’ work + C’s 15 days’work = 1
or (A + B)’s 5 days’ work + (B + C)’s 5 days’ work + C’s 10 days’ work = 1
or 5⁄10 + 5⁄18 + 10⁄x = 1 or x = 45 days
Answer C #### C
QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?
options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280
SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet.
The number of revolutions = distance/circumference = 5,280z/y.
Answer: A. #### A
QUESTION:In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
options: A)L(L-N) /L-M B)L(N-M) / L-M C)L-N D)M-N E)M+
SOLUTION:the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:
L = 200
M = 10
N =20.
So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect, A.
Out of which, i choose A. #### A
QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
options: A)6 B)4 C)2 D)5 E)1
SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
ANSWER B #### B
QUESTION:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth?
options: A)39 B)24 C)28 D)26 E)30
SOLUTION:x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
x+32
x+36
10x+180=340
10x=160
x=16
3rd question = x+8 = 16+8 = 24
Answer B #### B
QUESTION:A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream?
options: A)6 hr B)2 hr C)4 hr D)1 hr E)None of these
SOLUTION:Explanation :
Speed downstream = 96⁄8 = 12 kmph
Speed of current = 4 km/hr
Speed of the boatman in still water = 12-4 = 8 kmph
Speed upstream = 8-4 = 4 kmph
Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B #### B
QUESTION:In a division, divident is 725, divisior is 36 and quotient is 20. Find the remainder.
options: A)A)4 B)B)3 C)C)2 D)D)5 E)E)6
SOLUTION:Explanation:
725 = 36 x 20 + r
725 = 720 + r
r = 725 - 720 = 5
Answer: Option D #### D
QUESTION:What is the different between the place value and face value of 6 in the numeral 5468?
options: A)45 B)54 C)60 D)36 E)44
SOLUTION:place value of 6 = 6 * 10 = 60
face value of 6 = 6
60 - 6 = 54
Answer is B #### B
QUESTION:If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king?
options: A)6/13 B)7/10 C)4/11 D)7/13 E)5/26
SOLUTION:There are 26 black cards and 2 red kings.
P(black card or king) = 28/52 = 7/13
The answer is D. #### D
QUESTION:The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?
options: A)625 B)298 C)269 D)200 E)267
SOLUTION:Let the sum be Rs. x. Then,
[x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x
S.I. = (x * 4 * 2)/100 = 2x/25
51x/625 - 2x/25 = 1 or x = 625.Answer: A #### A
QUESTION:With 630 ml mixture of milk & water in the ratio 7:2. How much water mustbe added to make the ratio 7:3?
options: A)60 ml B)80 ml C)70 ml D)90 ml E)92 ml
SOLUTION:concentration of water in mixture1
=2/9 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2
=3/10
By rule of alligation,
concentration of water in mixture1
(2/9) concentration of water in pure water (1)
Mean concentration
(3/10)
1−3/10=7/10
=1:19
=> Quantity of water
=630×1/9=70 ml
C #### C
QUESTION:What is the remainder when 1014*1047*1050*1053 is divided by 33?
options: A)3 B)6 C)30 D)21 E)18
SOLUTION:OA is 'C'.
OE:
take the remainder from each of 1044/33, 1047/33 and so on..
1014/33 gives remainder = 24
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e = 24*24*27*30
break them into pairs 24*24/33 gives remainder 15
and 27*30/33 gives remainder 18
so 15*18/33 gives remainder 6.
B #### B
QUESTION:Two coins are tossed, find the probability that two Tails are obtained
options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3
SOLUTION:The sample space S is given by.
S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two heads are obtained".
E = {(T,T)}
P(E) = n(E) / n(S) = 1/4
B #### B
QUESTION:Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 4 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
options: A)30 B)20 C)18 D)12 E)6
SOLUTION:21-12 < no of hrs < 21-6
9< no of hrs < 17.
D #### D
QUESTION:A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform?
options: A)39.9 B)37.88 C)35 D)38.88 E)38.09
SOLUTION:Speed = [200 / 42] m/sec = 100/21 m/sec.
Let the length of the platform be x meters.
Then, x + 200 / 50 = 100/21
21(x + 200) = 5000 è x = 38.09 m. Answer: E #### E
QUESTION:If you throw two dice at a same time.
Can you find the probability of getting sum as 10 of the two numbers shown ?
options: A)1/16 B)2/14 C)1/12 D)1/19 E)1/17
SOLUTION:C
1/12
All possible cases can be 36 (6*6)
Case we need : [(4,6), (5,5), (6,4)] = 3
probability => 3/36 = 1/12 #### C
QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
options: A)11 B)77 C)36 D)47 E)99
SOLUTION:Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer:D #### D
QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash?
options: A)1000 B)3000 C)3500 D)2500 E)2250
SOLUTION:For 20 staffs: 300*100*20 = 60000
for driver and cleaning staff: 300*100*2 =6000
From petty Cash : 1000
Answer is 1000 #### A
QUESTION:Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 192, what is the area of the side face of the box?
options: A)13 B)16 C)18 D)29 E)32
SOLUTION:Lets suppose length= l, breadth= b, depth= d
Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l)
top face area= w*d
side face area= w*d = 1.5 d*l (w=1.5l)
Volume = l*w*d= 192
l*1.5l*2l= 192
l=4
Side face area= l*d= l*2l= 4*2*4
=32
E is the answer #### E
QUESTION:The sum of the non-prime numbers between 10 and 20, non-inclusive, is
options: A)60 B)75 C)90 D)105 E)120
SOLUTION:sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 * # of terms = (11 + 19)/2 * 9 = 15 *9 = 135
sum of non-prime numbers b/w 10 and 20, non inclusive ===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75
Answer: B #### B
QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
options: A)4/17 B)4/18 C)4/76 D)4/13 E)4/29
SOLUTION:P(SᴜK)
= P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK)
= 13/52 + 4/52 - 1/52
= 4/13
Answer: D #### D
QUESTION:The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
options: A)1/2 B)3/4 C)3/5 D)3/7 E)4/9
SOLUTION:Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B #### B
QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A - B is also a Even number.
(3) A^B is also a prime number.
options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3.
SOLUTION:Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A - B is also a Even number. : True
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans : C #### C
QUESTION:In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Roslin played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Roslin could have gotten?
options: A)30 B)25 C)20 D)15 E)10
SOLUTION:There are two conditions:
1. Roslin got at least one score of each of 1, 2, 3, 4, and 5.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Roslin could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30.
Answer: A. #### A
QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
options: A)1 B)7 C)3 D)8 E)5
SOLUTION:40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer: D #### D
QUESTION:There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?
options: A)36 B)77 C)88 D)99 E)22
SOLUTION:Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1)
Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get
=> 2r = 72 => r = 36.
Answer: A #### A
QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years?
options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 %
SOLUTION:Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11)
= 100/11 = 9.09 %
ANSWER:A #### A
QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction?
options: A)10% B)5% C)12% D)6% E)4%
SOLUTION:In such a case there is always a loss
Loss% = (20/10)^2 = 4%
Answer is E #### E
QUESTION:What is the area of a square field whose diagonal of length 20 m?
options: A)228 B)271 C)200 D)277 E)181
SOLUTION:d2/2 = (20 * 20)/2 = 200
Answer:C #### C
QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B?
options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above
SOLUTION:et ratio of A and B be 6x & 7x
so net loss = 6x+7x= 7800
x=600
A=6x=6(600)=3600
B= 7x=7(600)=4200
so, B= 4200
ANSWER:A #### A
QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES
SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 .
Number of pages typed by Kumar in 1 hour = 40/5 = 8.
Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 .
Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours
= 8 hours 15 minutes. ANSWER : E #### E
QUESTION:If w is a positive integer, then 3^w + 3^(w +1) =
options: A)4^a B)3^a − 1 C)3^(2a) + 1 D)3^a*(a − 1) E)4(3^w)
SOLUTION:3^w + 3^(w +1)
= 3^w + (3^w * 3^1)
= 3^w (1 + 3)
= 3^w(4)
Ans. E) 4(3^w) #### E
QUESTION:If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72?
options: A)24 B)36 C)12 D)18 E)16
SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.
72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12
C #### C
QUESTION:Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit?
options: A)1% B)2% C)3% D)4% E)5%
SOLUTION:A dozen toys cost $360, so each toy cost $30.
selling price / cost price = 30.60 / 30 = 1.02
The percentage profit is 2%.
The answer is B. #### B
QUESTION:If a person throw 2 dice simultaneously then find the probability of the sum of dots is 3 multiply ?
options: A)1/2 B)1/3 C)2/5 D)7/9 E)1/4
SOLUTION:If 2 dies are thrown E = event of getting a prime number = 12
total number of possible out comes = 36
probability = 12/36 = 1/3
Answer is B #### B
QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5
SOLUTION:Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8
ANSWER:B #### B
QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
options: A)9 B)10 C)11 D)12 E)13
SOLUTION:35 + 30 + 20 = 85
This number includes some people counted twice and some people counted three times.
85 - 66 = 19, and this number represents people counted twice or three times.
8% of the people are counted two extra times.
The percentage of people counted one extra time is 19 - 8(2) = 3.
The percentage of people who liked more than one product is 8% + 3% = 11%.
The answer is C. #### C
QUESTION:In a mixture of 60 liters, the ratio of milk and water is 4:1. What amount of water must be added to make the ratio of milk and water as 1:4?
options: A)60 liters B)42 liters C)68 liters D)65 liters E)62 liters
SOLUTION:4:1 --- 60
1:4
2:8
---------------
5
5 ----------- 60
5 ----------- ? => 60 liters
ANSWER:A #### A
QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present?
options: A)16 B)17 C)10 D)18 E)15
SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 2 = 26 => x = 8
Deepak's age = 3x = 18 years.
Answer: D #### D
QUESTION:A vendor bought Headphones at 5 for Rs 100.How many for Rs 100 must he sell to gain 50%?
options: A)8 B)3 C)5 D)6 E)None
SOLUTION:C.P. of 9 Headphones= Rs100
S.P. of 9 Headphones = 150% of Rs 100 = Rs150
For Rs.150 , Headphones sold = 9.
For Rs. 100,Pens sold=(9/150)*100=6
Answer: Option D #### D
QUESTION:Ayush was born two years after his father's marriage. His mother is five years younger than his father but 25 years older than Ayush who is 10 years old. At what age did the father get married ?
options: A)28years B)29years C)30years D)31years E)32years
SOLUTION:Explanation:
Ayush's present age = 10 years.
His mother's present age = (10 + 25) years = 35 years.
Ayush's father's present age = (35+ 5) years = 40 years.
Ayush's father's age at the time of Ayush's birth = (40 - 10) years = 30 years.
Therefore Ayush's father's age at the time of marriage = (30 - 2) years = 28 years.
Answer: A) 28 year #### A
QUESTION:Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 40 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
options: A)4:5 B)9:25 C)5:4 D)25:9 E)Cannot be determined from the information provided
SOLUTION:Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B
Time A = 2*pi*25/Speed A
Time B = 2*pi*20/Speed B
Since the times are same,
50pi/Speed A = 40pi/Speed B
SpeedA/Speed B = 50pi/30pi = 5/4
Correct Option: C #### C
QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling?
options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr
SOLUTION:Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*50 = 2500m = 2.5km
Speed = 60*2.5=150km/hr
Answer is D #### D
QUESTION:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 140800, how many purple chips were selected?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:140800 = 1*5^2*8^3*11
The factors of 8 must come from the purple point value, so there are 3 purple chips.
The answer is C. #### C
QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7740 km and comes back to the starting point. The total time taken by him is:
options: A)914.2 hours B)900 hours C)915 hours D)982.9 hours E)915 hours
SOLUTION:Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7740/18 + 7740/14 = 430 + 552.9 = 982.9 hours
Answer: Option D #### D
<<<Examples ends
QUESTION:Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east?
options: A)3.625 B)3 C)4.5 D)4 E)3.5
SOLUTION:Set up two R x T =D cases.
1. 1/12 km/ min x T = 2.75
from which T= 33 mins.
We know total journey time now is 51 +33 =84.
The rate is the same ie 1/12km/min.
set up second R x T =D case.
1/12 km/min x 84 = 7 km
Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5
E. #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 10 seconds. Find the length of the train and its speed.
options: A)10 m/sec B)15 m/sec C)18 m/sec D)19 m/sec E)25 m/sec
SOLUTION:If length of train is l and speed of train is s, then
l/s = 10
(l+180)/s = 20
(l+180)/l = 20/10 =2
l+180 =2l
l= 180
l=180 mtrs
s= l/10 = 180/8 = 10 m/sec
ANSWER:A #### A
QUESTION:A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these
SOLUTION:Explanation:
Volume of water displaced = (8 x 2 x 0.01) m3
= 0.16 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.16 x 1000)kg
= 160 kg.
Answer: D #### D
QUESTION:If a^x = b^y, then
options: A)log a/b= x/y B)log a/ log b = x/y C)log a/ log b = y/x D)log b/a = x/y E)log b/a = y/x
SOLUTION:a^x = b^y => log a^x = log b^y => x log a = y log b
=> log a/ log b = y/x
ANSWER:C #### C
QUESTION:A group of 4 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the three other students from the group?
options: A)5.55% B)16.67% C)15.75% D)20.45% E)25%
SOLUTION:The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 4!.
Desired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 2*2!.
P=(favorable)/(total)=(2*2!)/4!=1/6.
Answer: B. #### B
QUESTION:A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp?
options: A)248 B)312.5 C)346.5 D)392.5 E)424
SOLUTION:Area covered by lamp = Pi*r^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot)
where r= 21 m = length of part lit
So area = (22/7)*21*21/4 = 346.5 sq m
answer :C #### C
QUESTION:If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above?
A.
B.
C.
D.
E.
options: A)(−8,8) B)(4,−4) C)(5,−5) D)(2,−2) E)(−4,4)
SOLUTION:Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A)
Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B)
Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C)
Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D)
Answer: Option C #### C
QUESTION:A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
options: A)128228 B)12800 C)12819 D)12818 E)12812
SOLUTION:16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B #### B
QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
options: A)87 sec B)89 sec C)17 sec D)18 sec E)97 sec
SOLUTION:Speed = 240/24
= 10 m/sec.
Required time
= (240 + 650)/10
= 89 sec.
Answer:B #### B
QUESTION:Alex takes a loan of $8,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount.
options: A)680 B)700 C)720 D)730 E)750
SOLUTION:From the details given in the problem Principle = P = $8,000 and R = 9% or 0.09 expressed as a decimal.
As the annual Interest is to be calculated, the time period T =1.
Plugging these values in the simple Interest formula,
I = P x T x R
= 8,000 x 1 x 0.09
= 720.00
Annual Interest to be paid = $720
answer :C #### C
QUESTION:In a garment industry, 12 men working 9 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 15 hours a day, the number of men required is:
options: A)4 B)5 C)6 D)7 E)9
SOLUTION:Explanation :
Let the required number of men be x.
Less days, More men (Indirect Proportion)
More working hrs per day, Less men (Indirect Proportion)
Days 8 : 10
Working Hrs 15 : 9 :: 12 : x
=> 12 x 15 x x = 10 x 8 x 12
=> x = 10 x 9 x 12 / (12 x 15)
=> x = 7
Answer : D #### D
QUESTION:In the xy-plane, the point (-2, -1) is the center of a circle. The point (1, -1) lies inside the circle and the point (-2, 4) lies outside the circle. If the radius r of the circle is an integer, then r =
options: A)6 B)5 C)4 D)3 E)2
SOLUTION:An easy way to solve this question will be just to mark the points on the coordinate plane.
You'll see that the distance between the center (-2, -1) and the point inside the circle (1, -1) is 3 units
(both points are on y=-1 line so the distance will simply be 1-(-2)=3)
So the radius must be more than 3 units.
The distance between the center (-2,-1) and the point outside the circle (-2,4) is 5 units
(both points are on x=-2 line so the distance will simply be 4-(-1)=5)
So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4.
Answer: C. #### C
QUESTION:A room has both an entrance and an exit door. The room can fill up with people in 5 hours. The room can be empty of people in 15 hours. If it is desired that the room should be filled, from empty, exactly 6 hours after people begin entering the room at 9:30am, then at what time should people begin exiting the room?
options: A)10:00am B)10:45am C)12:00pm D)12:30pm E)1:30pm
SOLUTION:In 6 hours the entrance door is opened to fill the room equal to 6*1/5 = 6/5 of the room. So, 1/5 more than necessary, which should be compensated by people using the exit door. To empty out 1/5 of the people, the exit door needs 15/5 = 3 hours.
Therefore, the exit door should be used at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D. #### D
QUESTION:The volume of a cube is 3375 cc. Find its surface.
options: A)1350 B)1150 C)1456 D)1254 E)1489
SOLUTION:a3 = 3375 => a = 15
6a2 = 6 * 15 * 15 = 1350
Answer: A #### A
QUESTION:A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
options: A)32 B)88 C)67 D)11 E)66
SOLUTION:One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.
Answer:D #### D
QUESTION:How many ways could two people sit at a table with four seats in which two of the four seats will remain empty?
options: A)60 B)12 C)112 D)118 E)120
SOLUTION:ways in which 2 seats out 4 can be selected = 4C2
ways in which 2 people can be arranged in 2 seats = 2!
Total ways of arrangement = 4C2*2!
=4*3
=12
Ans = B #### B
QUESTION:2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost?
options: A)26 B)56 C)110 D)28 E)54
SOLUTION:Let the cost of 1 chair = x, let the cost of 1 table = y
2x + y = 110
y = 110 - 2x
Again,
4x + y = 166
4x + (110 - 2x) = 166
4x + 110 - 2x = 166
2x + 110 = 166
2x = 56
x = 28
Answer: D #### D
QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score?
options: A)662 B)678 C)652 D)642 E)721
SOLUTION:8 * 86 = 688 – 10 = 678
ANSWER:B #### B
QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years?
options: A)10000 B)12000 C)13000 D)10860 E)14400
SOLUTION:Formula :
( After =100 denominator
Ago = 100 numerator)
7800 × 118/100 × 118/100 = 10860
D #### D
QUESTION:The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
options: A)179 B)208 C)210 D)223 E)229
SOLUTION:Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 – 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 208
2x = 358
x = 179 runs
ANSWER A #### A
QUESTION:A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is:
options: A)260 B)262 C)270 D)272 E)None of these
SOLUTION:Explanation:
Volume will be length * breadth * height, but in this case two heights are given so we will take average,
Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3
Option C #### C
QUESTION:In a consumer survey, 88% of those surveyed liked at least one of three products: 1, 2, and 3. 55% of those asked liked product 1, 40% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
options: A)15 B)20 C)25 D)30 E)35
SOLUTION:55 + 40 + 20 = 115
This number includes some people counted twice and some people counted three times.
115 - 88 = 27, and this number represents people counted twice or three times.
7% of the people are counted two extra times.
The percentage of people counted one extra time is 27 - 7(2) = 13.
The percentage of people who liked more than one product is 7% + 13% = 20%.
The answer is B. #### B
QUESTION:If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor S of 2x and 3y?
options: A)1 B)S=Cannot be determined C)S=2 D)5 E)6
SOLUTION:My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B #### B
QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets?
options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes
SOLUTION:(350+250)t=800
600t=800
t=4/3
t=1 hour and 20 minutes
Answer: A #### A
QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is?
options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25
SOLUTION:The number of exhaustive events = 50C1 = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50
= 17/25.
Answer: E #### E
QUESTION:In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
options: A)5/6 B)2/7 C)2/8 D)9/2 E)8/9
SOLUTION:P (getting a prize) =10/(10 + 25) = 10/35 = 2/7 .
Answer:B #### B
QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
options: A)29 B)29 C)60 D)19 E)12
SOLUTION:Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5
= 60 km/hr.
Answer:C #### C
QUESTION:Before a salary increase, the weekly salary of a worker for 44 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour?
options: A)4 B)6 C)8 D)10 E)12
SOLUTION:Let x be the original salary per hour.
Let y be the salary per hour after the increase.
40y=44x
y=(44/40)x=1.1x
The salary increased 10%.
The answer is D. #### D
QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage?
options: A)80% B)50% C)75% D)40% E)53%
SOLUTION:L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 175 (35 * 5)
Profit percentage
= (175 - 100)/100 * 100 = 75%
Answer: C #### C
QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5
SOLUTION:The sum of three greatest should be more than sum of two lowest.
The total sum is; 5z
A. 6z; 6z is more than 5z. Not possible.
B. 4z; 5z-4z=z(Possible)
C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible
D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible
E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible.
Ans:B #### B
QUESTION:A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts?
options: A)6 B)8 C)10 D)12 E)14
SOLUTION:In one hour, the crow eats 1/24 of the nuts.
(1/4) / (1/24) = 6 hours
The answer is A. #### A
QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
options: A)11 B)77 C)12 D)99 E)887
SOLUTION:x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C #### C
QUESTION:The greatest number by which the product of three consecutive multiples of 5 is always divisible is
options: A)54 B)750 C)152 D)162 E)None of these
SOLUTION:Solution
Required number = Product of first three multiplies of 3
= (5 × 10 × 15)= 750.
Answer B #### B
QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres?
options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds
SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph
= 16 * 5/18 = 40/9 m/s
Hence time taken to cover 40 m = 40*9/40
= 9 seconds.
Answer: C #### C
QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
options: A)10years B)12 years C)5 years D)3 years E)24 years
SOLUTION:Explanation:
9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3 years
Answer:D #### D
QUESTION:A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n?
options: A)8/7 B)8 C)9/8 D)7 E)5
SOLUTION:Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 9x+xn and we are told that it equals to 9xn:
9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9
n = 9/8
Answer: C #### C
QUESTION:Sara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother.
options: A)24 years B)25 years C)26 years D)27 years E)28 years
SOLUTION:At the present,
Sara's age is x.
Sara's mother's age is y=6x.
Next year,
Sara's age will be x+1.
Sara's mother's age will be y+1=5(x+1).
From the two equations, we can calculate Sara's age:
y=6x
y+1=5 (x+1)
6x+1=5x+5
6x-5x=5-1
x=4
If Sara is currently 4 years old, and her mother is 6 times older, then her age is
6x=6×4=24.
ANSWER: A #### A
QUESTION:An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
options: A)2200 kmph B)1800 kmph C)1900 kmph D)2100 kmph E)none
SOLUTION:Explanation: Distance = (1500 x 2) = 3000 km.
Speed = Distance/Time
Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = 3000 x 3/5 km/hr = 1800 km/hr.
Answer: Option B #### B
QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit?
options: A)28000 B)30000 C)32000 D)34000 E)None of these
SOLUTION:Explanation :
Suppose B's investment = x. Then A's investment= 3x
Suppose Bs period of investment = y, then A's period of investment = 2y
A : B = 3x * 2y : xy
= 6 : 1
Total profit * 1/7 = 4000
=> Total profit = 4000*7 = 28000. Answer : Option A #### A
QUESTION:A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in?
options: A)12 B)13 C)13 5/7 D)13 ¾ E)None of these
SOLUTION:Explanation:
(A+B)’s 2 day work = 1/16 + 1/12 = 7/18
work done in 6 pairs of days=7/48 x 6 = 7/8
remaining work = 1/8
work done by A on 13th day =1/16 remaining work = 1/16
on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day
total time taken =13 ¾ days
Answer: Option D #### D
QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was?
options: A)23777 B)35000 C)29977 D)26777 E)19871
SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100)
(9x + 1100000 - 11x)/100 = 29000/3 = 9700
(9x + 1100000 - 11x) = 970000
x = 65000
Sum invested at 9% = Rs. 65000
Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000.
Answer: B #### B
QUESTION:What is the remainder of Q= 3^19 when divided by 10?
options: A)0 B)1 C)5 D)7 E)9
SOLUTION:I looked for patterns:
^2 - units digit 9
^3 - units digit 7
^4 - units digit 1
^5 - units digit 3
hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9
and we can then see:
^16 - units digit 1, or
^18 - units digit 9
and ^19 - units digit 7
therefore, Q=when divided by 10, the remainder must be 7.D #### D
QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
options: A)16cm B)18cm C)24cm D)Data inadequate E)None of these
SOLUTION:Explanation:
2(l+b)/b=5/1
2l + 2b = 5b
3b = 2l
b = 2/3 l
Then, Area = 216 cm2
l x b = 216
l x (2/3)l = 216
l2 = 324.
l = 18 cm.
Answer: B #### B
QUESTION:A runs 25% faster than B and is able to allow B a lead of 7 meters to end a race in dead heat. What is the length of the race?
options: A)10 meters B)25 meters C)45 meters D)15 meters E)35 meters
SOLUTION:Answer
A runs 25% as fast as B.
i.e., if B runs 100 m in a given time, A will run 125 m in the same time.
In other words, if A runs 5 m in a given time, then B will run 4 m in the same time.
Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat.
Ratio of length of start given : length of race :: 1 : 5
In this question, we know that the start given is 7 m.
Hence, the length of the race will be 7 * 5 = 35 m.
Choice E #### E
QUESTION:What is the number which when multiplied by 13 is increased by 180?
options: A)13 B)15 C)23 D)35 E)45
SOLUTION:13 × 15 = 195
Answer: B #### B
QUESTION:A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
options: A)10.18 p.m B)10.29 p.m C)10.30 p.m D)10.38 p.m E)10.32 p.m
SOLUTION:D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C #### C
QUESTION:When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is
options: A) 0.005 B) 0.002 C) 0.001 D) 0.0003 E) 0.0002
SOLUTION:It is very easy if x is the diameter, then the magnified length is 1000x.
ince 1000x=0.3 then x=0.3/1000=0.0003.
The answer is D #### D
QUESTION:If it is true that x > -3 and x < 7, which of the following must be true?
options: A)x > 3 B)x < -7 C)x < 3 D)-3 < x < 7 E)none of the above.
SOLUTION:the range is -3 < x < 7
A. x > 3 - no because x can be between -3 < x < 3
B. x < -7 - no because the values of x are always >-7
C. x < 3 - no because x can be between 3 < x < 7
D. -3 < x < 7 - true because x can be between -3 < x < 7
E. none of the above.
Answer: D #### D
QUESTION:A does half as much work as B in three- fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?
options: A)30 days B)35 days C)40 days D)45 days E)50 days
SOLUTION:Explanation:
Let ‘x’ be the number of days taken by B alone to finish the whole work
Then, A alone will finish the whole work in 3x/4 × 2 days = 3x/2 days.
Then, working together,
3x/2 × x/3x/2 + x = 18 days
3x × x/5x = 18
3x/5 = 18
Therefore, the number of days taken by B = x = 18 × 5/3 = 30 days.
Answer: Option A #### A
QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
options: A)11 B)10 C)8 D)12 E)15
SOLUTION:Suppose they meet x hours after 8 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 11 a.m.
Answer: A #### A
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)240 B)377 C)2908 D)287 E)201
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: A #### A
QUESTION:Two of his favorite buildings are Chicago’s Sears (Willis) Tower and
Dubai’s Burj Khalifa. If Burj Khalifa stands at 830 meters high and
Sears stands at 527 meters high, how much higher is Burj Khalifa than Sears?
options: A)300 B)250 C)130 D)303 E)111
SOLUTION:830-527=303. Answer is D. #### D
QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 37 kmph. Of how many minutes does the train stop per hour?
options: A)73 B)83 C)12 D)83 E)11
SOLUTION:Explanation:
T = 8/45 * 60 = 11
Answer: Option E #### E
QUESTION:A jogger jogs at 1/6 of his usual speed. how much % he has to increase speed to reach normal pace of walking
options: A)100 B)200 C)300 D)400 E)500
SOLUTION:suppose usual speed is x, then current speed is x/6.
to gain normal speed, he has to gain 5x/6
% increase = 100*(5x/6)/(x/6) = 500%
ANSWER:E #### E
QUESTION:If x and y are even integers, which of the following is an odd integer?
options: A)x+y B)xy C)xy+2 D)x^2+y^2 E)None of these
SOLUTION:even+even = even
even * even = even
even+even =even
Answer : E #### E
QUESTION:A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?
options: A)25 B)21 C)20 D)10 E)15
SOLUTION:Suppose the can initially contains 7x and 5x litres mixtures A and B
respectively
Quantity of A in mix. left =[7x –7/12 * 9 ] =[7x –21/4]
Quantity of B in mix. left =[5x –5/12 *9 ] = [ 5x - 15/4 ]
Therefore [ 7x-21/4 ] =7/9 or 28x-21 = 7/9
[5x-15/4]+9 20x+21
252x -189 =140x+147 or 112x =336 , x = 3.
Quantity of A in the can initially =7*3 =21
ANSWER:B #### B
QUESTION:Which is the middle even number between 6 and 14?
options: A)10 B)6 C)8 D)14 E)26
SOLUTION:6+x = 14-x
2 x = 8
X = 4
Now 6+x = 10
ANSWER:A #### A
QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place.
options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours
SOLUTION:1/5+2/8 + 3/x = 1
x =20 hours. ANSWER =D #### D
QUESTION:Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week?
options: A)$0.00 B)$133.00 C)$250.05 D)$66.74 E)$10000.00
SOLUTION:Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be
n/4, n/8, n/16, n/32
So, answer will be D #### D
QUESTION:Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
options: A)A)7 B)B)6 C)C)8 D)D)9 E)E)4.74
SOLUTION:1/5 + 1/15 - 1/x = 1/18
x = 4.74
Answer:E #### E
QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 24th of September 1990?
options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday
SOLUTION:19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 24th September was a Monday.
The answer is A. #### A
QUESTION:Find the average of all numbers between 1 and 76 which are divisible by 5
options: A)40 B)20 C)25 D)30 E)35
SOLUTION:Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75)/15=600/15=40
Answer: Option A #### A
QUESTION:Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24
options: A)22 B)62 C)28 D)16 E)11
SOLUTION:Answer:B #### B
QUESTION:A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is
options: A)2 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None
SOLUTION:Sol.
Speed of stream = 1/2(28-10) kmph = 4 kmph.
Answer B #### B
QUESTION:For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(99) – g(97)?
options: A)98 B)100 C)0 D)99 E)97
SOLUTION:g(99) = 1*3*5*7*9*...*99
g(97) = 1*3*5*7*9*...*97
g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98
hence:A. #### A
<<<Examples ends
QUESTION:The perimeter of a semi circle is 180 cm then the radius is?
options: A)22 B)28 C)35 D)37 E)13
SOLUTION:36/7 r = 180
=> r
= 35
Answer: C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price?
options: A)$1200 B)$1300 C)$1000 D)$1700 E)$1050
SOLUTION:C
$1000
90%
104%
--------
14% ---- 140
100% ---- ? => $1000 #### C
QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint?
options: A)9 B)16 C)19 D)25 1/3 E)28 1/2
SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
35 pints will require 9/17 * 35= 19 pints..
C #### C
QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine?
options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4
SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine"
The above statement is NOT clear
Still a solution:
For 8 students we have 3 posts
one post can be occupied by only one member
no two posts can be occupied by the same member
probability(P) for a member getting selected for particular 2 of the 3 posts=
probable outcomes=1(Caine)+1(Abel)=2
total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8
=2/8=1/4
Probability required for the given case= 1-P=1-1/4=3/4
Answer: E #### E
QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required ?
options: A)34 B)40 C)68 D)88 E)None of these
SOLUTION:Solution
We have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft.
∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D #### D
QUESTION:Car A leaves the airport at 9:00 am and travels at a constant rate of 30 km per hour. Car B leaves the airport at 9:30 am and travels in the same direction along the same highway at a constant rate of 40 km per hour. At what time will Car B be 40 km ahead of Car A?
options: A)3:00 pm B)3:30 pm C)4:00 pm D)4:30 pm E)5:00 pm
SOLUTION:At 9:30 am, Car A will be 15 km ahead of Car B.
Car B travels at a rate 10 km per hour faster than Car A.
Car B needs to travel 55 km more than Car A in order to be 40 km ahead.
This will take 55 km/10 km per hour=5.5 hours.
Car B will be 55 km ahead at 3:00 pm.
The answer is A. #### A
QUESTION:Sheena has a pet frog and it is growing fast and eating more flies each day. When she first brought it home on Monday it ate 3 flies, Tuesday it ate 6, Wednesday it ate 9, and Friday it ate 15.
How many flies did her frog eat on Thursday?
options: A)12 B)14 C)10 D)11 E)13
SOLUTION:A) 12. The frog started eating 3 more flies each day.
3 +3 =6
6+3=9
9+3=12
12+3=15 #### A
QUESTION:The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters?
options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000
SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume)
as 4/3.pi.r^3=4500pi
r=15
so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx)
E #### E
QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?
options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45
SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/800*1/600=1/4,800.
Answer: B. #### B
QUESTION:16, 23, 19, 19, 22, 15, 25, ?
What number should replace the question mark?
options: A)13 B)11 C)16 D)18 E)19
SOLUTION:B
11
There are two alternate sequences: +3 and –4; #### B
QUESTION:After working for 6 days, David was joined by Moore. Together they completed the remaining job in 3 days. How many days will it take both of them to complete the entire job, given that it would have taken David 12 days to complete the job alone?
options: A)7 B)4 C)6 D)2 E)7
SOLUTION:Explanation:
David and Moore complete half work in 3 days
=> they can complete whole work in 6 days
Answer: Option C #### C
QUESTION:On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 60% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?
options: A)10.5% B)12.5% C)15% D)25% E)30%
SOLUTION:suppose there are X motorists.
10% of them exceeded the speed limit and received the ticket, i.e. X/10.
Again, suppose total no. of motorists who exceeded the speed limit are Y.
60% of Y exceeded the speed limit but didn't received the ticket, i.e. 3Y/5.
it means 2Y/5 received the ticket.
hence, 2Y/5 = X/10
or Y/X=1/4
or Y/X * 100= 1/4 * 100= 25%
D #### D
QUESTION:A man can do a piece of work in 5 days, but with the help of his son he can do it in 2 days. In what time can the son do it alone ?
options: A)7 1/2 days B)6 1/2 days C)5 1/3 days D)3 1/3 days E)None of these
SOLUTION:Explanation:
In this type of question, where we have one person work and together work done. Then we can easily
get the other person work just by subtracting them. As
Son's one day work =
(1/2−1/5)=(5−2)/10=3/10
So son will do whole work in 10/3 = 3 1/3 days
Answer: D #### D
QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
options: A)7500 B)3600 C)8900 D)9000 E)5000
SOLUTION:35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
ANSWER A #### A
QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1?
options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200
SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700
P1’s income = Rs 5*700 = Rs.3500
ANSWER:D #### D
QUESTION:The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person?
options: A)76 kg B)76.5 kg C)75 kg D)Data inadequate E)None of these
SOLUTION:Explanation:
Total weight increased = (10 x 2.5) kg = 25 kg.
Weight of new person = (50 + 25) kg = 75 kg.
Answer: C #### C
QUESTION:The least number, which when divided by 12, 31, 20 and 54 leaves in each case a remainder of 8 is:
options: A)448 B)488 C)16748 D)548 E)560
SOLUTION:Required number = (L.C.M. of 12, 31, 20, 54) + 8
= 16740+ 8
= 16748.
answer :C #### C
QUESTION:The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:Also note here the relevance of 'K must be less than 400'.
21K is 180n (a multiple of 180).
180n = 2^2 * 3^2 * 5 * n = 3*7*K
n must have a 7 at least.
K must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60.
So K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 60*7 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 60*2 or 60*3*2 or 60*5 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has.
Answer (C) #### C
QUESTION:A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $3200 and the total price paid for type B products was $5800. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
options: A)$14,755 B)$15,325 C)$11,129 D)$16,225 E)$17,155
SOLUTION:cost of type A products next year = 1.3 * 3200 = 4160
cost of type B products next year = 1.2 * 5800 = 6960
total 4169 + 6960 = 11129
ANSWER:C #### C
QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these
SOLUTION:Explanation:
Let their ages be x and (x + 24) years.
5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11.
Their present ages are 35 years and 11 years
Option D #### D
QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
options: A)2:35:16 B)2:15:16 C)2:15:77 D)2:15:98 E)2:15:23
SOLUTION:Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer: B #### B
QUESTION:The number which exceeds 16% of it by 63 is :
options: A)75 B)52 C)58 D)60 E)62
SOLUTION:Solution
Solution
Let the number be x.
x-16% of x =63
x-16/100x =63
x-4/25x=63
21/25x=63
x=(63x25/21)= 75
Answer A #### A
QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
options: A)3377 B)2997 C)3600 D)2799 E)7719
SOLUTION:P = 144(100/5)2 => P
= 3600
Answer:C #### C
QUESTION:In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000
SOLUTION:total vote = N
vote cast by independent voters = 0.4 N
vote cast by registered voters = 0.6 N
vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N
Answer choice E #### E
QUESTION:The smallest 2 digit prime number is?
options: A)A)11 B)B)13 C)C)19 D)D)113 E)E)None
SOLUTION:The smallest 3-digit number is 10, which is divisible by 2.
10 is not a prime number.
11 is a prime number.
Hence 11 is the smallest 2-digit prime number.
A) #### A
QUESTION:A, Band C are three contestants in a kmrace. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ?.
options: A)540 m B)178 m C)936 m D)234 m E)713 m
SOLUTION:While A covers 1000 m, B covers (1000 - 40) m = 960 m and
C covers (1000 - 64) m or 936 m.
When B covers 960 m, C covers 936 m
Option C #### C
QUESTION:Forks, Spoons, and Knives in drawer are in the ratio of 4: 4 : 3. If there are 16 Forks, the number of Knives in the drawer is:
options: A)8 B)4 C)12 D)16 E)14
SOLUTION:Explanation :
Let Forks = 4x, Spoons = 4x & Knives = 3x. Now, 4x = 16 hence x = 4.
Number of Knives = 3x = 12.
Answer : C #### C
QUESTION:An elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children?
options: A)40: 20 B)42: 21 C)50: 100 D)15: 25 E)It cannot be determined by the information given.
SOLUTION:While you can figure out most of this question, there is not enough information to completely tell. the answer is E. #### E
QUESTION:In a lottery there are 100 prizes and 300 blanks. A lottery is drawn at random. What is the probability of getting a prize?
options: A)1/2 B)5/400 C)1/5 D)1/3 E)1/4
SOLUTION:total draws = prizes+blanks= 100+300=400
probability of getting a prize = 100/400 = 1/4
correct option is E #### E
QUESTION:3 men and 10 boys finish a job in 9 days, 7 men and 7 boys finish it in 8 days. 9 men and 9 boys shall finish it in how many days?
options: A)18 B)09 C)07 D)19 E)12
SOLUTION:3 M + 10 B ----- 09 days
7 M + 7 B ------- 8 days
9 M + 9 B -------?
21 M + 70 B = 63 M +63 B
7 B= 42 M => 6 M = 1 B =>1 B =6 M
3 M + 60 M = 63 M ---- 9 days
9 M + 54 M = 63 M -----? => 9 days
Answer: B #### B
QUESTION:The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.)
options: A) 1 B) 4 C) 7 D) 11 E) 10
SOLUTION:We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 3 ingredients...
3 ingredient blends:
ABC
ABD
ACD
BCD
Total blends = 4
B #### B
QUESTION:Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
options: A)12 to 1 B)6 to 1 C)5 to 1 D)20 to 7 E)1 to 5
SOLUTION:The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job;
The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 3*7=21
The ratio thus is 60 to 21, or 20 to 7.
Answer: D. #### D
QUESTION:The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n?
options: A)w– 2n B)w–n + 1 C)w– 2(n– 1) D)n– 6 + w E)w – n/2
SOLUTION:Another method would be to use the concept of Arithmetic Progressions. Consecutive even integers form an AP where the common difference is 2.
In an AP, Last term = First term + (n-1)*common difference
w = First term + (n-1)*2
First term = w - 2(n-1)
ANSWER:C #### C
QUESTION:A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?
options: A)8239 B)2900 C)2000 D)2393 E)2009
SOLUTION:Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 1000 => x = 1000.
B's share = Rs. 2x = 2 * 1000 = Rs. 2000.
Answer: C #### C
QUESTION:The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
options: A)1 : 96 B)1 : 48 C)1 : 84 D)1 : 68 E)None of these
SOLUTION:Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
ANSWER:A #### A
QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
options: A)1 B)3 C)4 D)5 E)6
SOLUTION:The distance between the nest and the ditch is 250 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 250 = 7500.
D = ST
7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km)
D) #### D
QUESTION:For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z?
options: A)(n/m)% B)(m × n)% C)(100 / [m × n]) % D)(100 × m/n)% E)(100 × n/m)%
SOLUTION:x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer E is 100n/m %.E #### E
QUESTION:The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is:
options: A)45 B)50 C)51.4 approx. D)54.6 approx. E)54
SOLUTION:Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 52 * 100
= 1600 + 775 + 55x = 5200
= 55x = 2825
= x = 565/11 = 51.4.
ANSWER:C #### C
QUESTION:In an encryption code 'PLAYS' is written as '{:SUD' when encoded and 'SLEEP' is written as 'D:RR{' when encoded. How is ''SLAPPY" written in that encryption code?
options: A)D:S{{U B)SLAPPY C){RUDD: D){:SUU{ E)U{{S:D
SOLUTION:D = S
: = L
S = A
P = {
P = {
Y = U
Correct Answer: A #### A
QUESTION:The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability.
options: A)1/120 B)1/235 C)1/24 D)1/76 E)1/53
SOLUTION:Explanation :
There are total 4 letters. The probability that P gets the first position is 1/4.
The probability that O is in the second position is 1/3.
Likewise, probability for C and Y are 1/2 and 1/1.
Hence, the required probability is:-
=> (1/4) x (1/3) x (1/2) x 1.
=> 1/24.
Answer : C #### C
QUESTION:Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 15 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
options: A)120 B)80 C)48 D)192 E)40
SOLUTION:Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 15hrs. hence, possible scenarios, if
(1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40
Hence Answer is D 192 which can not be any of these. #### D
QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots?
options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M
SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours.
The answer is A. #### A
QUESTION:A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
options: A)35 B)45 C)25 D)15 E)55
SOLUTION:A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=175×9/35=5×9=45
Answer is B. #### B
QUESTION:A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
options: A)$330.00 B)$331.00 C)$332.30 D)$333.30 E)$334.60
SOLUTION:The maximum interest in one month is 10%*$300=$30.
The combined payment (base plus interest) is $300 + $30 = $330.
The greatest possible payment is: 1.01*$330=$333.30.
The answer is D. #### D
QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?
options: A)46 B)42 C)56 D)70 E)58
SOLUTION:I'm going in on this one.
So let's say that we have the following
So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70.
Thus D is the correct answer choice #### D
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was:
options: A)14 B)16 C)19 D)22 E)24
SOLUTION:Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21.
Son's age 5 years back (21 - 5) = 16 years.
answer :B #### B
QUESTION:The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is:
options: A)30 B)28 C)24 D)20 E)35
SOLUTION:Product of two nos = product of HCF and LCM
Let one number = x
=> 25 * x = 5 * 150
x=5*150/25=30
ANSWER A #### A
QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his
original salary?
options: A)25% B)50% C)75% D)85% E)95%
SOLUTION:Salary he get after reduced 20% = 100-20% = 80%
So,percentage should be added to get back his salary = (20/80)*100 = 25%
ANSWER:A #### A
QUESTION:If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the
stream is
options: A)5 km/hr B)4 km/hr C)2 km/hr D)1 km/hr E)None of these
SOLUTION:Explanation:
Rate upstream = (15/3) kmph
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7 - 5)kmph = 1 kmph
Answer: D #### D
QUESTION:If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000?
options: A)$3500 B)$5000 C)$3150 D)$7200 E)$10000
SOLUTION:Saving = (45-30)% of 48000 = 7200.
Answer:D #### D
QUESTION:2 + 2 + 2 + 2 × 2^2 + 2 × 2^3 + 2 × 2^4 + 2 × 2^5 + 2 × 2^6 + 2 × 2^7 =
options: A)2^7 B)2^14 C)2^10 D)2^15 E)2^16
SOLUTION:We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*2^7 we would have: sum=9*(2*2^7)=18*2^7=~2^11, so the actual sum is less than 2^11 and more than 2^7 (option A) as the last term is already more than that. So the answer is clearly C.
Answer: C #### C
QUESTION:Find 30 % of 240
options: A)72 B)94 C)86 D)74 E)110
SOLUTION:We know that R % of m is equal to R/100 × m.
So, we have 30 % of 240
30/100 × 240
= 72
Answer:A #### A
QUESTION:The greatest number of four digits which is divisible by 12, 20, 36 and 60 is:
options: A)9000 B)9900 C)9500 D)9800 E)9700
SOLUTION:Greatest number of 4-digits is 9999.
L.C.M. of 12, 20, 36 and 60 is 180.
On dividing 9999 by 180, the remainder is 99.
Required number (9999 - 99) = 9900.
Answer: Option B #### B
QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:Solution
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
Tens place can be filled by any of the remaining 5 numbers.
So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it.
So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D
QUESTION:A box contains ten bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that exactly two bulbs are good?
options: A)7/21 B)10/21 C)9/21 D)8/21 E)5/21
SOLUTION:Required probability = (5C2 . 5C2)/10C4 = (10 * 10)/210
= 10/21
Answer:B #### B
QUESTION:There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:Let the number of men be m and so the number of women = 15-m
Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.
Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).
Let the total work be 360 units (LCM of 180 and 120).
1 man does 360/120 = 3 units per day
1 woman does 360/180 = 2 units per day
Based on above facts,
Total work by men + women in these 17 days = 360 units
m*9*3 + (15-m)*6*2 = 360,
27m + 180 -12m = 360, Solving m=12.
Num of men = 12 and number of women = 15-12 = 3
ANSWER:C #### C
QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
options: A)6/63 B)2/63 C)125/126 D)1/126 E)1/63
SOLUTION:Required probability = 1 - 1/126 = 125/126
ANSWER:C #### C
QUESTION:Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?
options: A)1 B)2 C)4 D)5 E)6
SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) = 5 (x + 8)
2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2.
B #### B
QUESTION:Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
options: A)33% less than N B)25% less than N C)equal to N D)20% greater than N E)25% greater than
SOLUTION:Correct answer is (A).
This year, the price of a tree is price1=P/N.
If this price increases by 50% it becomes price2=P/N*1.50
Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.50) i.e. N/1.5 i.e. .67% less*
A #### A
QUESTION:Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months.
options: A)Rs. 9009 B)Rs. 9008 C)Rs. 9002 D)Rs. 9202 E)Rs. 9001
SOLUTION:Explanation:
P = Rs. 78000, R = 77/5 % p.a and T = 9/12 years = ¾ years
Therefore,
S.I = (P*R*T)/100
= (78000* 77/5 * ¾ * 1/100)
= Rs. 9009
ANSWER: A #### A
QUESTION:Find the one which does not belong to that group ?
options: A)237 B)232 C)223 D)426 E)111
SOLUTION:Explanation:
525 => 5 52,
39 => 3 32,
24 => 2 22,
636 => 6 62. The above pattern is not followed in 426.
Answer: D #### D
QUESTION:11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
options: A)84 m B)88 m C)14 m D)137 m E)None
SOLUTION:Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22] = 1400cm = 14 m.
Answer C #### C
QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made?
options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these
SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000
ANSWER:C #### C
QUESTION:The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average?
options: A)69 B)70 C)71 D)72 E)75
SOLUTION:Sum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled.
The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72.
ANSWER:D #### D
QUESTION:Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.
options: A)5113 B)5117 C)5120 D)8119 E)10115
SOLUTION:Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, D,E The answer to be C
Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year.
If x = initial number of trees = 5120
Year 1 = 5/4x
Year 2 = (5/4)(5/4)x
Year 3 = (5/4)(5/4)(5/4)x
Year 4 = (5/4)(5/4)(5/4)(5/4)x
Only for Answer D: (5/4)(5/4)(5/4)(5/4) 5120 = 12500
Hence, correct answer = C #### C
<<<Examples ends
QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India.
Action:
I. Pollution committee should immediately take certain measures to control the pollution levels in India.
II. Licenses of polluting industries should be cancelled and owners should be put behind the bars.
options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow
SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided.
ANSWER IS A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?
options: A)25 B)30 C)45 D)20 E)50
SOLUTION:6p2 = 6 x 5 = 30
B) #### B
QUESTION:A man can row his boat with the stream at 16 km/h and against the stream in 12 km/h. The man's rate is?
options: A)8 kmph B)9 kmph C)2 kmph D)4 kmph E)1 kmph
SOLUTION:DS = 16
US = 14
S = ?
S = (16 - 2)/2 = 2 kmph
Answer:C #### C
QUESTION:A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ?
options: A)100 m B)120 m C)130 m D)150 m E)None of these
SOLUTION:Explanation :
Solution: Relative speed = (9 - 8) = 1 km/hr.
Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m.
.'. Distance between the criminal and policeman = (265 - 50) m = 215 m.
Answer : E #### E
QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
options: A)160 B)175 C)180 D)195 E)205
SOLUTION:Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 * 8 * 4) = 160.
Therefore, 160 * 2.40 + x * 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER:B #### B
QUESTION:B @ K I 9 D © 5 2 T $ M 4 E J # U R 1 A δ K 5 W 6 % F Q 7 H P 8 Z
Which of the following should come in place of the question mark(?) in the following series based on the elements in the above arrangement?
K9D 2$M JUR ?
options: A)δKW B)δK5 C)δ56 D)δW6 E)None of these
SOLUTION:Explanation:
K +6 2 +6 J +6 δ
9 +6 S +6 U +6 5
D +6 M +6 R +6 W
ANSWER IS E #### E
QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
options: A)4 B)5 C)34 D)7 E)9
SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7
Answer:D #### D
QUESTION:In a bag, there are 4 white, 1 brown and 5 red pens. One pen is picked up randomly. What is the probability that it is neither white nor red?
options: A)1/5 B)1/10 C)1/2 D)1/3 E)1/4
SOLUTION:Explanation :
Neither white nor red means the pen drawn is brown.
Total number of outcomes = (4+1+5) = 10.
Number of Favourable outcomes = 1 = Number of brown pens.
Hence, Probability of the event = 1/10.
Answer : B #### B
QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip?
options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph
SOLUTION:So The Answer is Plainly A....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles
in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours
so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles
Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A
QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour?
options: A)181 B)211 C)241 D)271 E)301
SOLUTION:In 2/5 of an hour there are 24*60 = 1440 seconds
The number of 6-second intervals = 1440/6 = 240
After the first flash, there will be 240 more flashes for a total of 241.
The answer is C. #### C
QUESTION:A person borrows Rs.5000 for 2 years at 5% p.a. simple interest. He immediately lends it to another person at 61⁄4% p.a for 2 years. Find his gain in the transaction per year.
options: A)62.5 B)150 C)225 D)112.5 E)212.5
SOLUTION:Explanation :
The person borrows Rs. 5000 for 2 years at 5% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×5×2/100=500
He also lends it at 6 1⁄4% p.a for 2 years
Simple interest that he gets = PRT/100=5000×25/4×2/100=625
His overall gain in 2 years = Rs.625 - Rs.500 = Rs.125
His overall gain in 1 year = 125/2 = Rs.62.5
Answer : Option A #### A
QUESTION:Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
options: A)228gallons B)267gallons C)120gallons D)767gallons E)167gallons
SOLUTION:Explanation:
Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying]
Volume of {\color{Black} \frac{1}{40}} part = 3 gallons
Volume of whole = (3 x 40) gallons = 120 gallons.
Answer: C #### C
QUESTION:In 6 years, A will be thrice as old as B was 4 years ago. If A is now 6 years older than B, find the present age of B.
options: A)16 years B)24 years C)8 years D)12 years E)18 years
SOLUTION:let present age of A be A
let presennt age of B be B
in 6 yrs
A+6:B+6=3(B-4):B=6
ie A+6=3(B-4)
but given A=B+6
so B+6+6=3(B-4)
B=12
ANSWER:D #### D
QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55
SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;
A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents.
Answer: C. #### C
QUESTION:In the class of 50 students, 30 speak Tamil and 30 speak Telugu. What is the lowest possible number of students who
speak both the languages?
options: A)A)8 B)B)10 C)C)20 D)D)30 E)E)32
SOLUTION:let the student who speaks tamil-x
let the student who speaks telugu-y
as (xuy)-(xny)=total
30+30-(xny)=50
=10
B) #### B
QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit?
options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these
SOLUTION:30,000 *12=45,000*8
1:1
Madhu's share=1/2*60,000
i.e. Rs. 30,000
ANSWER:C #### C
QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
options: A)90 B)2,700 C)3,300 D)5,400 E)324,000
SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 110*30=3,300 copies.
Answer: C. #### C
QUESTION:What is the maximum number of pieces of birthday cake of size 5” by 5” that can be cut from a cake 15” by 15”?
options: A)5 B)10 C)16 D)20 E)9
SOLUTION:The prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 3 'pieces' each, we have (3)(3) = 9 total smaller squares (at maximum).
E #### E
QUESTION:If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
options: A)16 1⁄6% B)25% C)33 1⁄3% D)50% E)66 2⁄3%
SOLUTION:This question can be dealt with conceptually or by TESTing VALUES.
We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.
Let's TEST 2/1
If we triple the numerator and double the denominator, we end up with....
(2x3)/(1x2) = 6/2 = 3
Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50%
D #### D
QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water.
options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20
SOLUTION:Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate of current = 1/2(a-b)
Rate in still water = 1/2(a+b)
=> Rate of current = 1/2(30-10) = 10 kmph
=> Rate in still water = 1/2(30+10) = 20 kmph
Option E #### E
QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
options: A)65 B)21 C)78 D)67 E)51
SOLUTION:Let the total number of workers be x. Then,
8000x = (12000 * 7) + 6000(x - 7)
= 2000x = 42000
= x = 21.
Answer: B #### B
QUESTION:One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel?
options: A)400 B)450 C)500 D)550 E)600
SOLUTION:The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour.
The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours.
The answer is A. #### A
QUESTION:It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish?
options: A)20 B)22 C)24 D)26 E)28
SOLUTION:The bacteria doubles each day, so after 29 days, the dish was half full.
After 28 days, the dish was one quarter full.
After 27 days, the dish was one eighth full.
After 26 days, the dish was one sixteenth full.
After 25 days, the dish was 1/32 full.
After 24 days, the dish was 1/64 full.
The answer is C. #### C
QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
options: A)277 B)277 C)120 D)882 E)272
SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C #### C
QUESTION:If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab is even
III. ab > 0
options: A)I only B)II only C)I and II D)I and III E)I, II, and III
SOLUTION:Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
II only.letter B #### B
QUESTION:A pair of articles was bought for $50 at a discount of 50%. What must be the marked price of each of the article?
options: A)$25 B)$12.50 C)$29.65 D)$35.95 E)$45.62
SOLUTION:S.P. of each of the article = 50/2 = $25
Let M.P = $x
50% of x = 25
x = 25*.5 =$12.50
Answer is B #### B
QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle?
options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE
SOLUTION:Solution
S.P = 85% of Rs.1200
= Rs.(85/100×1200)
Rs.1020.
Answer B #### B
QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h?
options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4
SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E #### E
QUESTION:The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
options: A)3:5 B)3:9 C)3:2 D)2:2 E)3:8
SOLUTION:The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r1^2 . h1/r2^2. h2 => 1/15
= (1)^2h1/(2)^2h2
=> h1/h2 = 3/5
i.e. h1 : h2 = 3:5
Answer: A #### A
QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
options: A)18% B)12% C)22% D)24% E)21
SOLUTION:1500 ---- 270
100 ---- ? => 18%
Answer:A #### A
QUESTION:What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
options: A)20(2/3)% B)20% C)21% D)22(2/3)% E)None of these
SOLUTION:Explanation :
Total numbers = 70
Total numbers in 1 to 70 which has 1 in the unit digit = 7
Total numbers in 1 to 70 which has 9 in the unit digit = 7
Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14
Required percentage = (14/70) × 100 = 140/7 = 20%
Answer : Option B #### B
QUESTION:The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
options: A)230 B)244 C)245 D)238 E)235
SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X = 235 m.
Answer: Option E #### E
QUESTION:The sum of money will be double itself in 30years and simple interest find rate of interest?
options: A)A)2.33% B)B)3.33% C)C)4.33% D)D)5.33% E)E)6.33%
SOLUTION:T = 30 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/30x =3.33%
Answer is B #### B
QUESTION:A customer pays 50 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
options: A)70 B)80 C)90 D)50 E)60
SOLUTION:Solution
Let x be the original price.
x - 20 = 50
x - 20 + 20 = 50 + 20
x + 0 = 70
x = 70
Answer A #### A
QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
options: A)80% B)105% C)88% D)124.2% E)138%
SOLUTION:x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,11 = 11/100
x= 80*11/100
x= 8.8
8.8/10 = 0.88 = 88%, Answer C #### C
QUESTION:What is the remainder when 25472 is divided by 2?
options: A)3 B)1 C)8 D)7 E)0
SOLUTION:If the digit in unit place is even, the number will be divisible by 2.
2 is an even number,so the number is divisible by 2
ANSWER:0 #### E
QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875
SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E #### E
QUESTION:The ratio of Laxmi's age to the age of her mother is 3:11. The difference of their ages is 24 years. The ratio of their ages after 3 years will be?
options: A)1 : 9 B)1 : 3 C)1 : 2 D)1 : 1 E)3 : 3
SOLUTION:Suppose age of Laxmi is x years.
The difference of their ages
\inline \therefore Ratio of their ages after 3 years = =
= 12 : 36 = 1 : 3
Answer:B #### B
QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ?
options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1
SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer:C #### C
QUESTION:If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?
options: A)$30.60 B)$60.60 C)$70.60 D)$40.60 E)$50.60
SOLUTION:The tip is 20% of what he paid for lunch. Hence
tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10
Total spent
50.50 + 10.10 = $60.60
correct answer B #### B
QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true?
options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t
SOLUTION:the question asks could be!!!!
this means that if at least one option works, it is the answer.
3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C
QUESTION:9log9(5) = ?
options: A)1 B)2 C)3 D)5 E)8
SOLUTION:Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
9log9(5) = 5
correct answer D #### D
QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss?
options: A)25 % B)50 % C)75 % D)85 % E)None of these
SOLUTION:Explanation :
Let the original expenditure = Rs. 100.
New final expenditure = 150% of (50% of Rs. 100)
= Rs.(150/10050/100100)
= Rs. 75.
Decrease = 100- 75 = 25 %
Answer : A #### A
QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?
options: A)8/35 B)34/35 C)27/35 D)21/32 E)33/35
SOLUTION:Solution:
P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35
ANSWER IS A #### A
QUESTION:A large research project was scheduled over the course of a 25-month period, and a budget of $100,000 was allotted for the course of the entire project. After 9 months, the project had spent $35,800. Was the project at this point over budget or under budget, and by how much?
options: A)under, $200 B)under, $1200 C)under, $7000 D)over $1800 E)over $5800
SOLUTION:cost per month = 100,000/25 = 4,000.
Now, multiply by nine months: 9*($4000) = $36,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is less than this, so it is under budget.
$36,000 – #35,800 = $200
Answer = (A) #### A
QUESTION:A certain bag contains 60 balls — 22 white, 18 green, 5 yellow, 6 red, and 9 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
options: A)0.09 B)0.15 C)0.54 D)0.75 E)0.91
SOLUTION:According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 18 + 5)/60 = 45/60 = 0.75.
Answer: D. #### D
QUESTION:The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together?
options: A)26 years B)30years C)15years D)24years E)20years
SOLUTION:The required average = (125*23+162*25)/125+162 = 24 years
Answer is D #### D
QUESTION:After decreasing 56% in the price of an article costs Rs.4400. Find the actual cost of an article?
options: A)12000 B)15000 C)1200 D)1000 E)10000
SOLUTION:CP* (44/100) =4400
CP= 100 * 100 => CP
= 10000
Answer:E #### E
QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is
options: A)70 B)71 C)72 D)73 E)74
SOLUTION:Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=264
<=>11x/3=264
=>x=72
Answer: Option C #### C
QUESTION:Jane and Ashley take 10 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
options: A)10.2 Days B)15.2 Days C)16.2 Days D)18 Days E)20 Days
SOLUTION:Let us assume that the work is laying 40 bricks.
Jane = 4 bricks per day
Ashley = 1 brick per day
Together = 5 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 16
Remaining bricks = 40 - 24= 16
So together, they would take 16/5 = 3.2
Total no. of days = 8 + 4 + 3.2 = 15.2
Answer is B #### B
QUESTION:How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet)
options: A)37×260^2 B)36×260^2 C)36×270^2 D)10^2×26^3 E)10^3×26^2
SOLUTION:We are given that License plate could be either of the form DDLLL or DDDLL
Now, every D could be filled in 10 ways and every L could be filled in 26 ways.
or Number of ways for DDLLL = 10 * 10 * 26 * 26 * 26 --(1)
Number of ways for DDDLL = 10 *10*10*26*26 --(2)
Total ways = (1) +
(2)
= \(36×260^2\)
Answer s B. #### B
QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is
options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5
SOLUTION:Work done by 20 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/(14×30)
Work done by 14 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×14)
Ratio of the capacity of a man and woman =1/(15×14) : 1/(14×30) = 1/15 : 1/30
= 1/3 :1/6 = 1/1=1/2=2:1
Answer is C #### C
QUESTION:A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much
options: A)0.60 loss B)0.70 loss C)0.80 loss D)0.50 loss E)0.40 loss
SOLUTION:CP when profit of 25% = 12.8
CP when loss of 20% = 20
Total CP = 32.8
Total SP = 32.00
Total loss = 0.80
ANSWER:C #### C
QUESTION:The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
options: A)17 litres B)21.3 litres C)11 litres D)07 litres E)38 litres
SOLUTION:262.85(32)+3,104.35x = 1,399.45(32 + x)
Solve the equation.
262.85(32)+3,104.35x = 1,399.45(32 + x)
8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x
8,411.2 + 1,704.9x = 44,782.4
1,704.9x = 36,371.2
x ≈ 21.3
Answer is B. #### B
QUESTION:What is the sum of all the prime numbers greater than 30 but less than 50?
options: A)126 B)199 C)198 D)188 E)122
SOLUTION:Required sum = (31 + 37 + 41 + 43 + 47) = 199
Note: 1 is not a prime number
Answer B #### B
QUESTION:Find the area of a parallelogram with base 24 cm and height 16 cm?
options: A)198 cm2 B)384 cm2 C)279 cm2 D)128 cm2 E)297 cm2
SOLUTION:Area of a parallelogram
= base * height
= 24 * 16 = 384 cm2
Answer:B #### B
QUESTION:Find the value of a from (15)^2 x 8^3 ÷ 256 = a.
options: A)250 B)420 C)440 D)650 E)450
SOLUTION:Given Exp. =(15)^2 x 8^3 ÷ 256 = a
= 225 x 512 ÷ 256 =
450
E #### E
QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint?
options: A)9 B)16 C)19 D)25 1/3 E)28 1/2
SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
35 pints will require 9/17 * 35= 19 pints..
C #### C
QUESTION:A train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds. What is the length of the train (in meters)?
options: A)190 B)200 C)210 D)220 E)230
SOLUTION:Let the length of the train be x meters.
The speed of the train is x / 15.
Then, x + 140 = 25*(x / 15)
10x = 2100
x = 210 meters
The answer is C. #### C
QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 9. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
options: A)s 1800 B)s 1500 C)s 1600 D)s 1900 E)s 1700
SOLUTION:Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 9x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2700.
Hence, (R - p) = (2700 - 900) = 1800
Answer : A #### A
QUESTION:A can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares?
options: A)600,400 B)500,500 C)300,700 D)800,1200 E)550,1450
SOLUTION:Ratio of their works A:B = 6:4
Ratio of their wages A:B = 2:3
A's share = (2/5)2000 = 800
B's share = (3/5)2000 = 1200
correct option is D #### D
QUESTION:Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?
options: A) 6 B) 4.8 C) 2.5 D) 2 E) 1
SOLUTION:Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?
(A) 6
(B) 4.8
(C) 2.5
(D) 2
(E) 1
If A is the answer, then the question means that the concentration of water the newt day became 96%.
Out of 12 kilograms 98%, or 11.76 kilograms was water and 0.24 kilograms was non-water.
The next day, after some water evaporated, oranges became 96% water and 4% of non-water, so the next day 0.24 kilograms of non-water composed 4% of oranges, which means that the new weight of the oranges was x*0.04=0.24 --> x=6 kilograms.
Answer: A. #### A
QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
options: A)12.6 B)12.0 C)12.1 D)12.3 E)12.2
SOLUTION:Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.Answer: B #### B
QUESTION:A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these
SOLUTION:Explanation:
Volume of water displaced = (8 x 2 x 0.01) m3
= 0.16 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.16 x 1000)kg
= 160 kg.
Answer: D #### D
QUESTION:On return from a business trip Mr. Chidambaram was to be picked up from the railway station by
his coachman. Someone he managed a train connection earlier and thus arrived two hours too early.
Immediately on arrived he rang up home for the coach and was told that it had just left in order to be
exactly in time for the train by which he was scheduled to come. To save the time he started walking
homeward at 3kmph. On the way he met the coachman who brought him home an hour before
schedule. How far is the Mr. Chidambaram’s house from the railway station?
options: A)22 B)18 C)99 D)27 E)11
SOLUTION:Very good questions. Appeared in Puzzles book of Ravi Nirula.
Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am.
But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance.
So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km.
We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km.
Answer:B #### B
<<<Examples ends
QUESTION:A train cross a 450 m bridge in 42 s and another bridge 650 m length in 50 s what is approximate speed of train in km/h?
options: A)90 Km /hr. B)25 Km /hr. C)30 Km /hr. D)20 Km /hr. E)None of these
SOLUTION:Explanation:
Let the length of the train be L.
Then,
=> (450 + L)/42 = (650+L)/50.
=> L= 600 m.
Now, speed = (450+600)/42 or (650+600)/50 = 25 m/s i.e. 25*(18/5) = 90 Km /hr.
ANSWER IS A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If the sides of a triangle are 52 cm, 48 cm and 20 cm, what is its area?
options: A)480 cm2 B)765 cm2 C)216 cm2 D)197 cm2 E)275 cm2
SOLUTION:The triangle with sides 52 cm, 48 cm and 20 cm is right angled, where the hypotenuse is 52 cm.
Area of the triangle
= 1/2 * 48 * 20
= 480 cm2
Answer: A #### A
QUESTION:If the area of a circle is 81pi square feet, find its circumference.
options: A)48 B)38 C)51 D)92 E)18
SOLUTION:The area is given by pi
pi × r × r = 81 pi
r × r = 81 ; hence r = 81 feet
The circumference is given by
2 × pi × r = 2 × pi × 9 = 18 pi feet
correct answer is E) 18 #### E
QUESTION:When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country?
options: A)166 2/7 B)166 2/1 C)166 2/2 D)166 2/3 E)166 2/8
SOLUTION:5% - 2% = 3%
3% ---- 5
100% ---- ?
=> 166 2/3
Answer:D #### D
QUESTION:Tough and Tricky questions: Work/Rate Problems.
If it takes 80 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?
options: A)40/3 B)11 C)7 D)8 E)9/7
SOLUTION:80 Workers = 3 hours then,
1 Worker = 3*80 Hours
30 Workers = (3*80) /(30) = 8 Answer.D #### D
QUESTION:Which number should replace both the asterisks in (* /18) x (*/162) = 1 ?
options: A)27 B)36 C)54 D)72 E)90
SOLUTION:Let (y/18) x (y/162) = 1
y^2 = 18 x 162 = 18 x 18 x 9
y = (18 x 3) = 54
The answer is C. #### C
QUESTION:A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?
options: A)75 ways B)87 ways C)66 ways D)108 ways E)21 ways
SOLUTION:Explanation:
The boy can select one trouser in five ways.
The boy can select one shirt in 15 ways.
The number of ways in which he can select one trouser and one shirt is 5 * 15 = 75 ways.
Answer: A #### A
QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet?
options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am
SOLUTION:meet x hrs after 8 a.m.
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
==>60x+75(x-1) = 330
x=3.
So,they meet at (8+3). i.e 11a.m.
ANSWER A #### A
QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 150. What is the rate of interest per annum?
options: A)8 B)2 C)10 D)4 E)6
SOLUTION:Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 150
15000[(1 + R/100)2 - 1 - 2R/100] = 150
15000[(100 + R)2 - 10000 - 200R]/10000 = 150
R2 = (159 * 2)/3 = 100 => R = 10
Rate = 10%
Answer: Option C #### C
QUESTION:100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads?
options: A)33/100 B)41/101 C)51/101 D)87/101 E)98/101
SOLUTION:Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C #### C
QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins
SOLUTION:The pool was 1/5 full initially.
In 6/5 hrs, it was filled to 8/9 of its capacity.
Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled.
So, 6/5 hrs = 8/9 - 1/5 = 31/45
Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins.
Hence D #### D
QUESTION:Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets.
options: A)4 B)6 C)8 D)10 E)24
SOLUTION:I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets.
Answer : E #### E
QUESTION:What is the value of: -9^7 + 9^9 ?
options: A) 9^2 B) -18^16 C) 63(9^7) D) -80(9^7) E) 80(9^7)
SOLUTION:-9^7 + 9^9 = 9^7 (-1 + 9^2) = 9^7 (-1 + 81) = 80 (9^7), Answer E. #### E
QUESTION:How many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately followed by an even number? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6
options: A)1 B)2 C)3 D)4 E)More than four
SOLUTION:A is followed by B means : A comes first,B comes next
A preceded by B means : B comes first, A comes next
The sets which satisfy the condition is: 5 3 8
1 3 8
7 3 4
ANSWER:C #### C
QUESTION:A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i
options: A)8 km / hr B)9 km / hr C)10 km / hr D)12.5 km / hr E)None
SOLUTION:Sol.
Man's rate in still in water = (12- 2) km / hr = 10km / hr.
Man's rate against the current = (10 - 2) km / hr = 8 km / hr.
Answer A #### A
QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
options: A)100 B)250 C)260 D)416 E)None of these
SOLUTION:Explanation:
Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 × 32 = 416.
Answer: D #### D
QUESTION:The sum of three consecutive integers is 102. Find the lowest of the three?
options: A)18 B)67 C)98 D)33 E)26
SOLUTION:Three consecutive numbers can be taken as (P - 1), P, (P + 1).
So, (P - 1) + P + (P + 1) = 102
3P = 102 => P = 34.
The lowest of the three
= (P - 1)
= 34 - 1 = 33.
Answer: D #### D
QUESTION:In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?
Look at this series: 1, 5, 7, 3, __, 1 ...Which number is missing?
options: A)2 B)4 C)12 D)0 E)13
SOLUTION:E
13
This is an alternating addition and subtraction series. In the first pattern, 6 is added to each number to arrive at the next. In the second, 2 is subtracted from each number to arrive at the next. #### E
QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean a. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than a+d?
options: A) 16% B) 32% C) 48% D) 84% E) 92%
SOLUTION:16%
________________________________________________ a+d
34%
________________________________________________ a
34%
________________________________________________ a-d
16%
since 68% lies one standard deviation from mean a, => 50% of 68% lies on either side as it is symmetric about a.
thus 16% lie below a-d and 16% lie above a+d
now below a+d = 16+34+34 = 84%
hence D #### D
QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is
options: A)2970 B)297 C)2997 D)300 E)30
SOLUTION:(1/10)*3000 - (1/10)%*3000 =
300 - (1/1000)*3000 =
300 - 3 = 297
The answer is B. #### B
QUESTION:If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite?
options: A)x^2 B)x^2 – y^2 C)y^2 D)(y + x)^2 E)(x – y)^2
SOLUTION:(y^2 − xy)/x=y-x
=> y^2 − xy = xy -x^2
=> x^2 - 2xy + y^2 = 0
=> (x-y)^2 = 0
Answer E #### E
QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made?
options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these
SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000
ANSWER:C #### C
QUESTION:A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by
1/2. What is the number of students in the class?
options: A)45 B)40 C)35 D)30 E)50
SOLUTION:Explanation:
Let the total number of students = x
The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks.
But total increase in the marks = 1/2×x=x/2
Hence we can write as
x/2=20
⇒x=20 x 2=40
Answer: Option B #### B
QUESTION:A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck?
options: A)2:1 B)3:4 C)4:3 D)1:4 E)5:6
SOLUTION:Given;
4 duck = 3 hen;
Or, duck/hen = 3/4;
Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter.
Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''Answer: 2:1; #### A
QUESTION:In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y?
options: A)6 B)3 C)4 D)5 E)7
SOLUTION:lets start from z, as per the question stem
z + 5 + 7 = 16
-->> z= 4
similarly, y + 4 + 5 = 7
--> y = -2
similarly,, x + -2 + 4 = 5
--> x = 3
hence , x-y = 3+2 = 5
ANSWER:D #### D
QUESTION:In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 45 percent of the vote. How many additional votes would James have needed to win the election?
options: A)901 B)989 C)990 D)891 E)1,001
SOLUTION:James = (0.5/100)*2000 = 10
Votes to win = (45/100)*Total Votes +1 = (45/100)*2000 +1 = 901
Remaining Voted needed to win election = 901 - 10 = 891
Answer: option D #### D
QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3%
SOLUTION:Let 100 is the enrollment in 1990.
Enrollment in 1980= 83.3
% increase= (Increase from 1980 to 1990)/Enrollment in 1983
=>16.7*100/83.3 =20%
ANSWER:C #### C
QUESTION:The instructions state that Cheryl needs 4/19 square yards of one type of material and 2/13 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/26 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
options: A)4/19 B)1/9 C)2/3 D)1 1/9 E)2 1/9
SOLUTION:Total bought = 4/19+2/13
left part 4/26--->2/13
so used part 4/19+2/13-2/13=4/19
ANSWER:A #### A
QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50
SOLUTION:Others equal 5650.
Answer D #### D
QUESTION:At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?
options: A)2/3 B)1 C)3/4 D)3/2 E)2
SOLUTION:Rate of A = 1/2 tank/hour;
Rate of B = 1/3 tank/hour;
Rate of C = 1/6 tank/hour.
Combined rate when A and B are used to pump-out water, while C is used to fill water into the tank is 1/2+1/3-1/6=2/3 tank hour.
So, to empty the full tank 3/2 hours (reciprocal of rate) are needed. To empty the half-full tank half of that time would be needed: 1/2*3/2=3/4 hours.
Answer: C. #### C
QUESTION:The average of first 13 even numbers is?
options: A)10 B)11 C)12 D)13 E)14
SOLUTION:Sum of 13 even numbers = 13 * 14 = 110
Average = 182/13 = 14
ANSWER:E #### E
QUESTION:If 5 < x < 11 and y = x + 7, what is the greatest possible integer value of x + y?
options: A)26 B)27 C)28 D)29 E)30
SOLUTION:x+y = x+x+7 = 2x+7
We need to maximize this value and it needs to be an integer.
2x is an integer when the decimal of x is .0 or .5
The largest such value is 10.5
Then x+y = 10.5 + 17.5 = 28.
The answer is C. #### C
QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
options: A)33 B)67 C)25 D)66 E)81
SOLUTION:A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer: C #### C
QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
options: A)38 B)41 C)30 D)31 E)29
SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: C #### C
QUESTION:During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
options: A)9/xz B)9zx C)9x/z D)9z/x E)xz/9
SOLUTION:Speed of Peter = x/9 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x
Option D
The values 100m and 200m have no role to play here and are just given to confuse you. #### D
QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.
options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter
SOLUTION:Explanation:
Speed = Distance/time = 300/18 = 50/3 m/sec
Let the length of the platform be x meters
then
Distance=Speed∗Timex+300=50/3 X 39
=>3(x+300)=1950=>x=350 meters
ANSWER IS D #### D
QUESTION:What is the value of m and n ?
if log3m/log3n=log 52
options: A)1,5 B)2,5 C)3,5 D)4,5 E)2,3
SOLUTION:log (base a) b=log(base n)b/log(base n)a
here base are same in reverse way of formula
so
log(base n)m=log(base 5) 2
hence
n=5,m=2
ANSWER:B #### B
QUESTION:If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be .
options: A)90 seconds B)150 seconds C)60 seconds D)100 seconds E)120 seconds
SOLUTION:2/3 filled in 100 seconds
1/3 filled in 50 secs
then 2/3+1/3=100 + 50 seconds = 150 seconds
ANSWER: B #### B
QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 35 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
options: A)33 1/3% B)51 23/27% C)50% D)62 1/2% E)75%
SOLUTION:P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
35% of (70-x) = x => 24.5 - 0.35x = x => x = 18 4/27% so only P = 70 -x = 51 23/27%
Answer B #### B
QUESTION:If f is a function defined for all k by f(k) = k^3 /16, what is f(2 k) in terms of f(k)?
options: A)1/8 f(k) B)8 f(k) C)2 f(k) D)10 f(k) E)32 f(k)
SOLUTION:f(k) = k^3 /16
f(2k) = (2k)^3 /16 =8 * k^3/16 = 8 x (k^3 /16) = 8 f(k).
So answer is B. #### B
QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is?
options: A)7 B)9 C)8 D)5 E)4
SOLUTION:x + y = 25
xy = 144
(x- y)2 = (x + y)2 – 4xy
(x- y)2 = 625 – 576 => (x – y) = 7
ANSWER: A #### A
QUESTION:105,100,...,90,85,80,75
Insert the missing number
options: A)95 B)78 C)83 D)84 E)none of the above
SOLUTION:Missing number : 95
Answer : A #### A
QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
options: A)47/5 B)13 C)17 D)21 E)23
SOLUTION:Let A contains A, B contains B liters
so, (A-4)/(B+4)= 1/3.......(1)
again, (B-5)/(A+5)= 1/2..........(2)
from (1)(2) we find A= 47/5
ans: (A) #### A
QUESTION:The greatest common factor of two positive integers is P. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?
options: A)PY⁄Z B)XZ + YZ C)X⁄Z + Y D)X + Y⁄Z E)X + Z⁄Y
SOLUTION:Say other integer is W
Formula
GCF(WZ)*LCM(WZ) = W*Z
P*Y = W*Z
So W= PY/Z
Answer A #### A
QUESTION:If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
options: A)2 days B)1 day C)3 days D)5 days E)7 days
SOLUTION:The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
B) #### B
QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1000 per sq.metre.
options: A)Rs. 15,000 B)Rs. 15,500 C)Rs. 15,600 D)Rs. 20,625 E)None
SOLUTION:Solution
Area of the floor = (5.5 x 3.75)m²
= 20.635m ²
Cost of paying = Rs. (1000 x 20.625)
= Rs.20625.
Answer D #### D
QUESTION:A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 845 in the same period of 2 years, What must be the rate of interest?
options: A)5% p.a. B)7.5% p.a. C)10% p.a. D)12.5% p.a. E)None of these
SOLUTION:Explanation:
Given: 800 = (P * R * 2) / 100
S.I. For 1 year = Rs. 400
Thus, (840 – 800) = S.I. on Rs. 400 for 1 year
40 = (400 * R * 1) / 100
R = 10% p.a.
ANSWER C #### C
QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item
options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these
SOLUTION:Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 1300
= 80/100 * 1300
= 1040
Option D #### D
QUESTION:In what ratio should a variety of rice costing $6 per kg be mixed with another variety of rice costing $8.75 per kg to obtain a mixture costing $7.50 per kg?
options: A)4/7 B)5/6 C)5/9 D)4/8 E)3/8
SOLUTION:B
5/6
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6 #### B
QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours?
options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44)
SOLUTION:Explanation:
Here clock-wise and anti-clockwise arrangements are same.
Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}}
Answer: C) 18!(6 x 24) #### C
QUESTION:If a fair die is rolled once, what is the probability that a 3 occurs on at least one roll?
options: A)25/36 B)125/216 C)1/6 D)1/36 E)5/6
SOLUTION:Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)
Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6) = 1-5/6 = 1/6
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
C is thus the correct answer. #### C
QUESTION:In an election between the two candidates ,The candidates who gets 60% of votes polled is winned by 280 votes majority. What is the total number of votes polled?
options: A)1200 B)1400 C)1600 D)1500 E)1540
SOLUTION:Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %)
20 % = 60 % - 40 %
20% -----> 280 (20×14 = 280 )
100% -----> 1400 (100×14 = 1400)
Option 'B' #### B
QUESTION:Four of the following five numbered parts (a), (b), (c), (d) and (e) are equal. The number of the part which is not equal to the other four parts is the answer.
options: A)115 × 8 ÷ 10 + 8 B)425 ÷ 17 × 4 C)36 × 5 ÷ 6 + 17 × 4 D)2(6) + √256 + 20 E)35 × 12 ÷ 14 + 14 × 5
SOLUTION:All others are equal to 100. But option (c) gives a value equal to 98.
Answer C #### C
QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more
men joined them. How many days will they take to complete the remaining work?
options: A)3days B)4days C)2days D)8days E)5days
SOLUTION:1 man's 1 day work = 1/108
12 men's 6 days work = 6/9 = 2/3
remaining work = 1 – 2/3 = 1/3
18 men's 1 days work = 18/108 = 1/6
1/6 work is done by them in 1 day
therefore, 1/3 work is done by them in 6/3 = 2 days.
ANSWER C 2days #### C
QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1
SOLUTION:1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: C #### C
QUESTION:If the length of the sides of two cubes are in the ratio 2:1, what is the ratio of their total surface area?
options: A)2:1 B)3:1 C)4:1 D)6:1 E)8:1
SOLUTION:Let x be the length of the small cube's side.
The total surface area of the small cube is 6x^2.
The total surface area of the large cube is 6(2x)^2=24x^2.
The ratio of surface areas is 4:1.
The answer is C. #### C
QUESTION:The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago?
options: A)1: 3 B)2: 3 C)3:3 D)4: 3 E)5: 4
SOLUTION:3x-25/2x-25 = 4/3
Therefore x=-25
Age cannot be negative.
Answer: D #### D
QUESTION:At what rate of annual simple interest,a certain sum will amount to four times in 15 year?
options: A)15% B)17.5% C)20% D)25% E)35%
SOLUTION:r=?
t=15 yrs
SI=p*r*t/100
Amount = SI+p = 4p
(p*r*15/100)+p = 4p
p(15r/100 + 1) = 4p
15r + 100 = 400
15r = 300
r = 20%
ANSWER:C #### C
QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
options: A)80% B)20% C)40% D)50% E)None of these
SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84
Number of students failed = 140 - 84 = 56.
Required percentage = 28/56 * 100 = 50%.
ANSWER:D #### D
QUESTION:The diagonals of a rhombus are 12 cm and 10 cm. Find its area?
options: A)158 B)129 C)150 D)123 E)60
SOLUTION:1/2 * 12 * 10 = 60
Answer:E #### E
QUESTION:The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum.
options: A)33498 B)17000 C)2665 D)28876 E)313
SOLUTION:The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000
Answer:B #### B
QUESTION:If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
options: A)6 B)8 C)6 D)5 E)4
SOLUTION:96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer:B #### B
QUESTION:In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
options: A)L(L-N) /L-M B)L(N-M) / L-M C)L-N D)M-N E)M+
SOLUTION:the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:
L = 200
M = 10
N =20.
So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect, A.
Out of which, i choose A. #### A
QUESTION:I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there?
options: A)12 B)44 C)56 D)120 E)200
SOLUTION:6C3*4C2
=120=D #### D
QUESTION:If ratio of profit of A and B is 4:5 and they together invested Rs.90,000 then money invested by B is
options: A)Rs.48,000 B)Rs.45,000 C)Rs.30,000 D)Rs.50,000 E)None of the above
SOLUTION:investment by B=(5*90000)/(4+5)
=50000
ANSWER:D #### D
<<<Examples ends
QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/6 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
options: A)12 greater B)12 fewer C)28 fewer D)36 fewer E)44 fewer
SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/6 * 480 =80
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 80-68 =12>>> therfore answer is 28 fewer
B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream
options: A)5 hours B)4 hours C)3 hours D)2 hours E)None of these
SOLUTION:Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 81 km
Time taken = distance/speed = 81/27 = 3 hours. Answer : Option C #### C
QUESTION:The present population of a town is 240. Population increase rate is 10% p.a. Find the population of town after 1 years?
options: A)100 B)120 C)200 D)220 E)264
SOLUTION:P = 240
R = 10%
Required population of town = P*(1 + R/100)^T
= 240*(1 + 10/100)
= 240*(11/10)
= 264
Answer is E #### E
QUESTION:If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?
options: A)10 B)15 C)20 D)25 E)None of them
SOLUTION:Let the required number of days be x.
More men, Less days (indirect proportion)
Less hours per day, More days (indirect proportion)
Men 18 : 15
Hours per day 8: 9 } : :16 : x
(18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15
Hence, required number of days = 15.
Answer is B. #### B
QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?
options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours
SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled
3 min--------1/30 parts
x min--------- 1 part(full)
x=90 min =1 hour 30 min
ANSWER:C #### C
QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525
SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
A) #### A
QUESTION:The H.C.F. of two numbers is 12 and their difference is 12. The numbers are :
options: A)66, 78 B)70, 82 C)94, 106 D)84, 96 E)None of these
SOLUTION:Explanation:
Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96.
ANSWER IS D #### D
QUESTION:The first half of a 600-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal to the average speed, in miles per hour, for the entire trip?
options: A)300/(x + y) B)600/(x + y) C)150/x + 150/y D)300/x + 300/y E)600/x + 600/y
SOLUTION:Time taken to cover first half i.e 300 miles of a 600 mile trip = x
time taken to cover the second half i.e 300 miles of a 600 mile trip = y
Total time taken = x+y
Average speed for the entire trip =total distance /total time
=600/(x+y)
Answer B #### B
QUESTION:George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is
options: A)28 B)H C)27 D)29 E)271
SOLUTION:Answer:B #### B
QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?
options: A)30sec B)45sec C)36sec D)29sec E)52sec
SOLUTION:Speed of the train = 50*5/18 = 250/18 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(250/18) = 500*18/250 = 36sec
Answer is C #### C
QUESTION:Tough and Tricky questions: Number Properties.
If (z + 3)/6 is an integer, what is remainder when z is divided by 6?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:6/6=1
Ans B #### B
QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water?
options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1
SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q
2P=4Q
P/Q = 2/1
The answer is D. #### D
QUESTION:Find the perimetri of trapezium with sides 4,6,12 and distance between two parallel side is 3.
options: A)27 B)26 C)28 D)25 E)24
SOLUTION:1/2*(6+12)*3=27
ANSWER:A #### A
QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.5
II. 15.3
III. 9.5
options: A)I only B)I and II only C)II only D)III only E)I and III only
SOLUTION:Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
14.5 and 9.5 lies in the range of 2SD from mean
Answer: Option C #### C
QUESTION:What is the tens digit of 36^12?
options: A)1 B)3 C)5 D)7 E)9
SOLUTION:36^10 = 6^24
(6^2)=6*6 = 36
(6^3)= 36*6 = .16
(6^4)= .16*6 = ..96
(6^5) = ..96*6 = ..76
(6^6) = ..76*6 = ...56
(6^7) = ....56*6 = ....36
If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on...
Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9 #### E
QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
options: A)22 B)30 C)88 D)266 E)121
SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer:B: #### B
QUESTION:The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
options: A)76 B)88 C)66 D)55 E)35
SOLUTION:Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer:E #### E
QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 150. What is the rate of interest per annum?
options: A)8 B)2 C)10 D)4 E)6
SOLUTION:Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 150
15000[(1 + R/100)2 - 1 - 2R/100] = 150
15000[(100 + R)2 - 10000 - 200R]/10000 = 150
R2 = (159 * 2)/3 = 100 => R = 10
Rate = 10%
Answer: Option C #### C
QUESTION:A coin is tossed live times. What is the probability that there is at the least one tail?
options: A)1/15 B)31/32 C)1/10 D)30/32 E)25/27
SOLUTION:Probability of getting least one tail at the coin tossed five times.
= There is not even a single tail.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
ANSWER B #### B
QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39?
options: A)3 B)8 C)12 D)32 E)35
SOLUTION:n = 5p + 1 = 6,11,16,21,26,31
n = 7q + 3 = 3,10,17,24,31
=>n = 39m + 31
To get this, we need to take LCM of co-efficients of p and q and first common number in series.
So we need to add 8 more to make it
39m + 39
Answer - B #### B
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter
SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer:A #### A
QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
options: A)11 B)77 C)12 D)99 E)887
SOLUTION:x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C #### C
QUESTION:At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married?
options: A)5⁄7 B)7⁄10 C)2/7 D)7⁄30 E)5⁄70
SOLUTION:--------------------M------W--------Total
Marrried----------20-----20---------40
Not married-----10-----50---------60
Total-------------30-----70--------100
need married woman/total woman, so 20/70=2/7
C #### C
QUESTION:Which of the following number is divisible by 24 ?
options: A)3100000 B)3115832 C)3115800 D)3125832 E)3125834
SOLUTION:31214 is not divisible by 3 and 8
=> 31214 is not divisible 24
61212 is not divisible by 8 though it is divisible by 3
=> 61212 is not divisible 24
512216 is not divisible by 3 though it is divisible by 8
=> 512216 is not divisible 24
3125832 is divisible by 3 and 8
=> 3125832 is divisible 24
D) #### D
QUESTION:A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently five spaces behind player B, what is the probability that player B will be frozen after player A rolls?
options: A)1/12 B)5/36 C)1/9 D)1/3 E)17/36
SOLUTION:no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 5 (as A is 5 spaces behind B) = 4 ( (1,4), (2,3), (3,2), (4,1) )
So, the probability = 1/9 (Option C) #### C
QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9
SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.
15 = x y and 16 = 2 x + 2 y
Solve the second equation for x
x = 8 - y
Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as
15 = (8 - y) y
Solve for y to find
y = 3 and y = 5
Use x = 8 - y to find x
when y = 3 , x = 5 and when y = 5 , x = 3.
The dimensions of the rectangle are 3 and 5.
As an exercise, check that the perimeter of this rectangle is 16 and its area is 15.
Answer A #### A
QUESTION:In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number?
options: A)26 B)28 C)32 D)36 E)38
SOLUTION:Solution
Let the ten digits be x. Then,units digit=3x
Therefore x + 3x = 8
‹=›4x = 8
‹=›x= 2.
So, ten's digit = 2, unit's digit = 6.
Hence, the required number is 26.
Answer A #### A
QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time?
options: A)70 min B)94 min C)110 min D)112 min E)120 min
SOLUTION:First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
And now we have 4 robots
So Total = (1) + (2) = 70 minutes
Answer - A #### A
QUESTION:If the length of a rectangular field is 30 metres more than its breadth and the perimeter of the field is 540 metres, what is the area of the field in square metres?
options: A)18000 B)40000 C)31000 D)19000 E)16000
SOLUTION:Let breadth is x then length is 30+x
Now the perimeter=2(x+30+x)=540
solving this we get x=120
Now the area is 120*150=18000
ANSWER:A #### A
QUESTION:A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?
options: A)450. B)412. C)432. D)502. E)522.
SOLUTION:Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30
Only option A satisfies the condition, and hence is the answer #### A
QUESTION:Each of the integers from 1 to 18 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even
options: A)19 B)12 C)11 D)10 E)3
SOLUTION:Out of the 18 integers: 9 are odd and 9 are even.
If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:
1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first
2. 10th number will be the first even number
So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even.
So, answer will be 10. (D) #### D
QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
options: A)5.78 B)5.79 C)5.76 D)5.74 E)5.721
SOLUTION:M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76.Answer: C #### C
QUESTION:In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is?
options: A)14 years 8 months B)15 years C)13 years 8 months D)17 years 10 months E)17 years
SOLUTION:Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 17 years - 3 years 4 months.
= 13 years 8 months.
ANSWER:C #### C
QUESTION:How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
options: A)14 B)13 C)12 D)11 E)10
SOLUTION:The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers.
The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form.
So, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number.
We get a total of 19−5=1419−5=14 numbers.
Answer A #### A
QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres
SOLUTION:I guess it should be
the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C) #### C
QUESTION:Find the value of a from (15)^2 x 8^3 ÷ 256 = a.
options: A)250 B)420 C)440 D)650 E)450
SOLUTION:Given Exp. =(15)^2 x 8^3 ÷ 256 = a
= 225 x 512 ÷ 256 =
450
E #### E
QUESTION:The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool?
options: A)1400 B)1600 C)1800 D)1500 E)2000
SOLUTION:volume of pool = 80*150*10 cu.ft ,100% full = 60*100*10*1 cu.ft water is available to drain.
draining capacity =60 cu.ft /min therefore time taken = 80*150*10*1/ 60 min= 2000 min
E #### E
QUESTION:At a meeting of the 8 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 8 Chiefs of Staff be seated around a circular table?
options: A)120 B)480 C)960 D)2520 E)5080
SOLUTION:Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E #### E
QUESTION:Select the one which is different from other Four alternatives.
options: A)988 B)1140 C)1064 D)1197 E)1352
SOLUTION:E
(A) 988 ÷ 19 = 52
(B) 1352 ÷ 19 = 71.15
(C) 1064 ÷ 19 = 56
(D) 1197 ÷ 19 = 63
(E) 1140 ÷ 19 = 60 #### E
QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0
SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B , if you put x = -5, you get -ve value for y co-ordinate.
Answer must be (B) #### B
QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
options: A)10 B)99 C)787 D)62 E)22
SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer: A #### A
QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?
options: A)120cc B)360cc C)450cc D)589C E)478cc
SOLUTION:Explanation:
r1 = x r2 = 3x
Π * x2 * h = 40
Π9 x2h = 40 * 9 = 360cc
Answer: B #### B
QUESTION:A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A.
options: A)237 B)126 C)971 D)611 E)150
SOLUTION:Explanation:
ANSWER: E #### E
QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
options: A)65 B)44 C)18 D)15.49 E)14
SOLUTION:Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 240/3 = 80 sq m
l b = 80 i.e., l * l/3 = 240
l2 = 240 => l =15.49
Answer:D #### D
QUESTION:A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 90 minutes later?
options: A)2(10^5) B)9(10^5) C)(2^9)(10^5) D)(10^9)(10^5) E)(10^5)^9
SOLUTION:Every 10 minutes, the population is double the previous population.
In 90 minutes, the population doubles 9 times.
The population then is 2^9*10^5.
The answer is C. #### C
QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is?
options: A)4452 B)4445 C)4330 D)4334 E)4336
SOLUTION:Divisor = (5 * 42) = 210
= 10 * Quotient = Divisor
=> Quotient = 210/10 = 21
Dividend = (Divisor * Quotient) + Remainder
Dividend = (210 * 21) + 42 = 4452
A #### A
QUESTION:A man can row upstream at 22 kmph and downstream at 42 kmph, and then find the speed of the man in still water?
options: A)29 B)92 C)30 D)32 E)23
SOLUTION:US = 22
DS = 42
M = (42 + 22)/2 = 32
Answer:D #### D
QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 231525, then population in 1978 was?
options: A)120000 B)120029 C)187899 D)178968 E)200000
SOLUTION:X * (105/100) * (105/100) * (105/100) = 231525
X = 231525/1.157625
X = 200000
Answer:E #### E
QUESTION:The sub-duplicate ratio of 25:49 is
options: A)4:3 B)5:7 C)6:4 D)1:4 E)2:3
SOLUTION:root(25):root(49)=5:7
ANSWER:B #### B
QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
options: A)3.25 B)3.6 C)4.2 D)4.4 E)5.14
SOLUTION:Time taken by First tank Fill 1/2 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank =12 hours
Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours
in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours
Answer: option E #### E
QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is?
options: A)26 km/hr B)17 km/hr C)60 km/hr D)42 km/hr E)46 km/hr
SOLUTION:Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/5 = 3x => x = 20/3.
So, speed of the faster train = 40/3 = 40/3 * 18/5
= 42 km/hr.
Answer:D #### D
QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94
SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 96, there are 47 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (47 + 12)/94
= 59/94
= 5/8
Ans is E #### E
QUESTION:In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate?
options: A)69 B)70 C)71 D)72 E)73
SOLUTION:number of ways = 2*3!*3! = 72
Answer is D #### D
QUESTION:Find the greatest number which leaves the same remainder when it divides 25, 57 and 105.
options: A)18 B)8 C)12 D)16 E)None of these
SOLUTION:105 - 57 = 48
57 - 25 = 32
105 - 25 = 80
The H.C.F of 32, 48 and 80 is 16.
ANSWER:D #### D
QUESTION:A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
options: A)20 B)24 C)25 D)26 E)30
SOLUTION:Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways #### A
QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km
options: A)200 Km B)222 Km C)224 Km D)248 Km E)None of these
SOLUTION:Explanation:
Let time taken to travel the first half = x hr
Then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x [because, distance = time*speed]
Distance covered in the the second half = 24(10 - x)
Distance covered in the the first half = Distance covered in the the second half
So,
21x = 24(10 - x)
=> 45x = 240
=> x = 16/3
Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]
Option C #### C
QUESTION:A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is
options: A)8 years B)2 years C)7 years D)8 years E)5 years
SOLUTION:Let's Son age is x, then Father age is x+22.
=> 3(x+3) = (x+22+3)
=> 3x+9 = x+25
=> 2x = 16 years = 8 YEARS
Answer: D #### D
QUESTION:What is the remainder when you divide 2^200-1 by 7?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:answer is C. this is very similar to the 32^32^32-1 divided by 7 question. #### C
QUESTION:In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
options: A)65 B)44 C)86 D)29 E)26
SOLUTION:Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: B #### B
QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700
SOLUTION:Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 8x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400.
Hence, (R - p) = (2400 - 900) = 1500
Answer : B #### B
QUESTION:John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip?
options: A) 24 B) 30 C) 48 D) 54 E) 75
SOLUTION:Speed = Distance/Time
Distance for John = Speed * Time = 40 * 1/2 = 20 miles
Distance for Beth = Distance for John +5 = 20+5 = 25 miles
Time taken by Beth = Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour
Hence, B is the answer. #### B
QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these
SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 4/5
5n + 5 = 4d + 4
5n + 5 = 4(2n - 1) + 4 => n = 5/3
d = 2n - 1 => d = 3/7
Hence the fraction is : 5/7
ANSWER:B #### B
QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money?
options: A)1489 B)6845 C)2598 D)1875 E)2600
SOLUTION:P = 75(100/20)5 => P = 1875
Answer: D #### D
QUESTION:Yesterday, a pie shop sold 6 apple pies, 5 peach pies, and 6 pumpkin pies. How many pies did the shop sell in all?
options: A)21 B)37 C)13 D)17 E)32
SOLUTION:Add the number of pies
6+5+6 =17.
Answer is D. #### D
QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ?
options: A)1000 B)1100 C)1200 D)1300 E)1400
SOLUTION:let profit rate of b = x
acc to question profit rate of a becomes 5/3 x
and that of c= 1/3 x which is given as 10%
1/3 x= 10
therefore x=30
now b=30% , a=50%
now we will find out c's price-
11/10 * price = 2145
price = 1950
in similar way we will find out b's price as we know that profit is 30%
therefore 130/100 * price = 1950
so b 's price =1500
similarly for a ('profit is 50%)
150/100 * price = 1500
on solving it we get
a's price = 1000
ANSWER:A #### A
<<<Examples ends
QUESTION:What is the measure of the angle Y made by the diagonals of the any adjacent sides of a cube.
options: A)30 B)45 C)60 D)75 E)90
SOLUTION:C.. 60 degrees
All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides.
options: A)12, 9 B)18, 3 C)15.16, 6 D)12, 12.37 E)12, 15.16
SOLUTION:CM=3
AREA=PM*CM/2, thus PM=12
By Pythagorean Theorem, we can now find the value of PC.
D is the correct option. #### D
QUESTION:A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
options: A)(a) 60/11 B)(b) 5 C)(c) 26/5 D)(d) 27/5 E)(e) 28/5
SOLUTION:from the uphill we can find out the distance = 5*2 = 10
average speed = total distance/total time
= 20/ (2+ (10/6)) = 60/11
Answer is A. #### A
QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner?
options: A)33 B)34 C)35 D)36 E)37
SOLUTION:Nearest to 1749≈1750
175/50=35 (Caution: Collection is 1750 - 1 = 1749)
Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members
51* 34 = 1734 >> 15 remains which will be adjusted with 15 members
52 * 15 + 51 * 19 = 780 + 969 = 1749
Answer = B #### B
QUESTION:A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price?
options: A)$1200 B)$1300 C)$1000 D)$1700 E)$1050
SOLUTION:C
$1000
90%
104%
--------
14% ---- 140
100% ---- ? => $1000 #### C
QUESTION:4y - 4x = xy and x ≠ 0. If x and y are integers, which of the following could equal y?
options: A)2 B)1 C)0 D)5 E)6
SOLUTION:Plug in the answer choices in the equation from the question stem.
A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE
B) y = 1 >>> 2 - x = 2x >>> Same, POE
C) y = 0 >>> -x = 0 >>> x can not equal 0
D) y = -1 >>> 8 - 4x = 4x >>> Holds true for x = 1, no need to check E. This is the answer.
Answer A #### A
QUESTION:A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)120 m B)225 m C)300 m D)360 m E)280 m
SOLUTION:Speed = 54 x 5/18 m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/35 = 15
x + 300 = 525
x = 225 m.Answer: Option B #### B
QUESTION:5 3 -2 -5 -3 2....What is the sum of first thirty number sequence?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2
=> 50-50=0.
ANSWER:A #### A
QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?
options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2
SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts
B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts
C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts
D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts
E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest.
Answer (E) #### E
QUESTION:What is the perimeter of a square field whose diagonal is 8√2?
options: A)82 m B)32 m C)27 m D)26 m E)76 m
SOLUTION:4a = 32 m
Answer: B #### B
QUESTION:In how many different ways can the letters of the word ‘INDIGO’ be arranged ?
options: A)420 B)520 C)620 D)720 E)820
SOLUTION:D
720
Required number of arrangements = 6! = 720 #### D
QUESTION:A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
options: A)76 seconds B)17 seconds C)40 seconds D)16 seconds E)14 seconds
SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C #### C
QUESTION:A coin is tossed six times. What is the probability that there is at the least one tail?
options: A)63/64 B)31/64 C)31/67 D)31/64 E)63/31
SOLUTION:Let P(T) be the probability of getting least one tail when the coin is tossed six times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/64 ; P(T) = 1 - 1/64
= 63/64
Answer: A #### A
QUESTION:Consider below info to be a table:
AMOUNT OF BACTERIA
TIME - AMOUNT
1PM - 10gms
4PM - x gms
7PM - 10.0 gms
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4PM ?
options: A)12.0 B)12.1 C)10.0 D)12.3 E)12.4
SOLUTION:let say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =10.0 => x^2 =1.00 or x = 1.0 => @4PM quantity = 10x =10*1.0 =10.
Answer C #### C
QUESTION:If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there?
options: A)22896 B)25423 C)26980 D)24698 E)24360
SOLUTION:Code consists of 3 digits and no digit is repeated.
First digit of the code can have 30 possibilities
Second digit can have 29 possibilities
Third digit can have 28 possibilities
Total number of possible codes = 30*29*28 = 24360
Answer: E #### E
QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
options: A)20 B)21 C)22 D)28 E)NONE
SOLUTION:Sol.
Let the total number of workers be x. Then,
8000x = (14000 × 7) + 6000 ( x – 7)
‹=› 2000x = 56000
‹=› x = 28.
Answer D #### D
QUESTION:In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together?
options: A)120 B)360 C)1440 D)13440 E)4320
SOLUTION:The word 'SOFTWARE' contains 8 different letters.
when the vowels OAE are always together, they can be supposed to form one letter.
Thus, we have to arrange the letters SFTWR (OAE)
Now, 5 letters can be arranged in 6!=720 ways.
The vowels (OAE) can be arranged among themselves in 3!=6 ways.
Required number of ways =(720*6)=4320.
Answer is E #### E
QUESTION:On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80?
options: A)18% B)21% C)33.35 D)33.3% E)37.5%
SOLUTION:let the total no of campers be 100
total amount = (25*110)+(35*80)+(40*65) = 2750+2800+2600= $8150
required percentage = (2800/8150)*100=33.35%
C #### C
QUESTION:Convert 2/5 to a decimal
options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5
SOLUTION:Divide 2 by 5: 2 / 5 = 0.4
Answer: 2/5 = 0.4 (D) #### D
QUESTION:Which of the following inequalities is equivalent to −4 < x < 8?
options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above
SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format
-4+y < x+y < 8+y
Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2
Thus, -6< x-2 < 6 => |x-2| < 6.
Hence, answer is D #### D
QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.
options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these
SOLUTION:Explanation:
=[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06
Answer: D #### D
QUESTION:On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is?
options: A)22 B)99 C)27 D)11 E)37
SOLUTION:Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.
S.I for one year = Rs. 330.
S.I. on Rs. 330 for 1 year = Rs. 36.30
Rate = (100 * 36.30)/(330 * 1) = 11%.Answer: D #### D
QUESTION:In how many no. between 10 and 50 exactly Two of the digits is 5?
options: A)47 B)65 C)1 D)35 E)65
SOLUTION:It's simple can be solved by elimination of answer choices.
Option B and D are too large, not possible. Even AE are large to have correct choice.
Ans : C #### C
QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
options: A)36 B)76 C)98 D)27 E)24
SOLUTION:(3x-9):(5x-9)
= 9:17
x = 12 => 3x
= 36
Answer:A #### A
QUESTION:A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn?
options: A) 188 B) 258 C) 376 D) 470 E) 517
SOLUTION:consider 5x acres of land used for bean
consider 2x acres of land used for wheat
consider 4x acres of land used for corn
Total given is 1034 acres
11x =1034
x = 94
land used for corn Y= 4 * 94 = 376
correct option - C #### C
QUESTION:The diagonal of a rhombus are 40 m and 30 m. Its area is:
options: A)600 B)450 C)350 D)500 E)620
SOLUTION:Area of the rhombus = 1/2 d1d2 = ( 1/2 × 40 × 30) Cm(power)2
= 40 × 15 = 600 Cm(power)2
Answer is A. #### A
QUESTION:Find all integers x NOT EQUAL TO 3 such that X-3|X^3-3
options: A)1,2,3,4,5 B)-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 C)1 D)6 E)-1,0,1
SOLUTION:Let x-3=t. Thus, t is an integer not equal to such'that t|(t+3)^2-3,
which is equivalent to the condition t|3^3-3, or t|24. Therefore, it is necessary
and sufficient for t to be an integer divisor of 24, hence t must be equal
to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x
= t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7,
9, 11, 15, and 27.
Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 #### B
QUESTION:If d<0, which of the following represents a positive number?
options: A)d|d| B)|d|d C)|d|/d D)-d|d| E)d/ |d|
SOLUTION:Answer : D #### D
QUESTION:A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
options: A)76 hrs B)99 hrs C)55 hrs D)90 hrs E)11 hrs
SOLUTION:1/9 - 1/x = 1/10
=> 90 hrs
Answer: D #### D
QUESTION:How many figures are required to number the pages the pages of a book containing 365 pages?
options: A)987 B)977 C)967 D)897 E)997
SOLUTION:1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 365 = 266 * 3 = 798
-----------
987
ANSWER:A #### A
QUESTION:Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36,
find P (E|F) and P(F|E)
options: A)5 B)8 C)2 D)6 E)12
SOLUTION:Here, E and F are events
P(E|F) = P(EnF)/P(F) = 36/36 = 1
P(F|E) = P(EnF)/P(E) = 36/24 = 2.
C) #### C
QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
options: A)15 B)30 C)36 D)72 E)46
SOLUTION:Explanation:
Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have : (2x - 16) = (x + 8) or x = 24.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72.
Answer: D #### D
QUESTION:For 1rs 6p interest
wat will be for 1000rs?
options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs
SOLUTION:For 1rs , 4p interest
for 1000rs, x
x= 1000/1 * 6p ==> 6000 paise
To express in rs, 6000/100 = 60rs
ANSWER:E #### E
QUESTION:A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars?
options: A)500 000 B)1 000 000 C)2 000 000 D)5 000 000 E)250 000
SOLUTION:The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is.
5+3+2 = 10
10/2 = X/100 000
5*100 000 = X
500 000 = X
Answer: A) #### A
QUESTION:A factory produces 6000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
options: A)4436 toys B)1500 toys C)6113 toys D)2354 toys E)1375 toys
SOLUTION:To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
6000 /4 = 1500 toys
correct answer B #### B
QUESTION:Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed?
options: A)502 B)512 C)523 D)521 E)500
SOLUTION:Let n be the total number of children.
More children, less notebooks(Indirect proportion)
If the number children = n, number of books each child will get = n/8
If the number children = n/2, number of books each child will get = 16
Hence we can write as
children n:n/2}::16:n/8
⇒n×n/8=n/2×16
⇒n8=16/2=8
⇒n=8×8=64
Then, total number of notebooks those were distributed = n×n/8=(64×64)/8=64×8=512
Answer is B. #### B
QUESTION:Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have?
options: A)5 B)10 C)30 D)40 E)50
SOLUTION:Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)*100% = 60%
Now by Alligation Rule:
A . ......... B
20% . . . 80%
. . 60% . .
(80-60) . (60-20)
=20 : =40
Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration)
So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%)
So as per above ration Qty B mixed will be 50 gallons.
Qty of water in mixture B = 20% of 50 = 10 gallons.
ANSWER:B #### B
QUESTION:The first half of a 600-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal to the average speed, in miles per hour, for the entire trip?
options: A)300/(x + y) B)600/(x + y) C)150/x + 150/y D)300/x + 300/y E)600/x + 600/y
SOLUTION:Time taken to cover first half i.e 300 miles of a 600 mile trip = x
time taken to cover the second half i.e 300 miles of a 600 mile trip = y
Total time taken = x+y
Average speed for the entire trip =total distance /total time
=600/(x+y)
Answer B #### B
QUESTION:The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result?
options: A)600 B)480 C)538 D)650 E)560
SOLUTION:23th result = sum of 45results - sum of 44 results
10*45-16*22+20*22 = 450-352+440 = 538
Answer is C #### C
QUESTION:Half of 2 percent written as decimal is
options: A)5 B)0.01 C)0.05 D)0.005 E)None of these
SOLUTION:Explanation:
It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01
Answer: Option B #### B
QUESTION:If a is a positive integer, which of the following could NOT be the square of a?
options: A) 5,008,644 B) 5,004,169 C) 4,999,696 D) 4,995,225 E) 4,990,752
SOLUTION:A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E) #### E
QUESTION:The wheel of an engine 30/7 metres in circumference makes seven revolutions in 4seconds. Find the speed of the train in km per hour?
options: A)15km/hr B)25km/hr C)32km/hr D)18km/hr E)27km/hr
SOLUTION:Distance travelled by the train in 4 seconds = 30*7/7 = 30 metres
speed of the train = 30/4 = 15/2 m/s = 27 km/hr
Answer is E #### E
QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
options: A)1200 B)1723 C)1129 D)2613 E)1372
SOLUTION:A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 150= 3k + 150 => 2k = 300 => k = 150
The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A
QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
options: A)122443 B)154546 C)165454 D)186545 E)220030
SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
E #### E
QUESTION:Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3
SOLUTION:26^2+26^3 = 26^2(1+26)=27*26^2
The answer is C. #### C
QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16
SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C #### C
QUESTION:A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
options: A)19 cm2 B)30 cm2 C)17 cm2 D)18 cm2 E)12 cm2
SOLUTION:The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5
= 30 cm2
Answer:B #### B
QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X
options: A)35 B)56 C)142 D)87 E)98
SOLUTION:(C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 142 #### C
QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
options: A)5 B)6 C)7 D)82 E)43
SOLUTION:US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A #### A
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
options: A)356 B)250 C)127 D)279 E)150
SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 250 m
Answer: B #### B
QUESTION:When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y?
options: A)96 B)75 C)50 D)25 E)12
SOLUTION:Guys, one more simple funda.
5/2= 2.5
now .5 x2 =1 is the remainder
25/4 = 6.25
now .25x4=1 is the remainder
32/5=6.4
now.4x5 = 2 is the remainder
given x/y = 6.12 and remainder is 6
So .12 X y = 6
hence y= 50
Ans C #### C
QUESTION:A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width?
options: A)12 by 2 B)11 by 3 C)20 by 5 D)10 by 4 E)9 by 3
SOLUTION:2x+2y=50
x+y=25
x+4x=25
5x=25
x=5
Answer C #### C
QUESTION:Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop?
options: A)128 B)64 C)32 D)16 E)8
SOLUTION:Before stop 3, there were 2 passengers on the bus.
Before stop 2, there were 4 passengers on the bus.
Before stop 1, there were 8 passengers on the bus.
The answer is E. #### E
QUESTION:Rectangular tile each of size 60cm by 56cm must be laid horizontally on a rectangular floor of size 560cm by 240cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
options: A)50 B)54 C)47 D)40 E)45
SOLUTION:Area of tile = 60*56 = 3360
Area of floor = 560*240 = 134400
No of tiles = 134400/3360 = 40
So, the no of tile = 40
ANSWER:D #### D
QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?
options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5
SOLUTION:Explanation:
Let the capacity of 1 bucket = x.
Then, capacity of tank = 25x.
New capacity of bucket = 2/5 x.
Required no of buckets = 25x / (2x /5) = 62.5
ANSWER IS B #### B
QUESTION:What is the greatest prime factor of 4^16 - 2^30?
options: A)2 B)3 C)5 D)7 E)11
SOLUTION:4^16 - 2^30
=(2^2)^16 - 2^30
= 2^32 - 2^30
= 2^30 (2^2 -1)
= 2^30 * (4-1)
= 2^30 * 3
The greatest prime factor is 3.
The answer is B. #### B
QUESTION:log3 N+log5 N what is 3 digit number N that will be whole number
options: A)629 B)729 C)829 D)125 E)727
SOLUTION:No of values N can take is 1
5^3=125
ANSWER:D #### D
QUESTION:John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease?
options: A)90% B)30% C)40% D)70% E)80%
SOLUTION:The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)*100 = (0.9)*100 = 90%.
A #### A
QUESTION:Find the average of all numbers between 1 and 76 which are divisible by 5
options: A)40 B)20 C)25 D)30 E)35
SOLUTION:Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75)/15=600/15=40
Answer: Option A #### A
QUESTION:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts?
options: A)6 B)14 C)19 D)20 E)81
SOLUTION:< 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100
Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5;
TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14;
Interns who areNot Tired S= 5 + 14 = 19.
Answer: C. #### C
QUESTION:If -2/(a - 6) = 4/(a + 4), then a = ?
options: A)2/3 B)1/2 C)5/3 D)8/3 E)7/3
SOLUTION:Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve
(a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ]
- 2 (a + 4) = 4 (a - 6)
a = 8/3
correct answer D #### D
QUESTION:There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:Let the number of men be m and so the number of women = 15-m
Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.
Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).
Let the total work be 360 units (LCM of 180 and 120).
1 man does 360/120 = 3 units per day
1 woman does 360/180 = 2 units per day
Based on above facts,
Total work by men + women in these 17 days = 360 units
m*9*3 + (15-m)*6*2 = 360,
27m + 180 -12m = 360, Solving m=12.
Num of men = 12 and number of women = 15-12 = 3
ANSWER:C #### C
QUESTION:In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter?
options: A)15 B)25 C)30 D)45 E)60
SOLUTION:This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...
We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats.
Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as...
15X/7X
When we add the 16 cats and factor in the 'ending ratio', we have an equation....
15X/(7X+16) = 15/11
Here we have 1 variable and 1 equation, so we can solve for X....
(15X)(11) = (7X+16)(15)
(X)(11) = (7X+16)(1)
11X = 7X + 16
4X = 16
X = 4
With this X, we can figure out the initial number of dogs and cats...
Initial dogs = 15X = 15(4) = 60
Final Answer: D #### D
QUESTION:The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
options: A)2888 B)1266 C)1000 D)2779 E)2661
SOLUTION:X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer: C #### C
QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?
options: A)1:4 B)3:5 C)3:9 D)3:7 E)1:3
SOLUTION:Number of men in the colony = 4/7 (70) = 40
Number of women in the colony = 3/7 (70) = 30
Number of educated women in the colony = 1/5 (30) = 6
Number of uneducated women in the colony = 4/5 (30) = 24
Number of educated persons in the colony = 8/35 (70) = 16
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30
Number of educated men and uneducated men are in the ratio 10:30 => 1:3
Answer:E #### E
<<<Examples ends
QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
options: A)4 B)16 C)8 D)1 E)2
SOLUTION:Explanation:
Let the required number of mats be x
More mat-weavers, more mats (direct proportion)
More days, more mats (direct proportion)
Hence we can write as
(mat-weavers) 4:8
(days) 4:8}::4:x
⇒4×4×x=8×8×4
⇒x=2×2×4=16
Answer: Option B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount?
options: A)$1200 B)$1400 C)$1600 D)$1800 E)$2000
SOLUTION:0.7(x-600)=0.6(x-400)
0.1x=420-240
x=1800
The answer is D. #### D
QUESTION:Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.7 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
options: A)1/6 B)1/2 C)5/8 D)5/4 E)15/16
SOLUTION:X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected
0.7(X) + 0.5(1-X) = 0.75
0.2X = 0.75 - 0.5
X = 0.25/0.2
X = 5/4
Therefore the answer is D: 5/4. #### D
QUESTION:Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
options: A)10 min. 20 sec. B)11 min. 45 sec. C)12 min. 30 sec. D)14 min. 40 sec. E)15 min. 40 sec.
SOLUTION:Take LCM of 15 and 20 and get the total capacity of tank as 60 .
Then A will fill 4li in 1 min and B will fill 3 li in 1 min so total will be 7 . A left after 4 min so they worked together for 4 min so 7*4= 28 . now subtract it from 60.(60-38=32). This will be filled by b so time taken would be..10 min 20 sec.
ANSWER:A #### A
QUESTION:If x is less than y by 45% then y exceed x by:
options: A)33.33% B)25% C)81.81% D)66.66% E)None of these
SOLUTION:Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 45/(100-45)*100
=81.81%
ANSWER:C #### C
QUESTION:In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way?
options: A)3 sec B)4 sec C)8 sec D)6 sec E)7 sec
SOLUTION:T = 52/24 * 18/5 = 8 sec
ANSWER:C #### C
QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
options: A)65 B)69 C)30 D)31 E)32
SOLUTION:Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: Option C #### C
QUESTION:45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours?
options: A)50 B)55 C)60 D)65 E)70
SOLUTION:45 workers * 8 hours / 30 meters = x * 6 / 55
x = 110 total workers
110 - 45 = 65 new workers
The answer is D. #### D
QUESTION:A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by :
options: A)7 only B)13 only C)11 only D)1001 only E)1003 only
SOLUTION:256256 = 256 x 1001; 678678 = 678 x 1001, etc.
So, any number of this form is divisible by 1001
ANSWER:D #### D
QUESTION:N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?
options: A)59 B)49 C)58 D)113 E)131
SOLUTION:You have 6 digits: 3, 4, 5, 6, 7, 8
Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.
The first digit (hundreds digit) of both numbers should be consecutive integers
Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options?
Try and make a pair with (4** and 5**). Make the 4** number as large as possible and make the 5** number as small as possible.
487 and 536 (difference is 49) or
Try and make a pair with (6** and 7**). Make the 6** number as large as possible and make the 7** number as small as possible. We get 685 and 734 (difference is 49)
B #### B
QUESTION:Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
.
options: A)20 B)30 C)50 D)80 E)100
SOLUTION:150 employees
80 are full-time
100 have worked at company X for at least a year
20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
150-80=70 employees not full time
70-20= 50 employees not full time who worked over a year
100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year
ANSWER:C #### C
QUESTION:What is the difference between local value & face value of 9 in the numeral 65793?
options: A)8453 B)8956 C)8991 D)9890 E)10000
SOLUTION:(Local value of 9) - (Face value of 9)
= (9000 - 9) = 8991
C #### C
QUESTION:All the students of class are told to sit in circle shape. Here the boy at the 8 th position is exactly opposite to 33 th boy. Total number of boys in the class?
options: A)40 B)50 C)28 D)38 E)48
SOLUTION:As half the circle shape consist of 33-8=25 boys,
So total number of boys in full circle=2*25=50
ANSWER: B #### B
QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
options: A)20 1/2 hours B)20 1/7 hours C)20 1/3 hours D)20 3/2 hours E)20 1/4 hours
SOLUTION:1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours
Answer: A #### A
QUESTION:In track last week, the boys ran 15 laps. The girls ran 5 more
laps. Each lap is a one-fifth of a mile. How many miles did the girls run?
options: A)2 miles B)3 miles C)4 miles D)5 miles E)6 miles
SOLUTION:The girls ran 15 + 5 = 20 laps. 20 x 1/5 = 20/5, which reduces to 4.
The girls ran 4 miles
correct answer C #### C
QUESTION:The area of a triangle is with base 18m and height 6m?
options: A)88 m2 B)10 m2 C)66 m2 D)54 m2 E)31 m2
SOLUTION:1/2 * 18 * 6 = 54 m2
Answer: D #### D
QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
options: A)20 B)34 C)38 D)40 E)46
SOLUTION:We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 40
Hence answer is D #### D
QUESTION:5 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
options: A)360 B)430 C)510 D)540 E)630
SOLUTION:we have to choose one from each set. 1 from 5 nouns and 1 from 4 verbs and 1 from 3 adjectives.
then we have to arrange 3 different sets in 3! ways.
so,
5c1*4c1*3c1*3!=360
ANSWER:A #### A
QUESTION:If the price of sugar rises from Rs. 3 per kg to Rs. 5 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
options: A)15% B)20% C)25% D)30% E)40%
SOLUTION:Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 3 = x × 5 = x = 60 kg.
∴ Reduction in consumption = 40%.
Answer E #### E
QUESTION:The remainder when 1!+2!+3!...+50! divided by 8! will be
options: A)21 B)5193 C)77 D)9275 E)19
SOLUTION:The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!.
So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!.
So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320)
So remainder is 5193.
Answer:B #### B
QUESTION:A sum of Rs.4000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
options: A)2888 B)3120 C)2877 D)2600 E)1277
SOLUTION:Let A be the amount received at the end of the three years.
A = 4000[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4000 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.6600
So the interest = 6600 - 4000 = Rs.2600
Answer: D #### D
QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share?
options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164
SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) .
x + 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs.145
B #### B
QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive?
options: A)–5040 B)–3600 C)–720 D)–600 E)–120
SOLUTION:Maximize the total product with a -ve sign
so -1 * 10 * 9 * 8 = 720 * -1 = -720
Answer is C. #### C
QUESTION:if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr).
options: A)18 kmph B)15.5 kmph C)12.5 kmph D)13.5 kmph E)22.5 kmph
SOLUTION:Speed in still water = (16 + 9)1/2 kmph = 12.5 kmph.
answer :C #### C
QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph
SOLUTION:Speed downstream = 50 + 20 = 70 kmph
Speed upstream = 50 - 20 = 30 kmph
Answer: C #### C
QUESTION:xy=1 then what is (6^(x+y)^2) / (6^(x-y)^2)
options: A)1296 B)4 C)8 D)16 E)32
SOLUTION:(x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
6^4 = 1296
Answer A #### A
QUESTION:The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area?
options: A)1:1 B)1:9 C)1:3 D)1:4 E)1:3
SOLUTION:1:4
Answer: D #### D
QUESTION:What is the place value of 0 in the numeral 2074?
options: A)0 B)1 C)2 D)5 E)6
SOLUTION:Note : The place value of zero (0) is always 0. It may hold any place in a number,
its value is always 0.
A #### A
QUESTION:Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is:
options: A)3776 B)1284.2 C)8400 D)1666.6 E)1671.8
SOLUTION:Ratio of their shares = 1000: 5000= 1:5
Deepak's share = 2000 * 5/6 = Rs. 1666.6.
Answer: D #### D
QUESTION:On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 48 centimeters assuming that 1-inch is 2.54 centimeters?
options: A)174.2 B)212 C)288.1 D)296 E)302
SOLUTION:1.5 inch = 2.54*1.5 cm.
So, 2.54*1.5 represents 24 miles.
So for 48 cm.:
48/(2.54*1.5) = x / 24 ---> x = 24*47/(3.81) = 302
Answer will be E. #### E
QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches
were made?
options: A)84 B)30 C)38 D)42 E)48
SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
240 / 20 = 12 sandwiches in one part
For bologna we have 7 parts so:
7 *12 = 84
Answer is A #### A
QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is
options: A)3 months B)4 months C)6 months D)8 months E)10 months
SOLUTION:Solution
S.I on Rs. 1600 = T.D on Rs. 1680.
Rs.1600 is the P.W of Rs.1680.
Rs.80 is S.I on Rs.1600 at 15%.
Time = (100x80 / 600x15)
= 1/3 year
= 4 months.
Answer B #### B
QUESTION:Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 81 hours respectively. The ratio of their speeds is?
options: A)4:9 B)9:4 C)4:5 D)4:1 E)4:2
SOLUTION:Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √81 : √16
= 9:4
Answer:B #### B
QUESTION:How many words can be formed by using all letters of the word “BIHAR”
options: A)452 B)320 C)365 D)456 E)120
SOLUTION:The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
Ans: E #### E
QUESTION:The average age of a group of persons going for picnic is 16 years. Twelve new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
options: A)5 B)10 C)12 D)40 E)50
SOLUTION:Solution
Let the initial number of persons be x. Then
16x + 12 x 15 = 15.5(x+20)
= 0.5x = 6
x = 12.
Answer C #### C
QUESTION:How many 7-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 5 different consonants?
options: A)4!*5c2 *21c2 B)4!*5c3 *21c2 C)5!*5c2 *21c2 D)7!*5c2 *21c5 E)6!*5c2 *21c2
SOLUTION:combination for 2 vowels out of 5 = 5c2 ways
combination for 5 consonants of 21 = 21c5 ways
Additionally the arrangement can be = 7!
total arrangements =7!*5c2 *21c5
D #### D
QUESTION:In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
options: A)67 kg. B)68 kg. C)69 kg. D)Data inadequate E)None of these
SOLUTION:EXPLANATION
Let Arun’s weight by X kg.
According to Arun, 65 < X < 72
According to Arun’s brother, 60 < X < 70.
According to Arun’s mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required Average =( 66 + 67 + 68 /3 )= (201/3) = 67 kg
Answer A #### A
QUESTION:The mean of 50 observations was 36. It was found later that an observation 43 was wrongly taken as 23. The corrected new mean is
options: A)35.2 B)36.1 C)36.2 D)36.4 E)None
SOLUTION:Solution
Correct sum= (36x50+43-23)
= 1820.
∴ Correct mean= 1820 / 50
= 36.4.
Answer D #### D
QUESTION:A 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
options: A)500 B)350 C)828 D)277 E)122
SOLUTION:Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/489 = 50/3
3x + 900 = 2400 => x = 500 m.
Answer: A #### A
QUESTION:Convert the 9/36 m/s into kilometers per hour?
options: A)0.9 kmph B)9.9 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph
SOLUTION:9/36 m/s = 9/36 * 18/5 = 9/10
= 0.9 kmph.
Answer: A #### A
QUESTION:4 shepherds were watching over the flocks and they were commenting on how many sheep they each had. If ram had 3 more sheep than he would have one less than rahul. wheras akar has the same number as the other 3 shepherds put togeher. If john had 3 less sheep he would have exactly trile the number of ram. If they were evenly distributed if they would each have 11 seep how many sheep did ram have?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:akar has=ram+rahul+john
after evenly distribution each has 11. so, total no. is 44
so, akar has=22 & ram+rahul+john=22 also ram=rahul-4 & john-3=3*ram solving these we get the sol.
ANSWER:B #### B
QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b?
options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given.
SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2.
Answer: A. #### A
QUESTION:A train 120 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
options: A)11 s B)10 s C)8 s D)12 s E)None of these
SOLUTION:We know from the formula Time = Distance/ Speed
Thus, Time = 120/ 54 x 5/18
or, Time = 8 sec.
ANSWER:C #### C
QUESTION:Zeeshan having a certain number of one rupee,fifty paise and twenty
five paise coins are in the ratio of 3:2:4, add up to
Rs 75. Then how many 1 rupee coins he have?
options: A)10 B)20 C)45 D)128 E)49
SOLUTION:Explanation :
Given ratio = 3:2:4.
Let us assume that there are 3 one rupee coins,2
fifty paise coins and 4 twenty-five paise coins in all.
Their value=(3*1)+(2*.50)+(4*.25)=3+1+1=Rs 5
If the total is Rs 5, number of 1 rupee coins are 3.
If the total is Rs 75, number of 1 rupee coins would be 75*3/5=45.
Answer : C #### C
QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face.
options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114
SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C #### C
QUESTION:Find the length of the wire required to go 12 times round a square field containing 104976 m2.
options: A)15840 B)3388 C)2667 D)8766 E)15552
SOLUTION:a2 = 104976 => a = 324
4a = 1296
1296 * 12 = 15552
Answer: E #### E
QUESTION:A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/5 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?
options: A)x + 2000 = 1/3*(x - 3000) B)1/3*(x - 3000) = x C)x + 3000 = 1/3*x D)x - 7000 = 1/3*x E)x - 3000 = 1/5*x
SOLUTION:Plane's original altitude = x
Plane's new altitude after ascending 2000 ft = x+2000
Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000
So, after two changes plane is at 1/5 its original altitude => x-3000 = x/5
Answer (E) #### E
QUESTION:A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
options: A)2: 7 B)2: 0 C)2: 4 D)2: 3 E)2: 1
SOLUTION:80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280.Answer:D #### D
QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision?
options: A)2008 B)2004 C)2005 D)2006 E)2007
SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008.
Answer: A. #### A
QUESTION:A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $3200 and the total price paid for type B products was $5800. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
options: A)$14,755 B)$15,325 C)$11,129 D)$16,225 E)$17,155
SOLUTION:cost of type A products next year = 1.3 * 3200 = 4160
cost of type B products next year = 1.2 * 5800 = 6960
total 4169 + 6960 = 11129
ANSWER:C #### C
QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats?
options: A)12 B)302 C)1 D)250 E)286
SOLUTION:Total number of hats = 13
Possible number of formations = 13C3 = 286
Correct answer is E #### E
QUESTION:A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 60% above the original cost per share of stock, then interns of m for how many dollars was each share sold?
options: A)a) 2m/300 B)b) m/300 C)c) 5m/900 D)d) m/300 + 50 E)e) 350/m
SOLUTION:Let Cost of 300 shares be $ 3000
So, Cost of 1 shares be $ 10 =>m/300
Selling price per share = (100+60)/100 * m/300
Or, Selling price per share = 5/3 * m/300 => 5m/900
Hence answer will be (C) #### C
QUESTION:A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 85 on the S scale?
options: A)39 B)41 C)43 D)45 E)47
SOLUTION:A change of +18 on the R scale is a change of +30 on the S scale.
R = (18/30)*S + K = 3S/5 + K
6 = 3(30)/5 + K
K = -12
R = 3S/5 - 12
R = 3(85)/5 - 12 = 51-12 = 39
The answer is A. #### A
QUESTION:69 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
options: A)20 B)23 C)24 D)25 E)26
SOLUTION:According to the chain rule,
M1 x T1 = M2 x T2
Therefore, 69 x 12 x 5 = 30 x 6 x X
X = 23
Hence, the number of days = 23.
ANSWER:B #### B
QUESTION:A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
options: A)9:32 B)9:30 C)32:9 D)19:32 E)18:30
SOLUTION:Water:soap = 3:4
Soap:Salt=15:20
=> For 15 soap, salt = 20
=> For 4 Soap, salt = (20/15)*4 = 80/15=16/3
So, water:soap:salt = 3:4:16/3= 9:12:16
After open container, water:soap:salt =4.5:12:16
So, water:salt = 4.5:16 = 9:32
ANSWER:A #### A
QUESTION:6 men, 8 women and 6 children complete a job for a sum of Rs.950. If their individual wages are in the ratio 4:3:2, the total money earned by the children is
options: A)Rs. 150 B)Rs. 170 C)Rs. 180 D)Rs. 190 E)None of these
SOLUTION:Explanation:
Ratio of wages of 6 men, 8 women and 6 children = 6 x 4 : 8 x 3 : 6 x 2
= 24 : 24 : 12
= 2 : 2 : 1
Money earned by children = 950 x (1/5) = Rs. 190
Answer: Option D #### D
QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.
options: A)12sec B)20sec C)15sec D)18sec E)10sec
SOLUTION:Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec
Answer : E #### E
QUESTION:If A,B,C,D,E,F,G,H,I,J are in an increasing Arithmetic Progression as such. Then Which of the following operations will result in only mean being modified but not the median.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed
options: A)1) A and B B)2) A and E C)3) A,C,E D)4) All of them E)5) None of them
SOLUTION:There are 10 equidistant numbers on the number line.
Mean and median will be the average of middle two numbers.
If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where mean will change and median will not change.
Answer: E #### E
QUESTION:In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 10 is
options: A)8 B)625 C)16 D)20 E)24
SOLUTION:I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 10
A. x+y+x-y = 10 --> x=5
B. x+y-x+y = 10 --> y=5
C. -x-y +x-y= 10 --> y=-5
D. -x-y-x+y=10 --> x=-5
The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be25*25=625
Answer: B #### B
QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number?
options: A)9 B)11 C)17 D)13 E)15
SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7.
Given (x + 1) + (x + 7) = 28
=> 2x + 8 = 28 => x = 10
The third number = x + 3 = 10 + 3 = 13.
Answer: D #### D
QUESTION:Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 70 white marbles. How many red marbles could be in bag A?
options: A)1 B)3 C)4 D)6 E)14
SOLUTION:6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4k
W = 70 = 6K+4k
=>k=7
Total Red's in bag A will be 2K = 14
E #### E
QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is:
options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62
SOLUTION:(3x-9):(5x-9) = 3:2
x = 1 => 3x = 3
Answer:A #### A
QUESTION:For 15 people each has to pay Rs.20.For 20 people each has to pay Rs.18. For 40 people--how much has each to pay?
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:15-->20
20-->18
25-->16
30-->14
35-->12
40-->10
ANSWER:B #### B
QUESTION:A group of 11 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?
options: A) E/(12 - n) B) (12 - n)/E C) E/[12(12-n)] D) nE / [11(11-n)] E) (12-n)E/(12n)
SOLUTION:total cost =E
no of people willing to participate initially =11
initial cost for each =E/11
when n people decided not to participate
Cost for each =E/11-n
D #### D
QUESTION:Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:
options: A)Rs. 4800 B)Rs. 5000 C)Rs. 5400 D)Rs. 5600 E)Rs. 6600
SOLUTION:let investment is x... den remaining investment is (9800-x)
x*9/75= (9800-x)*10/80
x=4800
9800-x=5000
ANSWER:B #### B
<<<Examples ends
QUESTION:If ty > 0 and yz < 0, which of the following must be negative:
options: A)tyz B)ty(z^2) C)t(y^2)z D)t(y^2)(z^2) E)(x^2)(y^2)(z^2)
SOLUTION:ty > 0 means that ty is positive.
yz < 0 means that yz is negative.
t(y^2)z = (ty)(yz) = positive*negative = negative. Thus option C is always negative. #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Anderson has a phone plan that charges a
monthly rate of $50 for the first 1,000 minutes
plus $0.25 for each additional minute.
Which of the following functions models
Anderson’s plan for all m > 1,000, with m as
the number of minutes per month and f(m)
as the monthly charge?
options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000
SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee
based on the number of minutes used plus a flat rate of $50. With this information, you can
create the following function:
f(m) = Usage fee + 50
The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So
the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify:
f(m) = 0.25(m – 1,000) + 50
f(m) = 0.25m – 250 + 50
f(m) = 0.25m – 200
correct answer C)f(m) = 0.25m – 200 #### C
QUESTION:If f(c)=c^2 and c is a positive integer, which of the following CANNOT be the value of f(f(c))?
options: A)81 B)16 C)300 D)256 E)625
SOLUTION:f(c)=c^2
f(f(c)) = (c^2)^2 = c^4
Therefore f(f(c)) will be numbers that are 4th power of other numbers.
Checking the options:
81 = 3^4
16 = 2^4
300. This cannot be written as the 4th power of any number
256 = 4^4
625 = 5^4
Answer: C #### C
QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
options: A)15 B)30 C)36 D)72 E)46
SOLUTION:Explanation:
Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have : (2x - 16) = (x + 8) or x = 24.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72.
Answer: D #### D
QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets?
options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes
SOLUTION:(350+250)t=800
600t=800
t=4/3
t=1 hour and 20 minutes
Answer: A #### A
QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
options: A)80% B)20% C)40% D)50% E)None of these
SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84
Number of students failed = 140 - 84 = 56.
Required percentage = 28/56 * 100 = 50%.
ANSWER:D #### D
QUESTION:A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is
options: A)8 years B)2 years C)7 years D)8 years E)5 years
SOLUTION:Let's Son age is x, then Father age is x+22.
=> 3(x+3) = (x+22+3)
=> 3x+9 = x+25
=> 2x = 16 years = 8 YEARS
Answer: D #### D
QUESTION:In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters?
options: A)125.5 meters B)126.5 meters C)127.5 meters D)128.5 meters E)None of these
SOLUTION:Explanation:
When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters.
Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters.
So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C.
So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters.
Answer: C #### C
QUESTION:A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
options: A)5.3 % B)7.6 % C)10.6 % D)12 % E)None of these
SOLUTION:Explanation:
Let Marked price be Re. 1 each
C.P. of 50 pens = Rs. 46
S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50
Profit % = (Profit /C.P.) x 100
Profit% = (3.50/46) x 100 = 7.6 %
ANSWER B #### B
QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?
options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45
SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/800*1/600=1/4,800.
Answer: B. #### B
QUESTION:If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 287 pounds. What is Jake’s present weight, in pounds?
options: A)178 B)182 C)186 D)190 E)194
SOLUTION:J + K = 287 and so K = 287 - J
J - 8 = 2K
J - 8 = 2(287-J)
3J = 582
J = 194
The answer is E. #### E
QUESTION:How many integers are between 3 and 86/7, inclusive?
options: A)8 B)9 C)10 D)11 E)12
SOLUTION:86/7 = 12.xx
We are not concerned about the exact value of 86/7 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 3 and 86/7 would be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Total number of integers = 10
Option C
If we need to find the number of integers between two numbers n and m, where m > n
The number of integers = m - n + 1
In the given question, the number of integers = 12 - 3 + 1 = 10
ANSWER:C #### C
QUESTION:How many integers between 263,205and 658,805 have tens digit 1 and units digit 3?
options: A)3,955 B)3,925 C)3,956 D)3,926 E)3,915
SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 263,205 and is 658,805 -263205=395,600 - one number per each hundred gives 133,900/100=3,956
Answer:C. #### C
QUESTION:Three unbased coins are tossed. the probability of getting at least two head is ?
options: A)1/4 B)1/2 C)3/4 D)2/3 E)2/5
SOLUTION:S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}
E be the event of getting at least two head is {THH,HTH,HHT,HHH}
P(E)=n(E)/n(S)=4/8=1/2
Answer(B) #### B
QUESTION:There has been successive increases of 25% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
options: A)23% B)27% C)31% D)35% E)39%
SOLUTION:Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.1*1.25*P = x*P
y = x / (1.1*1.25) which is about 0.73x which is a decrease of about 27%.
The answer is B. #### B
QUESTION:Three coins are tossed. Find the probability of at least 1 head and 1 tail ?
options: A)1/2 B)1/4 C)3/4 D)7/8 E)1/8
SOLUTION:n(s) = 2^3 = 8 ....(3 coins tossed)
let E is the event of getting at least 1 head and 1 tail
n(E) = TTH , HTT, THT, HHT, HTH, THH = 6
P(E) = n(E) / n(s)
= 6/8
= 3/4
Ans- C #### C
QUESTION:Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol.
What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol?
options: A)32 B)21 C)27 D)None of these E)18
SOLUTION:Explanation:
Let t be the time after Kajol starts, when she meets Ajay, then
\inline t=\frac{300}{(x+y)}
This should be less than 2.5 or (x+y)>120
Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72
This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol.
Answer: D #### D
QUESTION:If n is a positive integer, which of the following is a possible value of |36 - 5n|?
options: A)7 B)14 C)12 D)15 E)20
SOLUTION:When 36>5n, then |36- 5n| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1
When 36<=5n, then |36- 5n| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits.
Answer: B #### B
QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6?
options: A)300 B)992 C)772 D)552 E)280
SOLUTION:1/3:1/3:1/6 = 2:2:1
1/5*1400 = 280
560-280 = 280
Answer: E #### E
QUESTION:If G = 775 × 778 × 781, what is the remainder when G is divided by 14?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:G 775/14 leaves a remainder 5
778/14 leaves a remainder 8
781/14 leaves a remainder 11
5*8*11 =440
So the remainder will be the remainder of 440/14 which is 6
Ans A #### A
QUESTION:John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 : 1/4 : 1/5 . What is the minimum no. of pencils that the person should have?
options: A)65 B)68 C)70 D)77 E)80
SOLUTION:Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.
D) #### D
QUESTION:A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt?
options: A)100 B)102 C)104 D)108 E)90
SOLUTION:The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 10 = 90 ways.
E #### E
QUESTION:The speeds of three motor bikes are in the ratio 12 : 4 : 2. The ratio between the time taken by them to travel the same distance is :
options: A)1 : 3 : 4 B)1 : 3 : 6 C)1 : 2 : 6 D)1 : 3 : 5 E)1 : 4 : 6
SOLUTION:Ratio of time taken :
1/12 :1/4 : 1/2 = 1 : 3 : 6
ANSWER:B #### B
QUESTION:10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day?
options: A)4 days B)10 days C)20 days D)25 days E)26 days
SOLUTION:Explanation:
10*12*15/20 = 24*20*x/32
X=4
Answer: Option A #### A
QUESTION:In 6 years, A will be thrice as old as B was 4 years ago. If A is now 6 years older than B, find the present age of B.
options: A)16 years B)24 years C)8 years D)12 years E)18 years
SOLUTION:let present age of A be A
let presennt age of B be B
in 6 yrs
A+6:B+6=3(B-4):B=6
ie A+6=3(B-4)
but given A=B+6
so B+6+6=3(B-4)
B=12
ANSWER:D #### D
QUESTION:By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article?
options: A)72.0 B)75.0 C)70.00 D)68.00 E)None of these
SOLUTION:Let the cost price of the article be x.
Then,2(84 –x) = 96 – x
l68 – 2x= 96 – x \ x = 72
Answer A #### A
QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -.
options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7
SOLUTION:3!4! Required probability = 3!4!/6! = 1/5
ANSWER A #### A
QUESTION:If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king?
options: A)6/13 B)7/10 C)4/11 D)7/13 E)5/26
SOLUTION:There are 26 black cards and 2 red kings.
P(black card or king) = 28/52 = 7/13
The answer is D. #### D
QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision?
options: A)2008 B)2004 C)2005 D)2006 E)2007
SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008.
Answer: A. #### A
QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was
options: A)Rs. 2000 B)Rs. 10000 C)Rs. 15000 D)Rs. 20000 E)None of these
SOLUTION:Explanation :
Principal = Rs. (100×5400 / 12×3)
=> Rs. 15,000.
Answer : C #### C
QUESTION:During a trip on an expressway, Son drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
options: A)8.5% B)50% C)x/12% D)60/x% E)500/x%
SOLUTION:so Son drove (x-5) miles at 60mph and 5 miles at 30mph:
(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance
if the entire trip @60mph than time = x/60
so to get percent [(X+5)/60 ]/[x/60] x100
=(x+5)/x *100
=100+500/x
so increase of 500/x%[/u]=E #### E
QUESTION:If x + y = 8 and y − 3x = 7, then what is the value of y-x?
options: A)1/7 B)3 C)15 D)15/2 E)60/7
SOLUTION:x+y=8 ...equation 1
-3x+y=7 ...equation 2
adding both the equations
-2x+2y=15=>y-x=15/2
correct answer option D #### D
QUESTION:What least number must be added to 1056, so that the sum is completely divisible by 23 ?
options: A)2 B)3 C)16 D)18 E)23
SOLUTION:23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
Answer: Option A #### A
QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent .
options: A)50 B)45 C)40 D)60 E)55
SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m
Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33.
Gain%=[(11/22)*100]%=50%
Answer A) 50. #### A
QUESTION:The ratio between the number of sheep and the number of horses at the Stewart farm is 1 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
options: A)18 B)28 C)32 D)56 E)8
SOLUTION:Let the number of sheeps and horses be 1x and 7x.
Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8
Sheeps = 1x = 1*8 = 8.
Hence E #### E
QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute?
options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min
SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
68 kilometers per hour = 68 km/hr
= (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute
correct answer is B)1133.33m/min #### B
QUESTION:The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
options: A)70 B)72 C)75 D)78 E)80
SOLUTION:Income of 6 months = (6 × 85) – debt
= 510 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 780
Average monthly income = 780 ÷ 10 = 78
Answer D #### D
QUESTION:You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.
options: A)180 B)181 C)182 D)178 E)168
SOLUTION:add the max weights
52+50+78=180
ANSWER:A #### A
QUESTION:If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is
options: A)40 B)44 C)80 D)86 E)90
SOLUTION:Sol.
Let the numbers be x and y.
Then, (x+y) = 24 and x2 + y2 = 404.
Now, 2xy = (x+y)2 - (x2 + y2)
= (24)2 - 404 = 576- 404 = 172
xy = 86.
Answer D #### D
QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs?
options: A)362880 B)340009 C)250909 D)345008 E)1000
SOLUTION:number of ways =9! = 362880
Answer is A #### A
QUESTION:Rahul take a loan of sum Rs.550.This is to be repaid in two equal annual installments. If the rate of interest be 20% compounded annually,then find the value of each installment?
options: A)360 B)420 C)230 D)540 E)610
SOLUTION:Let the value of each installment be Rs.x
[x/(1+(20/100))]+[x/(1+(20/100))2]=550
(100x/120)+(10000x/14400)=550
(5x/6)+(25x/36)=550
x=360
Option A #### A
QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers?
options: A)1 B)5 C)7 D)8 E)9
SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6
y = mx + b => 12 2/3 = -22*5/6 + b => b = 31
y = -5x/6 + 31
Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point.
A #### A
QUESTION:Mary travels the first 9 hours of her journey at 40 mph speed and the remaining 6 hours at 30 mph speed. What is the average speed of Mary's travel in mph?
options: A)32 mph B)34 mph C)36 mph D)35 mph E)31 mph
SOLUTION:Explanation :
Average speed=Total Distance/Time.
Total distance travelled by mary = Distance covered in the first 9 hours + Distance covered in the next 6 hours.
Distance covered in the first 9 hours = 9×40=360 miles
Distance covered in the next 6 hours= 6×30=180 miles
Therefore, total distance travelled = 360+180=540 miles.
The total time taken = 9+6=15hours.
Hence, the average speed =540/15= 36 mph.
Answer : C #### C
QUESTION:If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?
options: A)17/140 B)29/180 C)26/143 D)1/5 E)39/121
SOLUTION:50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 7*2 = 14 hours;
In 1 hour 15 journeymen can finish 1/14 of the job.
Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job.
Answer: A #### A
QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
options: A)1.99 km B)2.88 km C)4.49 km D)2.99 km E)7.88 km
SOLUTION:M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B #### B
QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 80 and n is not prime, what is the greatest possible value of f(n)?
options: A)75 B)69 C)60 D)55 E)63
SOLUTION:Since we need the largest value of f (n), we will start with the largest option.
Option A: 75 = 3*5*5. This is not a product of distinct prime numbers. Hence incorrect
Option B: 69 = 3*23. This is a product of distinct prime numbers.
Rest all the options are smaller that 69.
Correct Option: B #### B
QUESTION:The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:Perimeter = 2(W+L) = 5W
3W = 2L
W = 2L/3
WL = 54
2L^2/3 = 54
L^2 = 81
L = 9 cm
The answer is D. #### D
QUESTION:5.005/4.004 =
options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25
SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25
The answer is E. #### E
QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x?
options: A)16 B)28 C)15 D)13 E)18
SOLUTION:HCF x LCM = Product of Numbers
2 x 144 = 16 x x
x = (2 x 144) / 16
x = 18
ANSWER : E #### E
QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {1,2,3}, what`s the probability that xy will be even?
options: A)1/6 B)1/3 C)2/3 D)1/2 E)5/6
SOLUTION:The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: C. #### C
QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is :
options: A)700 B)690 C)650 D)698 E)728
SOLUTION:Explanation :
Simple Interest (SI) for 1 year = 854-815 = 39
Simple Interest (SI) for 3 years = 39 × 3 = 117
Principal = 815 - 117 = Rs.698
Answer : Option D #### D
QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
options: A)10 B)12 C)15 D)20 E)25
SOLUTION:Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
ANSWER:B #### B
QUESTION:The average of two numbers is P. If one number is Q, then the other number is
options: A)2Q B)2P C)P - Q D)2P-Q E)None of these
SOLUTION:Explanation :
Let the other number be x,
According to the question,
=> ( x + Q ) / 2 = P.
=> x + Q = 2P.
=> x = 2P - Q.
Hence, the required number is 2P - Q.
Answer : D #### D
QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
options: A)2/7 B)3/8 C)3/10 D)4/11 E)5/13
SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C #### C
QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B?
options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above
SOLUTION:et ratio of A and B be 6x & 7x
so net loss = 6x+7x= 7800
x=600
A=6x=6(600)=3600
B= 7x=7(600)=4200
so, B= 4200
ANSWER:A #### A
QUESTION:The H.C.F. and L.C.M. of 0.63, 1.05 and 2.1
options: A)(i)0.20(ii)6.31 B)(i)0.21(ii)5.30 C)(i)0.21(ii)6.30 D)(i)1.21(ii)6.50 E)None of these
SOLUTION:Explanation :
Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10.
Without decimal places, these numbers are 63, 105 and 210.
Now, H.C.F. of 63, 105 and 210 is 21.
H.C.F. of 0.63, 1.05 and 2.1 is 0.21.
L.C.M. of 63, 105 and 210 is 630.
L.C.M. of 0.63, 1.05 and 2.1 is 6.30.
ANSWER IS C #### C
QUESTION:In how many W ways can 5 people from a group of 6 people be seated around a circular table
options: A)56 B)80 C)100 D)120 E)144
SOLUTION:W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner)
= 6 * 4!
= 6 * 24
= 144
Answer - E #### E
QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2
options: A)I only B)I,II only C)II only D)I,III only E)III only
SOLUTION:12=2*2*3
16=2*2*2*2
GCF =2*2=4
Answer : C #### C
QUESTION:If y exceeds x by 25%, then x is less than y by?
options: A)20% B)16 3/3% C)16 2/3% D)12 2/3% E)16 1/3%
SOLUTION:X=100 y=125
125------25
100-------? => 20%
Answer:A #### A
QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?
options: A)144 B)180 C)192 D)360 E)None of these
SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options.
Task 2 can be assigned to 3 or 4
So, there are only 2 options for task 2.
So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6.
= 2 × 3 × 4 × 3 × 2 × 1 = 144
Answer A #### A
QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red?
options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15
SOLUTION:P(Both are red),
=6C213C2=6C213C2
=5/26
C #### C
QUESTION:The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π
SOLUTION:=Square - Quarter circle
=12- pi*12/4
=12- pi*3
ANSWER:B #### B
QUESTION:A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
options: A)8p B)pq C)pq + 27 D)-p E)(p - q)^6
SOLUTION:A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject.
B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject.
C. Hold.
D. since p is a perfect cube, -p will also be a perfect cube. reject.
E. (p-q)^6, is a perfect cube, so reject.
By elimination C is the answer.
Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube.
ANSWER:C #### C
QUESTION:Which of the following is satisfied with |x-4|+|x-3|<6?
options: A)1<x<5 B)2<x<5 C)0.5<x<6.5 D)0.5<x<4 E)3<x<4
SOLUTION:--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5
Therefore, the answer is C. #### C
QUESTION:If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 24
III. P is a multiple of 23
options: A)I only B)II only C)III only D)None of the above E)All of the above
SOLUTION:The correct answer is B. #### B
<<<Examples ends
QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13
SOLUTION:Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 650 = 13
Answer: E #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
options: A)1227 B)2088 C)26788 D)8112 E)1871
SOLUTION:A = 7500(26/25)2 = 8112
Answer: D #### D
QUESTION:A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
options: A)35 B)20 C)47 D)36 E)30
SOLUTION:1: 2/5 = 5: 2
2/7 * 70 =20
Answer:B #### B
QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 12-meter platform and caught it after it had traveled 35.65 meters. How many times did the ball bounce?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Ans: 6
Division of total diatance travelled will be 12+12+6+3+1.5+.75+0.4 ANS B #### B
QUESTION:Zaya purchase 13 jars in a store then she returned 10 jars to store .Now how many jars she had?
options: A)A)5 B)B)11 C)C)19 D)D)3 E)E)4
SOLUTION:13-10=3. Answer is D #### D
QUESTION:What is the perimeter of a square with area 9p^2/25 ?
options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3
SOLUTION:Area of square, (side)^2 = (3p/5)^2
Therefore side of the square = 3p/5
Perimeter of square = 4*side = 4* (3p/5) = 12p/5
Answer is C. #### C
QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price
options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/-
SOLUTION:100 % ------> 200 (100 * 2 = 200)
120 % ------> 240 (120 * 2 = 240)
Selling price = Rs.240/-
Answer : D #### D
QUESTION:If n is a positive integer, which of the following is a possible value of |36 - 5n|?
options: A)7 B)14 C)12 D)15 E)20
SOLUTION:When 36>5n, then |36- 5n| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1
When 36<=5n, then |36- 5n| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits.
Answer: B #### B
QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
options: A)16 B)77 C)88 D)55 E)778
SOLUTION:P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days.
Answer:A #### A
QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers?
options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4
SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference D= 10k - 3 - (10k - 7)
= 4
Answer - D #### D
QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 1 buckles is how many times that of 5 buckles and 6 buttons?
options: A)7/15. B)2/5. C)6/11. D)5/9. E)8/15.
SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons)
6buttons + 6buckles = 11buckles + 3buttons
3buttons = 5buckles
Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles
Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles
(3buttons and 2buckles) = x * (6buttons and 5buckles)
6 = x*15
x = 6/15=2/5
Answer: B #### B
QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor?
options: A)163 B)785 C)852 D)456 E)852
SOLUTION:Divisor *quotient+remainder=dividend
divisor=(dividend)-(remainder)/quotient
(12401-13)/76=163
Answer(A) #### A
QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute?
options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min
SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
68 kilometers per hour = 68 km/hr
= (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute
correct answer is B)1133.33m/min #### B
QUESTION:In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together?
options: A)A)360 B)B)480 C)C)720 D)D)5040 E)of these
SOLUTION:The word 'SINGING' has 7 different letters.
When the vowels II are always together, they can be supposed to form one letter.
Then, we have to arrange the letters SNGNG (II).
Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.
The vowels (II) can be arranged among themselves in 1! = 1 way.
Required number of ways = (720 x 1) = 720.
ANSWER:C #### C
QUESTION:4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 weavers in 10 days?
options: A)10 B)15 C)20 D)25 E)30
SOLUTION:1 weaver can weave 1 mat in 4 days.
10 weavers can weave 10 mats in 4 days.
10 weavers can weave 25 mats in 10 days.
The answer is D. #### D
QUESTION:Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
8 minutes more to walk to work than to ride his bicycle, then x equals
options: A)4 B)7 C)12 D)15 E)20
SOLUTION:The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 8 mins or 8*60 secs in 8*60/40 =12 km
ANSWER:C #### C
QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is:
options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these
SOLUTION:Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (45 x 2) = 90 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv)
Subtracting (i) from (iv), we get : B = 35.
B’s weight = 35 kg.
Answer: D #### D
QUESTION:A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
options: A)4 min B)8 min C)9 min D)6 min E)1 min
SOLUTION:S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer:A #### A
QUESTION:In how many ways can 5 people, A, B, C, D, E, be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
options: A)384 B)396 C)576 D)24 E)696
SOLUTION:Number of total arrangements = 5!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
5! - (4!*2*2) = 120 - (24*2*2) = 24
Answer D #### D
QUESTION:James took a 3-hour bike ride. In the second hour he traveled 6 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
options: A)54.0 B)54.9 C)18.5 D)57.0 E)63.0
SOLUTION:Let the distance travelled in the first hour be x. Thus, 1.2x = 6, x = 5. Now, the distance travelled in the 3rd hour = 6+1/4∗6=7.5 The only option ending with a 0.5 in the decimal place is C.
ANSWER:C #### C
QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B?
options: A)7 B)9 C)8 D)11 E)10
SOLUTION:Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 22
⇒ 5x = 20
⇒ x = 4.
Hence, B's age = 2x = 8 years.
Answer: C #### C
QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr
SOLUTION:Work done by the tank in 1 hour
= (1/2 - 1/3)
= 1/14 Leak will empty the tank in 14 hrs.
Answer:D #### D
QUESTION:When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following T is a possible value for x + y?
I. 18
II. 19
III. 20
options: A)I only B)II only C)T=III only D)II and III only E)None
SOLUTION:TIP FOR SUCH QUESTIONS: Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about
i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as
m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7
i.e. Min Value of x = 8
AND
i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as
n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11
i.e. Min Value of y = 12
i.e. Minimum Value of x+y = 8+12 = 20
Hence III only can be True
Answer: Option
C #### C
QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet?
options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge
SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location.
In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle.
Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate.
The correct answer is (E). #### E
QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
options: A)14355 B)15432 C)17576 D)18543 E)16878
SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C #### C
QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q?
options: A)25 B)35 C)45 D)55 E)65
SOLUTION:P started with 7k stamps and Q started with 2k stamps.
(7k-15)/(2k+15) = 2/1
3k = 45
k = 15
P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps.
The answer is C. #### C
QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence?
options: A)−164 B)0 C)16 D)32 E)64
SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term)
sum of 64 terms = 32
ANSWER:D #### D
QUESTION:Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes. Each inlet pipe can fill the tank in 9 hours and each outlet pipe can empty the tank in 6 hours. On opening all the pipes, an empty tank is filled in 9 hours. How many inlet pipes are there?
options: A)2 B)4 C)3 D)5 E)6
SOLUTION:x / 9 – y / 6 = 1/9; 2x – 3y + 2
We can compute that x = 4 and y = 2.
Thus, Inlet pipe = x = 4.
Answer: B #### B
QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
options: A)40 B)50 C)60 D)70 E)80
SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: Option B #### B
QUESTION:In how many ways a committee of 10 men and 8 women can be made out of total of 15 men and 12 women?
options: A)336/987 B)1001/165 C)1245/789 D)3256/789 E)256/85
SOLUTION:Required number of ways = 15C10 * 12C8 = 15C5 * 12C4 = 3003/495 = 1001/165
Answer is B #### B
QUESTION:Find the odd man out. 14,35,49,60,70
options: A)14 B)35 C)49 D)60 E)70
SOLUTION:All except 60 are multiples of 7
Answer is D #### D
QUESTION:On Monday Joshua sold 90 phones, Rob sold 30% more phones than Joshua, Prerna sold 11 more phones than Rob, and Declan sold 3/4 of what Prerna sold. How many phones did Declan sell?
options: A)111 B)75 C)29 D)128 E)96
SOLUTION:E
96
Joshua sold 90 phones.
Rob sold 30 % more phones than Joshua
Rob = 90 + 90 × 30%
= 90 + 90 × 0.30
= 90 + 27
= 117
Prerna sold 11 more phones than Rob
Prerna = 117 + 11
= 128
Declan sold 3/4 of what Prerna sold.
Declan= 128 x 3/4
=96
Declan sold 96 phones.
The correct answer is E. #### E
QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are
options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44
SOLUTION:A
11, 42
Let the age of Priya = x years
Then, the age of her father = (x+ 31) years
ATQ,
(x+ 8) + (x+ 31 + 8) = 69
2x+ 47 = 69
2x= 69 – 47 = 22
x= 11
The age of Priya = 11 years
The age of her father = 11 + 31 = 42 years #### A
QUESTION:A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
options: A)48 km/hr B)56 km/hr C)60 km/hr D)52 km/hr E)None of these
SOLUTION:Explanation:
Method : 1
If a car covers a certain distance atxkmph and an equal distance at y kmph,
the average speed of the whole journey = 2xy/x+y kmph.
By using the same formula, we can find out the average speed quickly
Speed with which he travels from A to B = x = 40 km/hr
Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr
average speed = (2×40×60)/(40+60) = 48 km/hr
Assume that distance from A to B = x km
Speed with which he travels from A to B = x = 40 km/hr
Time to travel from A to B = distance/speed = x/40 hr
Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr
Time to travel from B to A = distance/speed = x/60
Total distance traveled = x+x = 2x
Total time taken = x/40 + x/60
Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60)
= 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr
Answer: Option A #### A
QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments.
options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3
SOLUTION:The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:21.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6.
ANSWER:A #### A
QUESTION:Convert 0.30 in to a vulgar fraction ?
options: A)18/50 B)16/50 C)3/10 D)19/50 E)None
SOLUTION:Answer
0.30 = 30/100 = 3/10
Correct Option: C #### C
QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer?
options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7
SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144.
Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520.
P = favorable/total = 2520/144 = 35/2.
Answer: B. #### B
QUESTION:How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2.
options: A)4:3 B)4:7 C)4:9 D)4:2 E)4:1
SOLUTION:Explanation:
No explanation is available for this question!
ANSWER: A #### A
QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 5 m wide at the bottom and the area of cross-section is 344 sq m, the depth of cannel is?
options: A)39 B)28 C)27 D)40 E)71
SOLUTION:1/2 * d (12 + 5) = 344
d = 40
Answer: D #### D
QUESTION:The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is?
options: A)126 B)156 C)190 D)300 E)260
SOLUTION:Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1950
X = 70
Required perimeter = 2(70+80) = 300
D #### D
QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1
SOLUTION:Explanation:
Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
Answer: D #### D
QUESTION:How much is 80% of 60 is greater than 4/5 of 25?
options: A)15 B)28 C)16 D)12 E)73
SOLUTION:(80/100) * 60 – (4/5) * 25
48 - 20 = 28
Answer: B #### B
QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
options: A)3 B)5 C)6 D)4 E)9
SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 20 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 5. Answer: B #### B
QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
options: A)1.09 B)1.6 C)1.2 D)1.5 E)1.1
SOLUTION:M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D #### D
QUESTION:A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1
SOLUTION:(4*6 + 8*6): (4*12)
72:48 =>
3:2
Answer:C #### C
QUESTION:Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets?
options: A)30 B)31 C)32 D)33 E)34
SOLUTION:Total price of 5 packet milk=5*20=100
Total price of 3 packet milk=3*12=36
Total price of 2 packet returned milk=100-36=64
Average price of 2 packet milk=64/2=32
Correct option Answer:C #### C
QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7?
options: A)1 B)2 C)3 D)5 E)6
SOLUTION:As per question => N=7P+2 for some integer p
hence 5N => 35Q + 10 => remainder =>10 for some integer Q
Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3
hence C #### C
QUESTION:In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 13 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
options: A)3 B)4 C)5 D)6 E)7
SOLUTION:The class borrowed a total of 40*2 = 80 books.
The 27 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 13*2 = 38.
To maximize the number of books borrowed by 1 student, let's assume that 12 students borrowed 3 books and 1 student borrowed the rest.
80 - 38 - 3*12 = 6
The maximum number of books borrowed by any student is 6.
The answer is D. #### D
QUESTION:John has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?
options: A)54 B)55 C)56 D)57 E)58
SOLUTION:Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5.
so answer is B #### B
QUESTION:Shekar scored 76, 65, 82, 47 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?
options: A)71 B)69 C)75 D)85 E)90
SOLUTION:Explanation :
Average= (76+65+82+47+85)/5 = 355/5 =71
Hence average=71
Answer : A #### A
QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons?
options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20
SOLUTION:5p3 =5 x4= 20
Option 'E' #### E
QUESTION:As a bicycle salesperson, David earns a fixed salary of $25 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>1
options: A)I,III only B)III only C)I only D)II only E)II,III only
SOLUTION:II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>1 --> if David sold 3 bicycles this week then this week he earned 25+3*6=$43, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $25. So y must be more than 1;
I. y<3x --> is not always true.
Answer: E #### E
QUESTION:At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?
options: A)1/12 B)5/14 C)4/9 D)1/2 E)2/3
SOLUTION:"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind).
C23∗C46C49=514C32∗C64C94=514.
C23C32 - # of ways to choose which 2 samples will be tasted;
C46C64 - # of ways to choose 4 cups out of 6 cups of two samples (2 samples*3 cups each = 6 cups);
C49C94 - total # of ways to choose 4 cups out of 9.
Answer: B #### B
QUESTION:The average of first ten prime numbers which are odd is?
options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5
SOLUTION:Sum of first 10 prime no. which are odd = 158
Average = 158/10
= 15.8
Answer:D #### D
QUESTION:The average marks of a class of 30 students is 50 and that of another class of 50 students is 60. Find the average marks of all the students?
options: A)56.25 B)52.9 C)52.1 D)52.3 E)42.5
SOLUTION:Sum of the marks for the class of 30 students = 30 * 50 = 1500
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1500 + 3000 = 4500
Average marks of all the students = 4500/80
= 56.25
Answer:A #### A
QUESTION:A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
options: A)40 sec B)50 sec C)44 sec D)49 sec E)60 sec
SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer:C #### C
QUESTION:A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
options: A)480 B)487 C)720 D)729 E)268
SOLUTION:1/x - 1/20 = -1/24
x = 120
120 * 6 = 720
Answer:C #### C
QUESTION:For 1rs 6p interest
wat will be for 1000rs?
options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs
SOLUTION:For 1rs , 4p interest
for 1000rs, x
x= 1000/1 * 6p ==> 6000 paise
To express in rs, 6000/100 = 60rs
ANSWER:E #### E
QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?
options: A)3 B)16 C)75 D)24 E)26
SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.
2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).
3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.
4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!
6) Answer choice E. #### E
QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec
SOLUTION:D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer: C #### C
QUESTION:A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased?
options: A)7 B)6 C)5 D)2 pineapples E)3
SOLUTION:Explanation:
The equation for this problem can be made as:
5x + 7y =38
Where x is the number of watermelons and y is the number of pineapples.
Now test for 2, 3 and 4:
For y = 2
5x + 14 =38
x is not an integer
For y = 3
5x = 17
X not an integer
For y =4
X = 2
So 4 pineapples and 2 watermelons can be bought by 38 Rs.
ANSWER:D #### D
QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these
SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 4/5
5n + 5 = 4d + 4
5n + 5 = 4(2n - 1) + 4 => n = 5/3
d = 2n - 1 => d = 3/7
Hence the fraction is : 5/7
ANSWER:B #### B
QUESTION:Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone?
options: A)6 B)12 C)14 D)15 E)17
SOLUTION:Renu’s one day’s work = 1/6
Suma’s one day’s work = 1/3 - 1/6 = 1/6
Suma can do it alone in 6 days.
ANSWER:A #### A
QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg?
options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42
SOLUTION:1000*(25/100) = 250 ---- 5
? ---- 1
=> Rs.50
Answer: A #### A
QUESTION:Solve for x
if (log2)(1-x/2)=x-2.
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:(log2)(1-x/2)=x-2
or,log2-(x/2)log2=x-2
or,2log2-xlog2=2x-4
or,log4+4=2x+xlog2
or,4.60=2.3x i.e.x=2.
ANSWER:B #### B
<<<Examples ends
QUESTION:The length of a rectangle is reduced by 10%. By what % would the width have to be increased to maintain the original area?
options: A)10% B)11.1% C)25% D)30% E)35%
SOLUTION:Sol. Required change = (10*100)/(100-10)=11.1%
B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:8^100 is divisible by 17. Find the remainder?
options: A)8 B)12 C)16 D)18 E)20
SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 = (816)6×8417
Now this problem simply boils down to (1)6×8417 = 8417
84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.
C #### C
QUESTION:The market value of a certain machine decreased by 20 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
options: A) $8,000 B) $5,600 C) $3,200 D) $2,400 E) $4,800
SOLUTION:E.
Market value in 1982= $ 8000
Market value in 1983 = $ 8000- ($ 8000 x 20/100) = 8000-1600= $ 6400
Market value in 1984 = Market value in 1983 - (20 % of $8000)= 6400-1600 = $4800 #### E
QUESTION:Thompson had the following scores in an exam (out of 100):
Social Studies: 60
Science: 89
Art: 62
Music: 69
Spanish:84
Biology: 89
What are his average marks ?
options: A)61.5 B)72.5 C)71.5 D)85.5 E)75.5
SOLUTION:Explanation:
Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75.
Answer: E) 75.5 #### E
QUESTION:A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 10% lemonade syrup?
options: A)1.5 B)1.75 C)2.14 D)2.34 E)2.64
SOLUTION:Let the total solution is 150 L with 80 L water70 L syrup.
To make 10% syrup solution, the result solution must have 135 L syrup and 15 L syrup.
Therefore we are taking 55 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
55 L syrup in 117.9 L solution
We started by multiplying 10
Now to get to the result we need to divide by 55 => amount of solution to be replaced with water = (117.9/55) = 2.14.
Correct option : C #### C
QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers.
options: A)28 B)30 C)32 D)34 E)36
SOLUTION:Given:
Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6)
Average = Sum of Quantities/Number of Quantities
= [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27
Simplifying we get, x = 24
Therefore,
Largest number = (x + 6) = (24 + 6) = 30
Smallest number = 24
ANSWER IS B #### B
QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13
SOLUTION:Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 650 = 13
Answer: E #### E
QUESTION:How much is 80% of 60 is greater than 4/5 of 25?
options: A)15 B)28 C)16 D)12 E)73
SOLUTION:(80/100) * 60 – (4/5) * 25
48 - 20 = 28
Answer: B #### B
QUESTION:The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is:
options: A)400 B)500 C)600 D)800 E)1000
SOLUTION:Let the sum be $. P.
(P(1+10/100)^2-P)=525
P((11/10)^2-1)=2500
SUM = 2500
So SI = 500
ANSWER B #### B
QUESTION:A cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm. Find the total area of the wet surface.
options: A)142 m sqaure B)122 m sqaure C)135 m sqaure D)188 m sqaure E)None of these
SOLUTION:Explanation:
Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(6*2.25+9*2.25)]+9*6 = 122 m square
Option B #### B
QUESTION:In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?
options: A)$9 x 10^4 B)$9.90 x 10^6 C)$1.00 x 10^7 D)$1.05 x 10^7 E)$9.90 x 10^7
SOLUTION:The max product of any two balls can be 9 * 10 = 9900 = 9 * 10
If we multiply it by $1000 the max amount will be 9 * 10^4.
A #### A
QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin?
options: A)$110 B)$150 C)$225 D)$54 E)$75
SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices.
110/3 = 36.67
150/3 = 50
225/3 = 75
54/3 = 18
75/3 = 25
A is not an integer amount.
Answer:A #### A
QUESTION:If (5+k)(5-k)=(5^2)-(2^3),then what is the value of K?
options: A)1 B)3 C)4 D)2 E)6
SOLUTION:Obviously,It is in the formula a^2-b^2=(a+b)(a-b)
So k is 2
Option D #### D
QUESTION:There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic?
options: A)70 % B)75 % C)80 % D)85 % E)90 %
SOLUTION:Chance of no picnic+chance of picnic= 100% ... (i)
Chance of picnic=100%-Chance of no picnic ... (ii)
Chance of no picnic= 50% of 30%= 15%
Therefore, According to (ii), Chance of picnic= 100%-15%= 85%.
Answer D #### D
QUESTION:The G.C.D. of 1.08, 0.36 and 0.8 is:
options: A)0.04 B)0.9 C)0.18 D)0.108 E)0.118
SOLUTION:Given numbers are 1.08, 0.36 and 0.80. H.C.F. of 108, 36 and 80 is 18,
H.C.F. of given numbers = 0.04.
Answer: Option A #### A
QUESTION:If A:B is 3:4 and B:C is 4:5 then A:C is equal to
options: A)1:3 B)3:5 C)3:4 D)3:7 E)1:5
SOLUTION:The two ratios given are having the same number 4 for B in both the ratios.
Hence- A:B = 3:4 B:C = 4:5
=> A:C = 3:5
Answer B #### B
QUESTION:Length of a rectangular plot is 28 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
options: A)54 m B)64 m C)74 m D)84 m E)94 m
SOLUTION:Let breadth = x metres.
Then, length = (x + 28) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 28) + x] = 200
2x + 28 = 100
2x = 72
x = 36.
Hence, length = x + 28 = 64 m
B #### B
QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie?
options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9
SOLUTION:There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9
Answer: E #### E
QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase?
options: A)80% B)90% C)70% D)60% E)50%
SOLUTION:Ans. Let previous income = Rs. 100
Previous savings = 10% of Rs. 100 = Rs. 10
Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120
Increased savings = 15% of Rs. 120 = Rs. 18
Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8
Therefore, Percent increase in savings = 8/10 x 100 = 80%
Answer A #### A
QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km
SOLUTION:Explanation:
Speed in still water = 6 kmph
Speed of the current = 1 kmph
Speed downstream = (6+1) = 7 kmph
Speed upstream = (6-1) = 5 kmph
Let the required distance be x km
Total time taken = 1 hour
⇒ x/7+x/5=1
⇒5x+7x=35
⇒12x=35
⇒x=2.9 km
Answer: Option C #### C
QUESTION:The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
options: A)10000 B)18999 C)16990 D)16007 E)16991
SOLUTION:100 * 100 = 10000
125 * 80 = 10000
Answer:A #### A
QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days
SOLUTION:B = 1/4 – 1/20 =0.2 days
ANSWER:E #### E
QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14
SOLUTION:answer isB
Total probability=7C3=48
4C3 +4C2*4C1+4C1*4C2=4+24+24=42
therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8
B #### B
QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is
options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12
SOLUTION:Explanation:
Given numbers are 1.08 , 0.42 and 0.90
H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F]
therefore H.C.F of given numbers = 0.06
Answer: C) #### C
QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?
options: A)4 B)6 C)10 D)12 E)24
SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5∗150=90
2nd Question : four fifths of the remainder answered the second question correctly so 4/5∗(150−90)=4/5∗60=48
total students who answered at least one Q correct =90+48=138
so students who answered BOTH incorrectly = 150−138=12
ANSWER:D #### D
QUESTION:Find the value of y from the given equation. 9^y = 3^12, what is y?
options: A)3 B)5 C)7 D)8 E)6
SOLUTION:3^2y = 3^12
2y=12, therefore y=6
E #### E
QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is
options: A)35 B)37 C)39 D)41 E)46
SOLUTION:Explanation:
Let B's age = x years.
Then, As age = (x+ 9) years.
(x+9+10)=2(x�10)
hence x=39.
Present age of B = 39 years
Answer: Option C #### C
QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is?
options: A)1 B)4 C)5 D)6 E)7
SOLUTION:4.5 4.5
45% 55%
45% ----- 4.5
55% ------? => 5.5 - 4.5 = 1 ml
ANSWER:A #### A
QUESTION:Tom read a book containing 1000 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 15 pages a day more, how many days did Tom spend reading the book?
options: A)20 B)18 C)16 D)15 E)15.39
SOLUTION:Actually u can set up 2 equation
P--stands for the pages
D--stands for the days
1) P*D=480 (we want to find the Days, soP=480/D)
2) (P+15)(D-5)=1000=> PD-5P+15D-75=1000
as the 1) stated u can put 1) into 2)
=> 1000-5P+15D-75=1000 => 15D-5P=75
put the bold one into it => 15D-5(480/D)=75the we get the final equation 16D^2-2400=80D (divide 16)
=> D^2-5D-160=0
so D=15.39days. Ans: (E) #### E
QUESTION:30 liters of a mixture contains milk and water in the ratio 2:1. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be?
options: A)3:2 B)3:1 C)4:1 D)5:2 E)2:1
SOLUTION:Quantity of milk in 30 liters if mix = 30*2/3 =20 liters
Quantity of milk in 35 liters of new mix = 20+5 = 25 liters
Quantity of water in it = 35-25 = 10 liters
Ratio of milk and water in new mix = 25:10 = 5:2
Answer is D #### D
QUESTION:8 men, working 8 hours a day can complete a work in 18 days. How many hours a day must 12 men work to complete the same work in 12 days?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:The number of hours required to complete the work is 8*8*18 = 1152
12 × 12 × (x) = 1152
x = 8
The answer is C. #### C
QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded?
options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these
SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :-
letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..)
Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get
IDAATRE
ANSWER:D #### D
QUESTION:A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
options: A)A.0.6 B)B.1 C)C.2.1 D)D.3 E)E.2.4
SOLUTION:30% of 6 = 1.8
50% of 6 = 3
shortage is 1.2
so we need to have 1.2/50% to get 50% alcohol content.
= 2.4 E #### E
QUESTION:The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres?
options: A)11 B)12 C)13 D)14 E)15
SOLUTION:Speed of the boat downstream = 90 + 18 = 108 kmph
= 108 * 5/18 = 30 m/s
Hence time taken to cover 330 m = 330/30 = 11 seconds.
Answer: A #### A
QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ?
options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these
SOLUTION:Explanation:
Part filled by A in 1 hour = 1/6
Part filled by B in 1 hour = 1/18
Part filled by C in 1 hour = 1/36
Part filled by (A+B+C) in 1 hour =
1/6+1/18+1/36=9/36
So all pipes will fill the tank in 4 hours.
Option C #### C
QUESTION:P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 12 days. How many days more will P take to finish the work?
options: A)12 B)15 C)18 D)20 E)22
SOLUTION:Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 12 days = 12 × (1/16) = 12/16 = 3/4
Remaining work = 1 = 3/4 = 1/4
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (1/4) / (1/48) = 12
Option A #### A
QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss?
options: A)25 % B)50 % C)75 % D)85 % E)None of these
SOLUTION:Explanation :
Let the original expenditure = Rs. 100.
New final expenditure = 150% of (50% of Rs. 100)
= Rs.(150/10050/100100)
= Rs. 75.
Decrease = 100- 75 = 25 %
Answer : A #### A
QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1
SOLUTION:distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
Answer :D #### D
QUESTION:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold?
options: A) 11 B) 13 C) 15 D) 17 E) 19
SOLUTION:(x+5)*150 +x*85=2160
=>x=6
total lens=6+(6+5)= 17
Answer D #### D
QUESTION:A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The
rate on interest per annum is.
options: A)4% B)5% C)6% D)7% E)10%
SOLUTION:Explanation:
S.I. on Rs 800 for 1 year = 80
Rate = (100*80)/(800*1) = 10%
Answer: E #### E
QUESTION:A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)?
options: A)1250 B)1280 C)1320 D)1340 E)1450
SOLUTION:Explanation:
Speed = 5 km/hr
Time = 15 minutes = 1/4 hour
Length of the bridge = Distance Travelled by the man = Speed × Time = 5×1/4 km
= 5 × 1/4 × 1000 metre=1250 metre
Answer: Option A #### A
QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None
SOLUTION:Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1250 x 2/5) = Sterling 500.
Answer: Option C #### C
QUESTION:(a/2)/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression?
options: A)8/2 B)2/4 C)1/8 D)2/4 E)4/6
SOLUTION:(a/2)/(b/c)
= (a*c)/2b
The expression will have the largest value when numerator (a*c) is the largest.
= (2*4)/2*1
=8/2
Answer A #### A
QUESTION:A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
options: A)42 B)43 C)46 D)47 E)49
SOLUTION:A
42
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
125 : 150 :: 35 : x 125 x x = 150 x 35
x = (150 x 35)/125
x = 42 #### A
QUESTION:If the product of 2 integers is negative, at most how many of the integers can be negative?
options: A)1 B)3 C)4 D)5 E)6
SOLUTION:The product of 2 integers is negative
Thus an odd number of integers need to be negative to have a negative product
We are asked at most how many are required.
So, the highest odd integer before 6,i.e. 1
Correct Option : A #### A
QUESTION:In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 10 is
options: A)8 B)625 C)16 D)20 E)24
SOLUTION:I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 10
A. x+y+x-y = 10 --> x=5
B. x+y-x+y = 10 --> y=5
C. -x-y +x-y= 10 --> y=-5
D. -x-y-x+y=10 --> x=-5
The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be25*25=625
Answer: B #### B
QUESTION:9.7 , 9.7 , 9.9 , 9.9 , 10.0 , 10.1 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.25 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
options: A)90% B)85% C)80% D)75% E)70%
SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.25; 10+0.25} = {9.75; 10.25}.
From the 8 listed numbers, 5 are within this range so 5/8=75%.
Answer: D. #### D
QUESTION:If 7a = 2b = 15, then 42ab =
options: A)75 B)125 C)675 D)1100 E)1250
SOLUTION:7a * 2b = 15 * 15 = 225
14 ab = 225
i.e. 42 ab = 675
Answer: Option C #### C
QUESTION:The value of (34.5*0.473*1.567)/(0.0673*23.25*7.57) is close to
options: A)2 B)1.15 C)2.05 D)2.16 E)2.35
SOLUTION:(34.5*0.473*1.567)/(0.0673*23.25*7.57) = 25.5710895/11.845
= 2.16
ANSWER:D #### D
QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:Solution
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
Tens place can be filled by any of the remaining 5 numbers.
So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it.
So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D
QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
options: A)22 B)88 C)27 D)20 E)98
SOLUTION:Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D #### D
QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have?
options: A)5 B)12 C)19 D)36 E)50
SOLUTION:A+P+G= 39*3
A=3G
P=2.5G
3G+2.5G+G= 39*3
G=39*3/6.5= 18
A= 6*3=54
Difference = 36
'D' is the answer #### D
QUESTION:The area of a triangle is with base 18m and height 6m?
options: A)88 m2 B)10 m2 C)66 m2 D)54 m2 E)31 m2
SOLUTION:1/2 * 18 * 6 = 54 m2
Answer: D #### D
QUESTION:Find the value of x which satisfies the relation
Log10 3+log10 (4x+1)=log10 (x+1)+1
options: A)2.5 B)3.5 C)3.2 D)6.8 E)9.8
SOLUTION:[log10a + log10b = log10 ab]
and also 1 can be written as log10 10,
so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)),
this can be solved to get 12x+3=10x+10,
that gives x=7/2=3.5
ANSWER:B #### B
QUESTION:A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
options: A)2ft. 7 inches B)4ft. 7 inches C)1ft. 7 inches D)3ft. 7 inches E)None of them
SOLUTION:Length of board=7ft. 9 inches=(7*12+9)inches=93 inches.
Therefore, Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches
Answer is A. #### A
QUESTION:110 is increased by 50%. Find the final number.
options: A)100 B)110 C)150 D)155 E)165
SOLUTION:Final number = Initial number + 50%(original number) = 110 + 50%(110) = 110 + 55 = 165.
Answer E #### E
QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q?
options: A)25 B)35 C)45 D)55 E)65
SOLUTION:P started with 7k stamps and Q started with 2k stamps.
(7k-15)/(2k+15) = 2/1
3k = 45
k = 15
P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps.
The answer is C. #### C
QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed?
options: A)21005 B)10500 C)25200 D)5376 E)None of these
SOLUTION:Solution
Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4)
8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224
Number of group,each having 3 consonants and 1 vowels = 224 .
Each group contains 4 letter.
Number of ways of arranging 5 letters among themselves
= 4 ! = (4 × 3 × 2 × 1) = 24 .
So, Required number of words = (24 × 224) = 5376 .Answer D #### D
QUESTION:A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
options: A)60 km/hr B)50 km/hr C)36 km/hr D)26 km/hr E)87 km/hr
SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 15 = 45 => x = 60 km/hr.
Answer:A #### A
QUESTION:The list price of an article is Rs.69. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
options: A)9.33% B)9.44% C)9.45% D)9.56% E)9.67%
SOLUTION:69*(90/100)*((100-x)/100) = 56.16
x = 9.56%
ANSWER:D #### D
QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is:
options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62
SOLUTION:(3x-9):(5x-9) = 3:2
x = 1 => 3x = 3
Answer:A #### A
QUESTION:A parking garage rents parking spaces for $12 per week or $30 per month. How much does a person save in a year by renting by the month rather than by the week?
options: A) $140 B) $160 C) $220 D) $240 E) $264
SOLUTION:12$ per week!
An year has 52 weeks.
Annual charges per year = 52* 12 = 624$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 30 = 360$
624 - 360 = 264
Ans E #### E
QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)18, 24, 32 E)None of these
SOLUTION:Explanation:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
Answer: B #### B
QUESTION:we have 7 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg one of 15 kg one of 20 kg by using only five weight how many weight u can weight
options: A)19 B)18 C)24 D)21 E)32
SOLUTION:select 5 weight out of 7, 7C5=21
ANSWER:D #### D
QUESTION:A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
options: A)15 m, 12 m B)15 m, 11 m C)15 m, 20 m D)15 m, 10 m E)15 m, 11 m
SOLUTION:lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
D #### D
<<<Examples ends
QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
options: A)230 B)783 C)291 D)112 E)221
SOLUTION:Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer:A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is?
options: A)5 kmph B)7.5 kmph C)8 kmph D)9 kmph E)4 kmph
SOLUTION:US = 20
DS = 35
M = (35 - 20)/2 = 7.5
Answer:B #### B
QUESTION:Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive?
options: A)$444 B)$445 C)$446 D)$447 E)$448
SOLUTION:A+B+C = 1200
Given ratio 10:12:13
Let us say the shares of A,B,C deducting 10,20,15 be a,b,c
a+b+c = 1200-45= 1155 = 35K
c share = (1155X13)/35 = 429
C = chandran share = 429+15 = 444
Option A #### A
QUESTION:Find the odd man out
2, 5, 14, 41, 122, 365, 1125
options: A)2 B)14 C)41 D)365 E)1125
SOLUTION:1*3-1 = 2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3-1 = 122
122*3-1= 365
365*3-1= 1094
ANSWER:E #### E
QUESTION:On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is:
options: A)364724 B)365387 C)365737 D)366757 E)366767
SOLUTION:Required number= 999*366+103
= (1000-1)*366+103
= 366000-366+103
= 365737.
ANSWER:C #### C
QUESTION:Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
options: A)2288 B)2677 C)6000 D)2700 E)2881
SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x
10 * 20 * 90 = 15 * 2 * x => x = 6000
Answer: C #### C
QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age.
options: A)14 B)15 C)20 D)22 E)23
SOLUTION:Explanation:
Present age is 4x and 3x,
=> 4x + 6 = 26 => x = 5
So Deepak age is = 3(5) = 15
Answer: Option B #### B
QUESTION:Three friends X, Y, Z rented a auto for Rs.520. A used it for 6 hours, B used it for 9 hours and C used it for 11 hours. What is the hire charges paid by Y:
options: A)Rs 140 B)Rs 160 C)Rs 180 D)Rs 200 E)None
SOLUTION:X : Y : Z = 7 : 8 : 11. Hire charges paid by Y = Rs(520×9/26) = Rs.180.
Answer C #### C
QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00
SOLUTION:Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer: Option D #### D
QUESTION:The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer?
options: A)5 B)3 C)4 D)2 E)1
SOLUTION:Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 9
=> 5x + 2 + a = 36
=> 5x + a = 34
=> a = 34 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=6
This gives us a= 34 - 30 = 4
Therefore the minimum value that the fourth integer can have is 4.
Answer:C #### C
QUESTION:How much water must be added to 64 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
options: A)16 litres B)12 litres C)15 litres D)18 litres E)None of these
SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 64 litres of milk
= (1⁄4 × 64) litres = 16 litres.
Answer A #### A
QUESTION:P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}?
options: A){6, 12} B){6, 15} C){21,28} D){9, 15} E){15, 24}
SOLUTION:p/q= d=p/q+7
d= .75 q
d= .6(q+7)
we get d = 21 and q = 28. Answer = C. #### C
QUESTION:For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b - 4| + |ab + b| = ?
options: A)a) ab - 4 B)b) 2b - ab - 4 C)c) ab + 4 D)d) ab - 2b + 4 E)e) 4 - ab
SOLUTION:|a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b+4
Since ab is Positive and b is Negative so |ab - b| = ab + b
i.e. |b - 4| + |ab - b| = -b+4 + ab + b =ab + 4
Answer: Option C #### C
QUESTION:Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket
to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
options: A)$8 B)$14 C)$5 D)$15 E)$0
SOLUTION:1/5 x $60 = $12 for sandwich
1/6 x $60 = $10 for museum
1/2 x $60 = $30 for book
$12 + $10 + $30 = $52 spent
$60 - $52 = $8 left over
correct answer A #### A
QUESTION:For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| =
options: A)ab-4+b B)2b-ab-4 C)ab+4 D)ab-2b+5 E)4-ab
SOLUTION:Given: |ab| = ab and |a| = -a
Question: |b-3| + |ab-b| = ?
**** Looking at |ab| = ab tells us that a and b are either both positive or negative
**** Looking at |a| = -a tells us that a must be negative
**** Combine two observations: a and b are both negative values
Let a=-1 and b=-1
|b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5
Test a) ab-4 = (-1)(-1)-4 = -5
Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7
Test c) ab+4 = 1 + 4 = 5
Answer: C #### C
QUESTION:The timing of a college is from 12 p.m to 5.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
options: A)56 minutes B)45 minutes C)30 minutes D)48 minutes E)44 minutes
SOLUTION:Explanation:
Total time a student spends in college = 5 hours 00 minutes = 300 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (300 – 20)/5
= 56 minutes
ANSWER A #### A
QUESTION:A 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
options: A)500 B)350 C)828 D)277 E)122
SOLUTION:Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/489 = 50/3
3x + 900 = 2400 => x = 500 m.
Answer: A #### A
QUESTION:A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
options: A)10 B)20 C)50 D)30 E)40
SOLUTION:Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 15 - 2.5 = 12.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 12.5 - 2.5 = 10 km/hr
Answer is A. #### A
QUESTION:A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?
options: A)576 B)800 C)726 D)484 E)500
SOLUTION:(4/15) * A = (2/5) * B
A / B = 3 / 2
Therefore A's share is = (1210 * (3/5)) = 726
Ans - C #### C
QUESTION:A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
options: A)22 seconds B)77 seconds C)40 seconds D)57 seconds E)57 seconds
SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C #### C
QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 2. Find his average after 17th inning.
options: A)36 B)39 C)42 D)45 E)None of the above
SOLUTION:Let the average after 17th inning = x.
Then, average after 16th inning = (x – 2).
∴ 16(x – 2) + 87 = 17x or x = (87 – 32) = 55.
Answer E #### E
QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score?
options: A)662 B)678 C)652 D)642 E)721
SOLUTION:8 * 86 = 688 – 10 = 678
ANSWER:B #### B
QUESTION:A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 2 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.
options: A)1/7 B)1/12 C)1/14 D)1/18 E)1/21
SOLUTION:The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 2 bottles of apple juice is 6C2*4C4 = 15*1 = 15
P(selling 2 bottles of apple juice) = 15/210 = 5/70 = 1/14
The answer is C. #### C
QUESTION:In a recent head-to-head run-off election, 10,000 absentee ballets were cast. 2/3 of the absentee ballets were thrown out and 2/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?
options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000
SOLUTION:1/3 * 3/5 (total absentee votes) = 1/5 (total votes)=1/5*10000=2000
Answer is A #### A
QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
options: A)11 B)77 C)36 D)47 E)99
SOLUTION:Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer:D #### D
QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
options: A)36 B)76 C)98 D)27 E)24
SOLUTION:(3x-9):(5x-9)
= 9:17
x = 12 => 3x
= 36
Answer:A #### A
QUESTION:The area of a triangle is with base 4m and height 6m?
options: A)11 m2 B)10 m2 C)18 m2 D)19 m2 E)12 m2
SOLUTION:1/2 * 4 * 6
= 12 m2
Answer: E #### E
QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
options: A)20 B)15 C)25 D)18 E)12
SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
ANSWER B #### B
QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
options: A) 15 B) 17 C) 10 D) 25 E) 30
SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
50 will be in team A
50 will be in team B
The larger diff is
70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10.
Answer choice C #### C
QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?
options: A)144 B)180 C)192 D)360 E)None of these
SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options.
Task 2 can be assigned to 3 or 4
So, there are only 2 options for task 2.
So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6.
= 2 × 3 × 4 × 3 × 2 × 1 = 144
Answer A #### A
QUESTION:A horse chases a pony 8 hours after the pony runs. Horse takes 12 hours to reach the pony. If the average speed of the horse is 320 kmph, what s the average speed of the pony?
options: A)182kmph B)192kmph C)193kmph D)196kmph E)190kmph
SOLUTION:pony take 20 hours and horse take 12 hours...then Distance chased by them is 320*12.so speed of pony is (320*12)/20=192kmph.
ANSWER IS B #### B
QUESTION:20 balls are numbered 1 to 20. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
options: A)7/30 B)3/14 C)9/38 D)4/21 E)5/26
SOLUTION:P(1st ball is even) = 10/20
P(2nd ball is also even) = 9/19
P(both balls are even) = 10/20 * 9/19 = 9/38
The answer is C. #### C
QUESTION:For what value of “k†will the equation (2kx2 + 5kx +1)=0 have equal roots?
options: A)2/7 B)9/4 C)8/25 D)7/1 E)7/2
SOLUTION:for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0
in the given equation
(5k)^2-4*2k*1=0
by solving this equation
we get k=0, k=8/25
ANSWER:C #### C
QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper?
options: A)30 B)40 C)42 D)44 E)46
SOLUTION:here two cases are possible.
case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3
case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2
thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30
ANS:A #### A
QUESTION:An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
options: A)4.04 B)4.02 C)4.01 D)4.05 E)4.06
SOLUTION:Formula for Calculation of Percentage error is:
=(x−y−(xy)/100)%
=(2+2+(2×2)/100)%=4.04%
Answer is A. #### A
QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
options: A)72 6/7% B)82 6/7% C)22 6/7% D)42 6/7% E)82 2/7%
SOLUTION:Explanation:
SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D #### D
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
options: A)150 meter B)299 meter C)666 meter D)155 meter E)144 meter
SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9
= 150 meter
Answer: A #### A
QUESTION:Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days.
options: A)11 B)12 C)13 D)15 E)16
SOLUTION:Work done by Kamal in 1 day = 1/20
Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16
=> Suresh can complete the work in 16 days
Answer is E. #### E
QUESTION:In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
options: A)7000 B)7200 C)7400 D)7600 E)8000
SOLUTION:State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
E) #### E
QUESTION:A man divides $8600 Among 5 Sons, 4 Daughters and 1 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
options: A)A)$200 B)B)$1000 C)C)$819 D)D)$1200 E)E)$400
SOLUTION:Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 5*5X+4*4X+1*X=8600
25X+16X+X=8600
42X=8600, X=204.76.
Daughter receives four times of nephew so 4 * 204.76= 819.
So Each Daughter receives $800. answer is option C) $819. #### C
QUESTION:Find the one which does not belong to that group ?
options: A)3 B)4 C)5 D)9 E)7
SOLUTION:Explanation:
3, 5, 9 and 7 are odd numbers, but not 4.
ANSWER IS B #### B
QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
options: A)1178 B)144 C)66 D)8 E)55
SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer: B #### B
QUESTION:By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
options: A)9 B)4 C)8 D)7 E)65
SOLUTION:80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A #### A
QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ?
options: A)1000 B)1100 C)1200 D)1300 E)1400
SOLUTION:let profit rate of b = x
acc to question profit rate of a becomes 5/3 x
and that of c= 1/3 x which is given as 10%
1/3 x= 10
therefore x=30
now b=30% , a=50%
now we will find out c's price-
11/10 * price = 2145
price = 1950
in similar way we will find out b's price as we know that profit is 30%
therefore 130/100 * price = 1950
so b 's price =1500
similarly for a ('profit is 50%)
150/100 * price = 1500
on solving it we get
a's price = 1000
ANSWER:A #### A
QUESTION:A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 7 minutes less than they can row it in still water. How long would they take to row down with the stream
options: A)45 or 23 minutes B)73 or 12 minutes C)77 minutes D)19 minutes E)25 minutes
SOLUTION:A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-7))
giving t = 77
C #### C
QUESTION:Find the average of first 4 multiples of 11?
options: A)10 B)12.6 C)27.5 D)31.3 E)40.8
SOLUTION:average = (11+22+33+44)/4 = 27.5
Answer is C #### C
QUESTION:If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?
options: A)44 B)48 C)45 D)47 E)49
SOLUTION:Let the required length be x meters
More men, More length built (Direct proportion)
Less days, Less length built (Direct Proportion)
Men 20:35 and Days 6:3::56:x
Therefore (20 x 6 x (X))=(35 x 3 x 56)
x=(35x3x56)/120=49
Hence, the required length is 49 m.
Answer is E. #### E
QUESTION:All the students of class are told to sit in circle shape. Here the boy at the 8 th position is exactly opposite to 33 th boy. Total number of boys in the class?
options: A)40 B)50 C)28 D)38 E)48
SOLUTION:As half the circle shape consist of 33-8=25 boys,
So total number of boys in full circle=2*25=50
ANSWER: B #### B
QUESTION:Which of the following is closer to (3!+2!)+(3!-2!)?
options: A)8 B)22 C)10 D)14 E)12
SOLUTION:(3!+2!)+(3!-12!)=6+2+6-2
= 12
Answer: E #### E
QUESTION:The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what is the width of the field?
options: A)50 B)60 C)70 D)80 E)90
SOLUTION:Let L be the length and W be the width. L = (7/5)W
Perimeter: 2L + 2W = 240, 2(7/5)W + 2W = 240
Solve the above equation to find: W = 50 m and L = 70 m.
correct answer A)50 #### A
QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have?
options: A)50 B)78 C)267 D)20 E)27
SOLUTION:A+B+C = 500
A+C = 200
B+C = 320
--------------
A+B+2C = 520
A+B+C = 500
----------------
C = 20
Answer: D #### D
QUESTION:At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate?
options: A)134 B)178 C)195 D)166 E)194
SOLUTION:C
195
The number of votes the winning candidate received was
963 + 53 + 79 + 105 /4= 300.
The second received 300 – 53 = 247,
The third received 300 – 105 = 195. #### C
QUESTION:On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price Q per glass on the second day?
options: A) $015 B) $0.20 C) $0.30 D) $0.40 E) $0.45
SOLUTION:On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.
Answer: D. #### D
QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours.
Working together how long will it take both pipes to fill the tank ?
options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes.
SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour.
Pipe B has a rate of 400 liters per hour.
400 + 600 (A+B) = Together they have a rate of 1000 liters per hour.
1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes
Answer -E #### E
QUESTION:Tough and Tricky questions: Ratios
1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?
options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5
SOLUTION:let total no. of students be 30
students left on a field trip = 1/5(30) =6
thus 24 students left behind
1/3(24)=8 students did not want to go. thus 16 students want to go on the trip
1/2(16)=8 were able to join the other students on the field trip.
thus total number of students that went on a field trip =6+8 =14
thus required fraction = 14/30 =7/15
C #### C
QUESTION:A line of 24 children walk single file down the 54-meter hallway of their school at a speed of 20 meter/min. If each child takes up 1/4 meter of space in line, how long does it take for all of them to traverse the full length of the hallway?
options: A)1 min B)2 min C)3 min D)4 min E)5 min
SOLUTION:C
3 min
d = 24 * 1/4 m + 54 m = 60 m
T = 60 meters / 20 meters/min = 3 min #### C
QUESTION:If n is an integer, which of the following must be an even integer?
options: A)n^2-n-1 B)n^2-4n+6 C)n^2-5n+5 D)n^2+3n+8 E)n^2+2n+10
SOLUTION:Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: n^2-n-1 = -1 { If n = 1 }
B: n^2-4n+6 = 3 { If n = 1 }
C: n^2-5n+5 = 1 { If n = 1 }
D: n^2+3n+8 = 12 { If n = 1 }n^2+3n+8 = 18 { If n = 2 }
E: n^2+2n+10 = 13 { If n = 1 }
Thus the only possible answer is (D) #### D
QUESTION:What is the are of an equilateral triangle of side 8 cm?
options: A)64√5 B)64√9 C)16√3 D)64√3 E)64√2
SOLUTION:Area of an equilateral triangle = √3/4 S2
If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2;
Answer: C #### C
QUESTION:What is the sum of the different positive prime factors of 1092?
options: A)5 B)12 C)20 D)25 E)27
SOLUTION:First, we make a prime factorization by dividing 1096 by 2 then 3, etc.
1096=2^2*3*7*13
2*2+3+7+13=27
Answer (E) #### E
QUESTION:Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other?
options: A)1.5 hours B)1.27 hours C)1.73 hours D)2 hours E)1.69 hours
SOLUTION:The cars travel (145+150=295) miles in one hour.
500 miles/295 miles/hour= 1.69 hours
Answer is E #### E
QUESTION:In order to fulfill a local school’s request for x cakes, B parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?
options: A)px/B B)px/(B(B - P)) C)x/(B - P) D)p/(B - Px) E)p/(B(B - p))
SOLUTION:No of cakes each parent has to bake : x/B
No of parents did not bake cake = p
No of cakes that were not baked by p parents = p*x/B
No of parents has to bake additional cakes = B-p
additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(B(B - P))
Answer B #### B
QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
options: A)22 B)28 C)27 D)80 E)21
SOLUTION:1/2 * d (10 + 6) = 640
d = 80
Answer:D #### D
QUESTION:A person was going through train from Bombay to Pune. After every five minutes he finds a train coming from opposite direction. Velocity of trains are equal of either direction. If the person reached Pune in one hour then how many trains he saw in the journey ?
options: A)9 B)10 C)11 D)12 E)13
SOLUTION:11
ANSWER:C #### C
QUESTION:Ayesha's father was 31 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
options: A)2 years B)4 years C)6 years D)8 years E)1 years
SOLUTION:Explanation:
Mother's age when Ayesha's brother was born = 34 years.
Father's age when Ayesha's brother was born = (31 + 4) years = 35 years.
Required difference = (35 - 34) years = 1 years.
Answer: E #### E
QUESTION:There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?
options: A)9:6 B)3:2 C)118:126 D)193:122 E)201:132
SOLUTION:m=portion of milk in solution
m=(4/7+2/3+3/5)/3➡193/315
315-193=122
122/315=portion of water in solution
ratio of milk to water=193/122
ANSWER:D #### D
<<<Examples ends
QUESTION:Bat is bought for Rs.400 and sold at a gain of 20% find its selling price?
options: A)Rs.320 B)Rs.350 C)Rs.370 D)Rs.480 E)None of these
SOLUTION:Explanation :
100 % = 400 (100 * 4 = 400)120 % = 480 (120 * 4 = 480)Selling price = Rs.480/-
Answer : D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Find the odd man out. 187, 264, 386, 473, 682, 781
options: A)386 B)187 C)781 D)682 E)564
SOLUTION:Explanation :
In all numbers except 386, the middle digit is the sum of other two digits. Answer : Option A #### A
QUESTION:What is 2 2/3 - 1 1/4 divided by 1/5 - 1/6 ?
options: A)17/36 B)36/17 C)17/6 D)85/2 E)51/4
SOLUTION:2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12
1/5 - 1/6 = (6-5)/30 = 1/30
So 17/12/1/30 = 17/12 * 30 = 85/2
Answer - D #### D
QUESTION:The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
options: A)16 seconds B)34 seconds C)14 seconds D)18 seconds E)15 seconds
SOLUTION:Speed of the boat downstream = 9 + 3 = 12 kmph
= 12 * 5/18 = 10/3 m/s
Hence time taken to cover 60 m = 60*3/10
= 18 seconds.
Answer: D #### D
QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor?
options: A)163 B)785 C)852 D)456 E)852
SOLUTION:Divisor *quotient+remainder=dividend
divisor=(dividend)-(remainder)/quotient
(12401-13)/76=163
Answer(A) #### A
QUESTION:The product of all the prime numbers less than 25 is closest to which of the following powers of 10?
options: A)10^9 B)10^8 C)10^7 D)10^8 E)10^5
SOLUTION:Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19,23
=2.2 *10^8
D #### D
QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is
options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm
SOLUTION:Explanation:
Required Length = H.C.F of 700 cm, 385 cm and 1295 c
= 35 cm. Answer: C #### C
QUESTION:A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
options: A)4/19 B)7/19 C)12/19 D)21/99 E)26/77
SOLUTION:Solution
P( None is defective)
= 18C2 / 22C2
= 51/77
P( at least one is defective)
= (1- 51/77)
= 26/77.
Answer E #### E
QUESTION:The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 60 percent of b, what is the value of m/x?
options: A)2/5 B)3/4 C)4/5 D)5/4 E)2/7
SOLUTION:a/b = 4/5
m/x = (2/5)*5 / (7/4)*4 = 2/7
The answer is E. #### E
QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
options: A)10 m B)16 m C)245 m D)19 m E)235 m
SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30
= 25/2 => 2(140 + x) = 750 => x
= 235 m.
Answer: E #### E
QUESTION:I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there?
options: A)12 B)44 C)56 D)120 E)200
SOLUTION:6C3*4C2
=120=D #### D
QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
options: A)3% B)4% C)5% D)6% E)7%
SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate =(100 x 3000)/(12500 x 4)% = 6%
answer :D #### D
QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse?
options: A)A)5 B)B)8 C)C)10 D)D)15 E)E)30
SOLUTION:Total number of ways to choose 6 chairs from 5= 6C2=15
Total number of combination=150
That means we need get 10 combinations from the selection of tables....
Screening through the answers.... 5C3=10..... 10*15=150
Answer is 5... A #### A
QUESTION:If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is
options: A)not an even B)an even C)a perfect square D)an odd E)a prime
SOLUTION:x^2 - 2x + 2y + 3 = 2x^2 - 3x + y + 1
y = x^2 - x - 2
y = (x-2)(x+1) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B. #### B
QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
options: A)1 B)2 C)8 D)31 E)30
SOLUTION:Total outcome is 2^3 = 8
Favourable cases = H_ H
The second place can be occupied by either H or T
There are 2^1 =2 ways that can be done.
Hence, the correct option is B #### B
QUESTION:A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
options: A)6 ½ days B)1 ½ days C)8 ½ days D)5 ½ days E)2 ½ days
SOLUTION:Explanation:
3/20 * 2 + (2 + x)/5 = 1
x = 1 ½ days
Answer:B #### B
QUESTION:One card is drawn from a pack of 52 cards. What is the probability that the card drawn is not a face card?
options: A)4/15 B)5/17 C)9/13 D)3/13 E)7/15
SOLUTION:Out of 52 cards there will be 16 face cards are there.
probability of getting not a face card = 36/52 = 9/13
Answer is C #### C
QUESTION:William earned $3,200 per month as a
teacher for the ten months from September
to June. Then he took a job as a barista at a
local café, where he earned $2,000 per
month during July and August. What was
his average monthly pay for the 12 months?
options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500
SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a
barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into
the formula for the mean:
mean=sum of values/number of values=>36.000/12=3.000
correct answer D)$3.000 #### D
QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
options: A)8 B)15 C)16 D)18 E)None
SOLUTION:Solution
Capacity of the tank = (12×13.5) litres
= 162 litres.
Capacity of each bucket = 9 litres.
Number of buckets needed = (162/9)
‹=› 18.
Answer D #### D
QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent?
options: A)10% B)20% C)30% D)40% E)50%
SOLUTION:5*SP = 7*CP
SP = 1.4*CP
The profit percent is 40%.
The answer is D. #### D
QUESTION:There is a biased dice..wen d dice is thrown. probability of occurrence of odd numbers is thrice that of even numbers. If the dice is thrown twice..find the probability of the products of the numbers appeared being odd.
options: A)8/16 B)9/16 C)10/16 D)11/16 E)7/16
SOLUTION:since, p(odd)=3p(even)
and p(odd)+p(even)=1
hence p(odd)=3/4
now only odd*odd=odd
hence two odd i s p(odd)=3/4*3/4=9/16
ANSWER:B #### B
QUESTION:Find the remainder of the division (3^33)/7.
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:Find the pattern of the remainders after each power:
(3^1)/7 remainder 3
(3^2)/7 remainder 2
(3^3)/7 remainder 6
(3^4)/7 remainder 4
(3^5)/7 remainder 5
(3^6)/7 remainder 1 -->this is where the cycle ends
(3^7)/7 remainder 3 -->this is where the cycle begins again
(3^8)/7 remainder 2
Continuing the pattern to (3^33)/7 gives us a remainder of 6
Final Answer:
E) 6 #### E
QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2
SOLUTION:RT = W
Given:
R = 1/3 + 1/3 = 2/3
T = ?
W = 1
T = 1 / (2/3) = 3/2 = 1 1/2
Answer: E #### E
QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke?
options: A)16 B)17 C)18 D)19 E)20
SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree.
From the diagram, (36−x)2=x2+122(36−x)2=x2+122
⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144
⇒72x=1296−144⇒72x=1296−144
⇒x=16
Answer:A #### A
QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems?
options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625
SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625.
Hence, the probability that Alex will solve at least one problem
= 1 - 256/625 = 369/625.
ANSWER:D #### D
QUESTION:A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts?
options: A)6 B)8 C)10 D)12 E)14
SOLUTION:In one hour, the crow eats 1/24 of the nuts.
(1/4) / (1/24) = 6 hours
The answer is A. #### A
QUESTION:By selling 50 mangoes, a shopkeeper gains the price of 10 mangoes. His gain per cent is
options: A)25% B)35% C)20% D)23% E)30%
SOLUTION:Suppose S.P of 50 mangoes = Rs 50
Therefore, Gain = Rs 10 => C.P = Rs 40
Gain % = 10/40 x 100 = 25%
Gain = 25%
ANSWER:A #### A
QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph
SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10)
= 50 kmph.
Answer:B #### B
QUESTION:The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books?
options: A)7 B)12 C)13 D)5 E)26
SOLUTION:Surface area of each shelf= 2ab + 2ac + 2bc
848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c
848 = 32 + 2c + 32c
816 = 34c
c = 24 in. (i.e. the length of each shelf)
Each book is 4 in thick
24/4 = 6 books per shelf
26/6 = 4.333=5 shelves
Answer is D #### D
QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
options: A)25 B)34 C)50 D)67 E)50
SOLUTION:Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 6 oz can = 300 oz/6 oz = 50
Answer E, 50 cans #### E
QUESTION:. The average of first ten prime numbers which are odd is?
options: A)22.9 B)28.1 C)12.9 D)15.8 E)11.2
SOLUTION:Explanation:
Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer:D #### D
QUESTION:Series Problem like 4 12 x 44 46 132 134 begin of the Skype highlighting 44 46 132 134 end of the Skype highlighting. Find x?
options: A)13 B)14 C)15 D)16 E)17
SOLUTION:134-132=2
46-44=2
x-12=2
x=14
ANSWER:B #### B
QUESTION:If x + y = 8 and y − 3x = 7, then what is the value of y-x?
options: A)1/7 B)3 C)15 D)15/2 E)60/7
SOLUTION:x+y=8 ...equation 1
-3x+y=7 ...equation 2
adding both the equations
-2x+2y=15=>y-x=15/2
correct answer option D #### D
QUESTION:A toy train started on a 12-feet loop trail at a rate of 4 feet per minute. One minute afterwards, a toy scooter from the same starting point on the loop trail at 6 feet per minute. What is the shortest time that the scooter would take on the trail in order to catch up with the train?
options: A)4 minutes B)3 minutes C)2 minutes D)1 minutes E)0.8 minutes
SOLUTION:we don't need to assume here the direction.we need to find which will take less time
so there are 2 cases
1)both moving in same direction...then time would be 2 minutes
2)both moving in opp direction then time would be 0.8 minutes
as we need the shortest time it would be the second case
Answer:E #### E
QUESTION:If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?
I. LCM : 24; HCF : 6
II. LCM : 18; HCF : 8
III. LCM : 16; HCF : 9
options: A)I only B)II and III only C)I and II only D)I and III only E)I, II and III
SOLUTION:We need to keep two things in mind here:
1. Product of two numbers = LCM*HCF
2. LCM should be a multiple of HCF
Only Statement I follows these two rules.
Correct Option A #### A
QUESTION:After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B?
options: A)N/15 B)7N/8 C)14N/15 D)N/5 E)4N/5
SOLUTION:1/4 of tested had infection A, thus N/4 had infection A;
Of those with infection A, 1/2 also had infection B, thus 1/2*N/4 = N/8 had both infections A and B.
Therefore, N - N/8 = 7N/8 did not have both infection A and B.
Answer: B. #### B
QUESTION:1 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
options: A)12/9 days B)15/4 days C)82/8 days D)22/76 days E)3/2 days
SOLUTION:1M = 6W ---- 20 days
12M + 8W -----?
72W + 8 W = 80W ---?
6W ---- 20 80 -----?
6 * 20 = 80 * x => x = 3/2 days
Answer:E #### E
QUESTION:Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his?
options: A)24/64 B)32/64 C)36/64 D)40/64 E)42/64
SOLUTION:Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5.
Expected value of three dice is 3*3.5=10.5.
Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2 = 32/64.
That's because the probability distribution is symmetrical for this case:
The probability of getting the sum of 3 (min possible sum) = the probability of getting the sum of 18 (max possible sum);
The probability of getting the sum of 4 = the probability of getting the sum of 17;
The probability of getting the sum of 5 = the probability of getting the sum of 16;
...
The probability of getting the sum of 10 = the probability of getting the sum of 11;
Thus the probability of getting the sum from 3 to 10 = the probability of getting the sum from 11 to 18 = 1/2.
Answer: B. #### B
QUESTION:At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married?
options: A)5⁄7 B)7⁄10 C)2/7 D)7⁄30 E)5⁄70
SOLUTION:--------------------M------W--------Total
Marrried----------20-----20---------40
Not married-----10-----50---------60
Total-------------30-----70--------100
need married woman/total woman, so 20/70=2/7
C #### C
QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ?
options: A)6 B)2 C)-1 D)-3 E)-4
SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even
now subtract X + (X+2) - (X+4)
doing this leaves us with X -2
what even number can we substitute in X to yield an answer choice
B works 2 (plug in 4 for X) #### B
QUESTION:A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than five people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
options: A)x/4 B)x/5 C)x/9 D)x/20 E)4x/9
SOLUTION:If 5 people share the rent, each person would pay x/5.
If 4 people share the rent, each person will pay x/4.
The extra amount each person pays is x/4 - x/5 = 5x/20 - 4x/20 = x/20
The answer is D. #### D
QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean m. 72 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.6 years and the standard deviation is 2.6 years, what percent of the distribution has more than 10.2 years as a shelf’s average life?
options: A)17% B)16% C)15% D)14% E)13%
SOLUTION:Average = 7.6
SD = 2.6
7.6 - 2.6 < 72% of distribution < 7.6 + 2.6
5.0 < 72% of distribution < 10.2
28% is outside this range.
Given: Distribution is symmetric. So 14% of distribution is less than 5.0 and the other 14% of distribution is greater than 10.2.
Answer: D #### D
QUESTION:What percent of 7.2 kg is 18 gms ?
options: A)25 B)66 C)288 D)19 E)17
SOLUTION:Explanation:
Required percentage = (18/7200 * 100)% = 1/4% = 0.25%
Answer: A) .25% #### A
QUESTION:A sum of money at simple interest amounts to $ 980 in 3 years and to $1024 in 4 years. The sum is:
options: A)$153 B)$848 C)$398 D)$549 E)$675
SOLUTION:B
$848
S.I. for 1 year = $(1024 - 980) = $44.
S.I. for 3 years = $(44 x 3) = $132.
Principal = $(980 - 132) = $848. #### B
QUESTION:If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
options: A)1/4 B)1/2 C)3/4 D)3/5 E)None of these
SOLUTION:The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer : B #### B
QUESTION:Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have.
options: A)16.5 B)17.5 C)18.5 D)19.5 E)20.5
SOLUTION:Let Siri has x Rs, then Christine has 20+x Rs
Given x + (20+x)= 21
=> 2x= 1 or x= 0.5
So Christine and Siri has 20.5 and 0.5 Rs respectively.
ANSWER:E #### E
QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo
options: A)61 B)62 C)63 D)64 E)65
SOLUTION:4C1+4C2+4C3+4C4=15.
If their positions also takes into consideration then the ans will be 64
ANSWER:D #### D
QUESTION:If f(x) = (x^2 - 1)/(x), what is f(1/x) in terms of f(x)?
options: A)-1*f(x) B)f(x) C)1/f(x) D)-1/f(x) E)2*f(x)
SOLUTION:f(1/x) = ((1/x)2 - 1) / ((1/x))
= ((1/x^2) - 1) / (1/x)
= ((1-x^2)/(x^2)) / (1/x
= (1-x^2)/(x^2)
= - ( (x^4) -1) / (x)
= -1* f(x)
Answer is A. #### A
QUESTION:A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long?
options: A)2.5 B)3 C)5 D)7 E)9
SOLUTION:D = 25 * 60 + 1000 = 2500 m
T = 2500/60 * 18/5 = 150 sec = 2.5 mins
Answer: A #### A
QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 6:4. If 60% of the Toyota bought and 40% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase?
options: A)66% B)64% C)68% D)52% E)72%
SOLUTION:let total no of Vehicles bought be 100, Toyota 60 and Honda 40, so total number of SUV's bought for Toyota and Honda respectively 60* 60/100=36 and 40* 40/100=16
so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52%
ANSWER:D #### D
QUESTION:In a survey of parents, exactly 7/8 of the mothers and 3/4 of the fathers held full-time jobs. If 60 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs?
options: A)25.5% B)21.5% C)17.5% D)13.5% E)9.5%
SOLUTION:Fathers without full-time jobs are 1/4*2/5 = 2/20 of all the parents surveyed.
Mothers without full-time jobs are 1/8*3/5 = 3/40 of all the parents surveyed.
The percent of parents without full-time jobs is 2/20 + 3/40 = 7/40 = 17.5%
The answer is C. #### C
QUESTION:Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.
options: A)2088 B)2000 C)3087 D)None of these E)Cannot be determined
SOLUTION:Solution:
Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11
Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400
Therefore Shyam's share = (441/841) * 5887 = 3087.
Answer C #### C
QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender?
options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2
SOLUTION:There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128
case 2 .all girls.
1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128
We will add the cases to get 1/64 #### A
QUESTION:What is the maximum number of pieces of birthday cake of size 5” by 5” that can be cut from a cake 15” by 15”?
options: A)5 B)10 C)16 D)20 E)9
SOLUTION:The prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 3 'pieces' each, we have (3)(3) = 9 total smaller squares (at maximum).
E #### E
QUESTION:If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.
options: A)7/25 B)3/25 C)8/25 D)2/13 E)3/17
SOLUTION:P (A n B) = P(A) . P(B)
P (A n B) = 4/5 . 2/5
P (A n B) = 8/25.
C #### C
QUESTION:A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
options: A)32 B)88 C)67 D)11 E)66
SOLUTION:One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.
Answer:D #### D
QUESTION:In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate?
options: A)358000 B)368000 C)357000 D)358000 E)367000
SOLUTION:Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357000
Answer:C #### C
QUESTION:If x > y and y > z, which of the following represents the greatest number W?
options: A) x − z B) x − y C) y − x D) z − y E) z − x
SOLUTION:Because x>y>z
thus W=x- z wil lbe greatest
Ans: A #### A
QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
options: A)165 B)771 C)245 D)177 E)121
SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C #### C
QUESTION:Today is Monday. After 61 days, it will be:
options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY
SOLUTION:Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer: Option B #### B
QUESTION:A committee of three students has to be formed. There are six candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
options: A)3 B)4 C)5 D)6 E)8
SOLUTION:Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE.
D #### D
QUESTION:What is the sum of the first 22 natural numbers (starting from 1)?
options: A)223 B)233 C)243 D)253 E)263
SOLUTION:The sum of n natural numbers = n*(n+1) / 2 = 22*23/2 = 253
The answer is D. #### D
QUESTION:Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 7 hours?
options: A)675 B)750 C)1,800 D)5,900 E)1,575
SOLUTION:8 machines/ 360 cans = 5 machines/ x cans
8x= 1800
x=225
(225)(7 hours)= 1575 cans. The answer is E. #### E
QUESTION:In a family, there are six members A, B, C, D, E and F.
A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died.
How many male members are there in the family ?
options: A)1 B)9 C)3 D)4 E)6
SOLUTION:Explanation:
A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A.
A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males.
Answer: C) 3 #### C
QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1
SOLUTION:1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: C #### C
<<<Examples ends
QUESTION:If the price of gold increases by 40%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
options: A)331/8% B)26.67% C)28.5% D)332/3% E)131/3%
SOLUTION:100
140
------
140-------40
100-------? => 28.5%
Answer:C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P?
options: A)20% B)40% C)50% D)60% E)80%
SOLUTION:65% is 15%-points below 80% and 10%-points above 55%.
So the ratio of solution P to solution Q is 2:3.
Mixture P is 2/5 = 40% of the volume of mixture PQ.
The answer is B. #### B
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was:
options: A)14 B)16 C)19 D)22 E)24
SOLUTION:Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21.
Son's age 5 years back (21 - 5) = 16 years.
answer :B #### B
QUESTION:A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
options: A)30 B)39 C)87 D)27 E)91
SOLUTION:Let the side of the square(ABCD) be x meters.
Then, AB + BC = 2x metres.
AC = = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = = 30% (approx)
Answer:A #### A
QUESTION:How many numbers between 11 and 90 are divisible by 7 ?
options: A)23 B)11 C)22 D)32 E)15
SOLUTION:The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, Tn = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Required number of terms = 11
ANSWER B 11 #### B
QUESTION:Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
options: A) 3 B) 6 C) 7.2 D) 5 E) 9
SOLUTION:Answer is D.
x/x+36=1/5
x=9
14-9=5 #### D
QUESTION:The sum of two numbers is 18. Their difference is 4. What are the numbers?
options: A)8,6 B)9,9 C)11,7 D)15,3 E)13,9
SOLUTION:Let two numbers be x and y.
Equation (i): x + y = 18
Equation (ii): x - y = 4
Solve system of equations:
2x=22
x=11
y=7
Answer C is correct. #### C
QUESTION:For what value of “k†will the equation (2kx2 + 5kx +1)=0 have equal roots?
options: A)2/7 B)9/4 C)8/25 D)7/1 E)7/2
SOLUTION:for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0
in the given equation
(5k)^2-4*2k*1=0
by solving this equation
we get k=0, k=8/25
ANSWER:C #### C
QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 50 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week?
options: A)40 B)45 C)50 D)55 E)60
SOLUTION:Annie earned 40x + 10(2x) = 60x
Let H be the number of hours that Harry worked.
Harry earned 30x + 1.5x(H-30) = 60x
(1.5x)(H) = 75x
H = 50 hours
The answer is C. #### C
QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3
SOLUTION:distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr
Answer is B. #### B
QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity?
options: A)7/18 B)9/18 C)2 D)18/7 E)18/5
SOLUTION:Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D
QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day?
options: A)10 B)41 C)31 D)21 E)22
SOLUTION:Explanation:
1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12
1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16
1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48
Let ‘x’ be the No. of boys required.
Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1
= (4 + 3 + x)/48 = 1
i.e. 7 + x= 48 and x = 41.
Answer: Option B #### B
QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39?
options: A)3 B)8 C)12 D)32 E)35
SOLUTION:n = 5p + 1 = 6,11,16,21,26,31
n = 7q + 3 = 3,10,17,24,31
=>n = 39m + 31
To get this, we need to take LCM of co-efficients of p and q and first common number in series.
So we need to add 8 more to make it
39m + 39
Answer - B #### B
QUESTION:During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
options: A)9/xz B)9zx C)9x/z D)9z/x E)xz/9
SOLUTION:Speed of Peter = x/9 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x
Option D
The values 100m and 200m have no role to play here and are just given to confuse you. #### D
QUESTION:A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 25 hours, 50 percent worked 40 hours, and the rest worked 50 hours?
options: A) $180,000 B) $185,000 C) $180,000 D) $200,000 E) $192,500
SOLUTION:30% of 1000 = 300 worked for 20 hours
Payment @ 5/hr
Total Payment = 300*25*5 = 37500
50 % of 1000 = 500 worked for 40 hours
Payment @ 5/hr
Total payment = 500*40*5 = 100000
Remaining 200 worked for 50 Hours
Payment for first 40 Hours @ 5 /hr
Payment = 200*40*5 = 40000
Payment for next 10 hr @ 7.5/hr
Payment = 200 * 10 * 7.5 = 15000
Total Payment = 37500+100000 + 40000 +15000 = 192500
Hence , answer is E #### E
QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her
options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger
SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1996 has to be the ring finger
Answer is (D) #### D
QUESTION:If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex?
options: A)1/3 B)2/3 C)1/4 D)1/2 E)3/5
SOLUTION:No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 4 = 4C2
Total possible outcomes - 2^4 (each child can be either a girl or a boy)
Probability=2C1*4C2/2^4= 2*4/2*2*2*2=8/16=1/2
Ans=D #### D
QUESTION:A ship sails out to a mark at the rate of 19 kmph. and sails back at the rate of 13 kmph. The average rate of sailing is ?
options: A)15 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None
SOLUTION:Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 19 x 13 ) / (19 +13 ) km/hr.
= 15 km/hr.
Correct Option: A #### A
QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of :
options: A)45 hours B)47 hours C)48 hours D)50 hours E)None
SOLUTION:Explanation:
Basic rate per hour = Rs.(20/40)= Rs.1/2
Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8
Suppose he worked x hours overtime.
Then,20+5/8x=25 or 5/8x=5
x=5×8/5=8 hours
So he worked in all for (40+8) hours = 48 hours.
Correct Option: C #### C
QUESTION:The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers?
options: A)10 B)12 C)14 D)15 E)16
SOLUTION:Solution
Let the number be x and (28 - x) = Then,
x (28 - x) = 192
‹=›x2 - 28x + 192 = 0.
‹=›(x - 16) (x - 12) = 0
‹=›x = 16 or x = 12.
Answer B #### B
QUESTION:If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x?
options: A)308 B)154 C)70 D)44 E)21
SOLUTION:If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that.
LCM of 2,7,11= 154
Hence x must be divisible by 154
Hence B #### B
QUESTION:A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 125 in his diary to remember his PIN. He also wrote out the way to calculate 125 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 125".
Once, Prafull saw his diary in which Pinaki wrote this number 125. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?
options: A)874 B)872 C)876 D)875 E)879
SOLUTION:Explanation :
Let, the PIN is x.
According to the question,
The card number =996 and Remainder =125.
Thus, (996 × x)/997=125.
=>x= 872.
Answer : B #### B
QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2
SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2
= 62 m2.
answer :D #### D
QUESTION:A rectangular block 15cm by 30cm by 75cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
options: A)6 B)40 C)15 D)10 E)22
SOLUTION:Volume of the block = 15*30*75 = 33750 cm^3
Side of the largest cube = H.C.F of 15,30,75 = 15cm
Volume of the cube = 15*15*15 = 3375 cm^3
Number of cubes = 33750/3375 = 10
Answer is D #### D
QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
options: A)3% B)4% C)5% D)6% E)7%
SOLUTION:65*(90/100)*((100-x)/100) = 56.16
x = 4%
ANSWER:B #### B
QUESTION:Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 5 days before the completion of the work. How long did the work last?
options: A)6 B)7 C)8 D)8 1/9 E)10
SOLUTION:Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains
Then if Ben had to leave 5 days before the completion, this means that Carla had to work alone for these 5 days in which she completed 1/3 of the job.
Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 7/15
3/20 (t) = 7/15 ---> t = 3 1/9
Therefore, these 3 1/9 days worked plus the 5 days that Carla had to work by herself add to 8 1/9 days
Answer: D #### D
QUESTION:A man spends Rs. 1900 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
options: A)2075 B)2175 C)2275 D)2375 E)2475
SOLUTION:Explanation:
Total expenditure for the first 3 months = 3 × 1900 = 5700
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 5700 + 6200 + 9000 + 5200 = Rs. 25200
So, Average monthly income = 26100/12 = Rs. 2175
Answer B #### B
QUESTION:4, 6, 12, 14, 28, 30, ?
options: A)32 B)64 C)62 D)60 E)52
SOLUTION:The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60
Answer : D. #### D
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
options: A)200 metres B)180 metres C)324 metres D)228 metres E)150 metres
SOLUTION:Speed= 60 x 5/18 m/sec = 50/3 m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3 x 9 m = 200 m.
Option A #### A
QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is?
options: A)40m2 B)45m2 C)49m2 D)51m2 E)55m2
SOLUTION:39/360 * 22/7 * 12 * 12
= 49m2
Answer:C #### C
QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition
options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980
SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum.
i,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) }
so,here by putting the values as,
(0+1+2+3+4){(5-1)!*(11111)-(5-2)!*1111}
= 10{(4!*11111)-(3!*1111)}
= 10{266664-6666}
= 2599980
ANSWER:A #### A
QUESTION:The volume of a rectangular box is 330 square inches. The length on one side of the top is 11
inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing
may help you with this one.)
options: A)100 B)130 C)120 D)110 E)101
SOLUTION:3 x 11 = 33
V = 33 x missing measure
V is 330
330 ÷ 33 = 10 which is the missing
measure of the side of the box top
10 x 11 = 110 sq. ft. which is area
of the top of the box.
correct answer D #### D
QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these
SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 4/5
5n + 5 = 4d + 4
5n + 5 = 4(2n - 1) + 4 => n = 5/3
d = 2n - 1 => d = 3/7
Hence the fraction is : 5/7
ANSWER:B #### B
QUESTION:The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 25 feet on a side. What will be the volume of the new building in cubic feet?
options: A)3,937,500 cubic feet B)15,750 cubic feet C)11550√3 cubic feet D)7,160,947 cubic feet E)3,937,500√3 cubic feet
SOLUTION:Volume of the Hexagon with side 200 and height 70 = Area * height
= 6*(sqrt(3)/4)(200^2)(70)
Volume of the center bull's eye that is similar in shape of a hexagon but side 25
= 6 * (sqrt(3)/4)(25^2)*70
Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(25^2)*70=7,160,947
Answer is D #### D
QUESTION:What is the remainder when 1014*1047*1050*1053 is divided by 33?
options: A)3 B)6 C)30 D)21 E)18
SOLUTION:OA is 'C'.
OE:
take the remainder from each of 1044/33, 1047/33 and so on..
1014/33 gives remainder = 24
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e = 24*24*27*30
break them into pairs 24*24/33 gives remainder 15
and 27*30/33 gives remainder 18
so 15*18/33 gives remainder 6.
B #### B
QUESTION:If Shreehari walks in the speed of 4.5 km/hr from his house, in what time will he reach his school which is 750 m long from his house?
options: A)5 B)30 C)10 D)12 E)15
SOLUTION:Speed = 4.5 * 5/18 = 1.25 m/sec
Time taken = 750/1.25 = 600 sec ie. 10 mins.
Answer:C #### C
QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
options: A)160 B)175 C)180 D)195 E)205
SOLUTION:Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 * 8 * 4) = 160.
Therefore, 160 * 2.40 + x * 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER:B #### B
QUESTION:At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock
options: A)47 B)76 C)28 D)66 E)99
SOLUTION:Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 45/5 = 9 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 9 = 99 secs.
Answer: E #### E
QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600
SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.
Let p be the population of the least populated district.
Then 160,080 = p + 7(1.1)p
8.7p=160,080
p = 18,400
The answer is C. #### C
QUESTION:The sum of three integers A, B and C is 60. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
options: A)40 B)45 C)35 D)50 E)55
SOLUTION:A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=60
so 1/3(B+C)+B+C=60
4(B+C)/3= 60
B+C =60*3/4 = 45
A=60-45=15
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=60
so 1/5(A+C)+A+C=60
A+C=60*5/6=50
but A=15, so C=50-15=35
Answer :C #### C
QUESTION:A factory produces 6000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
options: A)4436 toys B)1500 toys C)6113 toys D)2354 toys E)1375 toys
SOLUTION:To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
6000 /4 = 1500 toys
correct answer B #### B
QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is?
options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000
SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
M + O = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv)
Subtracting (ii) from (iv), we get M = 4000.
M's monthly income = Rs. 4000
C #### C
QUESTION:6x + 2y = -4
4x + y = 1
In the system of equations above, what is the value of x?
options: A)5 B)4 C)3 D)2 E)1
SOLUTION:6x + 2y = -4 can be written as 3x + y = -2
Let's subtract the second equation from this equation.
-x = -3
x = 3
The answer is C. #### C
QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased?
options: A) 100% B) 500% C) 300% D) 600% E) 800%
SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times.
The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%.
Answer: B. #### B
QUESTION:The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
options: A)12.5% B)13% C)13.15% D)14% E)15%
SOLUTION:Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
A) #### A
QUESTION:If A got 70 marks and B got 60 marks, then what percent of A's mark is B's mark?
options: A)A)60% B)B)85.7% C)C)65% D)D)75% E)of these
SOLUTION:A's marks = 70 ; B's marks = 60.
Let x% of A = B => x/100 *70 = 60
=> x = (60 * 100)/80 = 85.7
B's marks is 85.7% of A's marks.
ANSWER:B #### B
QUESTION:There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women?
options: A)8/12 B)6/16 C)4/16 D)6/10 E)4/10
SOLUTION:w = m+4
w+m = 20
m+4+m = 20
2m = 16
m = 8
w = 12
ratio:8:12
Ans: A #### A
QUESTION:Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 36 have long fur, 27 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
options: A)26 B)19 C)11 D)8 E)6
SOLUTION:No of dogs=45
Long fur=36
Brown=27
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=36+27-Both
Both=26
Answer A #### A
QUESTION:76^77 /7
remainder is ?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1
and 5^3/3 remainder=2 and also 5/3=2
so it does not matter on the power value
so the answer will be 76/7 remainder=6
ANSWER:B #### B
QUESTION:Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 80 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
options: A)70 miles B)80 miles C)90 miles D)100 miles E)110 miles
SOLUTION:Every hour, Nil gets ahead of Ethan 80 - 20 =
60 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 80 × 1 = 80 miles.
correct answer B #### B
QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced?
options: A)70% B)15% C)20% D)25% E)30%
SOLUTION:price of a coat in a certain store = $500
the price of the coat is to be reduced by $350
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (350)*100 / 500 = 70%
Answer: Option A #### A
QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value
options: A)31 B)32 C)46 D)47 E)48
SOLUTION:- a + b + ((-a)(b)/100)
= -25+75+(-25*75)/100
= -25+75-19
=31
ANSWER:A #### A
QUESTION:In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?
Look at this series: 1, 5, 7, 3, __, 1 ...Which number is missing?
options: A)2 B)4 C)12 D)0 E)13
SOLUTION:E
13
This is an alternating addition and subtraction series. In the first pattern, 6 is added to each number to arrive at the next. In the second, 2 is subtracted from each number to arrive at the next. #### E
QUESTION:The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
options: A)5 B)4 C)1/2 D)1/5 E)1/8
SOLUTION:If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5.
The answer is D. #### D
QUESTION:In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 70% average total marks, it is necessary for him in third yearly examination to secure marks :
options: A)300 B)350 C)400 D)450 E)550
SOLUTION:total marks:1500 for three exams
70% of 1500=1050
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =1050
X=550
ANSWER:E #### E
QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D?
options: A) 1 B) 8 C) 19 D) 20 E) 27
SOLUTION:I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.
C #### C
QUESTION:If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r?
options: A)2 B)3 C)4 D)5 E)Cannot be determined
SOLUTION:\frac{15^r( 1+ 15)}{4^y} = 15^y
(15^r . 4^2 ) / 4^y = 15^y. 4^0
15^r . 4^(2-y) = 15^y. 4^0
Equating the powers, r = y; 2-y = 0; So r = y = 2=A #### A
QUESTION:In how many ways can the letters of the CHEATER be arranged
options: A)20160 B)2520 C)360 D)80 E)None of these
SOLUTION:Explanation:
As we can see the letter "E" is twice in given word, so Required Number
=7!/2!=7∗6∗5∗4∗3∗2!/2!=2520
Option B #### B
QUESTION:Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?
options: A)ab/(a+b) B)(a-b)/(a+b) C)b/(b+a) D)a/(a+b) E)b/(a-b)
SOLUTION:Randy can do the job in a hrs, Alvin can do the job in b hrs.
When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.
Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)
So Randy does a/(a+b) of the work and Alvin does b/(a+b) of the work.
Answer (C). #### C
QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
options: A)876 m B)157 m C)235 m D)156 m E)167 m
SOLUTION:Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2
=> 2(140 + x) = 750 => x
= 235 m.
Answer: C #### C
QUESTION:If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10?
options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5
SOLUTION:92p × 5p+w + 11w × 6pw--1=B #### B
QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
options: A)3999 B)7799 C)2500 D)2772 E)2912
SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500.Answer: C #### C
QUESTION:2+2+2²+2³ ... +2^9
options: A)2^9 B)2^10 C)2^16 D)2^35 E)2^37
SOLUTION:2+2=2^2
2^2+2^2=(2^2)*(1+1)=2^3
2^3+2^3=(2^3)*(1+1)=2^4
so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10
Answer B #### B
QUESTION:Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
options: A)2:3 B)4:3 C)7:3 D)9:3 E)4:2
SOLUTION:Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3. #### B
QUESTION:A man can row 7 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
options: A)3.3 B)3.4 C)3.5 D)3.6 E)3.7
SOLUTION:M = 7
S = 1.2
DS = 7 + 1.2 = 8.2
US = 7 - 1.2 = 5.8
x/8.2 + x/5.8 = 1
x = 3.40.Answer: B #### B
<<<Examples ends
QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres?
options: A)20 B)200 C)300 D)400 E)100
SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 9540
[4L - 40] = 9540 / 26.50 = 360
4L = 400
L = 400/4= 100 meters. Answer: E #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:At a circular table for nine will sit seven adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the nine people be arranged around the table.
options: A)120 B)240 C)480 D)600 E)720
SOLUTION:Consider the two parents and two children as one unit.
Then there are five adults and one family unit.
The number of ways 6 can form a line is 6!
Around a circular table, there would be 6 rotations so we divide this number by 6.
There are 5! ways for 6 to sit around the circular table.
Then the two children have two options and the two parents have two options.
Then the total number of ways is 5!*2*2= 480
The answer is C. #### C
QUESTION:A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
options: A)5 B)6 C)21 D)8 E)9
SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [385 * 3/55] sec = 21 sec
Answer: C #### C
QUESTION:S is a set containing 8 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
options: A) The median of S is prime. B) The median of T is prime C) The median of S is equal to the median of T. D) The sum of the terms in S is prime. E) The sum of the terms in T is prime.
SOLUTION:Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A) The median of S is prime.
Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime.
(B) The median of T is prime.
Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number.
(C) The median of S is equal to the median of T.
Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true.
(D) The sum of the terms in S is prime.
Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime.
(E) The sum of the terms in T is prime.
Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime.
C #### C
QUESTION:The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
options: A)2197 B)1267 C)1750 D)2267 E)1262
SOLUTION:Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8) = Rs. 1750
Answer:C #### C
QUESTION:The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is :
options: A)1520 m2 B)2420 m2 C)2480 m2 D)2520 m2 E)None of these
SOLUTION:Solution
We have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103.
Solving the two equations, we get, l = 63 and b = 40.
∴ Area = (l × b) = (63 × 40) m2 = 2520 m2. Answer D #### D
QUESTION:70,76, 74,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74.
Answer: C. #### C
QUESTION:If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses?
options: A)1/8 B)1/3 C)1/4 D)1/2 E)1
SOLUTION:P(THH) = 1/2*1/2*1/2=1/8
The answer is A. #### A
QUESTION:A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
options: A)76 seconds B)17 seconds C)40 seconds D)16 seconds E)14 seconds
SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C #### C
QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h?
options: A)6 B)12 C)24 D)36 E)48
SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24.
ANS :C #### C
QUESTION:"A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap?
options: A)90 seconds B)54.44 seconds C)110 seconds D)63 seconds E)77 seconds
SOLUTION:A is faster than B. Every second he increases distance between A and B. They will meet for the first time again when he increases distance between them by one full circle. (Say the lap is of 100m. He keeps increasing distance between them. When he is 90 m ahead of him, it is the same as 10 m behind him because they are moving in a circle. Finally when he is 100 m ahead of him, he is exactly 1 lap ahead and hence both are at the same point).
A takes 70 secs for one full lap. So he covers 4.5 laps in exactly 70*4.5 = 315 seconds.
In 315 secs, B completes 3.5 laps. So for each lap, he takes 315/3.5 = 90 secs
Answer (A) #### A
QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required?
options: A)34 B)40 C)68 D)88 E)26
SOLUTION:We have: l = 20 ft and lb = 60 sq. ft.
So, b = 3 ft.
Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft.
ANSWER:E #### E
QUESTION:The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is
options: A)64 sq.m B)70 sq.m C)78 sq.m D)84 sq.m E)None
SOLUTION:Solution
Perimeter of the rhombus = 56 m
Each side of the rhombus = 56 / 4 m
= 14 m.
Height of the rhombus = 5 m
Area = (14 x 5) m²
= 70 m²
Answer B #### B
QUESTION:Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec
SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 100 + 280 = 380m.
The time required = d/s = 380/20 = 19 sec.
Answer:E #### E
QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ?
options: A)–4 B)–3 C)–2 D)–1 E)0
SOLUTION:Just putting values, the LHS becomes
n=0 --> 11
n=-1 --> 11/10
n=-2 --> 11/100
n=-3 --> 11/1000
Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3.
Answer is B. #### B
QUESTION:There are different 10 circles. What is the number of the greatest possible points with which the circles intersect?
options: A)90 B)100 C)110 D)180 E)200
SOLUTION:Maximum points of intersection between n different circles = n*(n - 1) = 10*9 = 90
Answer: A #### A
QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 6?
options: A)82,650 B)64,850 C)64,749 D)49,700 E)56,720
SOLUTION:Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 6
Seeing the Options After Dividing an Finding the Reminder of 2
My Answer was A #### A
QUESTION:P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 12 days. How many days more will P take to finish the work?
options: A)12 B)15 C)18 D)20 E)22
SOLUTION:Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 12 days = 12 × (1/16) = 12/16 = 3/4
Remaining work = 1 = 3/4 = 1/4
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (1/4) / (1/48) = 12
Option A #### A
QUESTION:A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?
options: A)4 days B)8 days C)12 days D)9 days E)3 days
SOLUTION:2/5 + (2 + x)/10
= 1 => x
= 4 days
Answer: A #### A
QUESTION:In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
options: A)20% B)25% C)30% D)35% E)40%
SOLUTION:Let x be the number of cars and let y be the number of cars parked illegally.
4%*x = 20%*y
y/x = 1/5 = 20%
The answer is A. #### A
QUESTION:A runs 25% faster than B and is able to allow B a lead of 7 meters to end a race in dead heat. What is the length of the race?
options: A)10 meters B)25 meters C)45 meters D)15 meters E)35 meters
SOLUTION:Answer
A runs 25% as fast as B.
i.e., if B runs 100 m in a given time, A will run 125 m in the same time.
In other words, if A runs 5 m in a given time, then B will run 4 m in the same time.
Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat.
Ratio of length of start given : length of race :: 1 : 5
In this question, we know that the start given is 7 m.
Hence, the length of the race will be 7 * 5 = 35 m.
Choice E #### E
QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec
SOLUTION:Speed = 45 * 5/18
= 25/2 m/sec
Total distance covered
= 360 + 140
= 500 m
Required time = 500 * 2/25
= 40 sec
Answer:A #### A
QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549
SOLUTION:A+B+C = 2600
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 2600 = Rs.1200
Answer: A #### A
QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13?
options: A)6 B)7 C)8 D)9 E)3
SOLUTION:We have to include 3 also.As 13*0 + 3 =3
If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3.
Answer is E #### E
QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
options: A)2 B)8 C)9 D)11 E)15
SOLUTION:220 + 43 = 263/17 = 8 (Remainder)
B #### B
QUESTION:A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid?
options: A)$2.25 B)$3.25 C)$2.00 D)$3.50 E)$3.00
SOLUTION:Explanation:
3 1 2
$3.00 $2.50 $4.00
$9.00 + $2.50 + $8.00 = $19.50/6 = $3.25
B #### B
QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd?
options: A)45 B)50 C)30 D)60 E)55
SOLUTION:90 numbers between - 10 and 100
Out of which half would be even, half odd.
Number of odd unit digit number = 45.
correct option is A #### A
QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
options: A)5.79 B)5.73 C)5.76 D)5.75 E)5.71
SOLUTION:M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
\Answer:C #### C
QUESTION:Which of the following must be true?
1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1
2) Every prime number greater than 5 can be written as 4n+1 or 4n-1
3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number.
options: A)1,2,3 B)2,3 C)1,2 D)only 1 E)only 2
SOLUTION:Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible.
3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1.
C #### C
QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 11, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
options: A)1/2 B)17/36 C)26/165 D)11/36 E)25/216
SOLUTION:Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 11 = (5,6)(6,5)= 2 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 11 in any attempt =2/36=1/18
Probability of NOT getting sum as 11 in any attempt = 1-(1/18)= 17/18
Probability of losing game =(17/18)*(17/18)*(17/18)=139/165
I.e. Probability of wining game = 1-(139/165) =26/165
Answer : Option C #### C
QUESTION:The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?
options: A)21/55 B)28/55 C)34/55 D)5/8 E)139/220
SOLUTION:Prob of selecting one blue and two green is (4*8*7/12*11*10)
one blue and two green can be arranged in 3!/2! ways
hence the prob becomes 3*4*8*7/12*11*10=28/55
Correct answer is B #### B
QUESTION:Find the odd man out. 18, 7, 12, 24, 48, 34, 46
options: A)16 B)46 C)24 D)11 E)7
SOLUTION:Explanation :
7 is the only odd number in the given series
Answer : Option E #### E
QUESTION:Two numbers when divided by a divisor leave remainders of 238 and 362 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
options: A)276 B)552 C)414 D)1104 E)2202
SOLUTION:Let x be the divisor.
N1 = xa + 238
N2 = xb + 362
N1 + N2 = x(a+b) + 600 = xc + 68
x(c-a-b) = 532 but we know that x>362, thus (c-a-b) must equal 1.
The answer is B. #### B
QUESTION:A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is?
options: A)1 B)22 1/7 C)2 D)22 1/2 E)3
SOLUTION:100 --- 10 DS = 10
? ---- 1
200 ---- 30 US = 8
? ----- 1 S = (10 - 8)/2
= 1 kmph.
Answer:A #### A
QUESTION:A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?
options: A)22 days B)4 days C)13 days D)6 days E)9 days
SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Answer is D. #### D
QUESTION:A 16% stock yielding 10% is quoted at :
options: A)83.33 B)110 C)112 D)120 E)160
SOLUTION:Solution
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160.
∴ Market value of Rs. 100 stock =Rs. 160
Answer E #### E
QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing?
options: A)191 B)400 C)737 D)840 E)1,560
SOLUTION:Let weight of side of beef before processing = x
(60/100)*x = 240
=> x = (240 * 100)/60 = 400
Answer B #### B
QUESTION:A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
options: A)24/78 B)24/709 C)24/76 D)24/71 E)24/72
SOLUTION:Explanation:
Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles
2 marbles are drawn from 13 marbles at random. Therefore,
n(S) = 13C2 = 78 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 24/78
ANSWER:A #### A
QUESTION:On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
options: A)2.04% B)6.12% C)8% D)8.25% E)10%
SOLUTION:Per quarter, interest = 2%
So for a year, interest = 8%
Due to quarter cumulation, effective yield (YTM) would be slight higher than 8%
Answer = 8.25% =ANSWER:D #### D
QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove?
options: A)$240 B)$260 C)$280 D)$300 E)$320
SOLUTION:J+K=700 so K=700-J
2J=K+80
2J=(700-J)+80
3J=780
J=260
The answer is B. #### B
QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?
options: A)10 B)20 C)30 D)40 E)50
SOLUTION:Asha=25 Nisha =n Usha =3n
Asha=2a Nisha =a Usha =34
The difference of all ages must be same
25-2a=n-a=3n-34
We will get two equation
2n+a=34
n+a=25
From the equation we will get n=9 and a=16
The ages are Asha=2a=32 Nisha =16 and Usha =34
Sum of the ages =100
(32+x)+(16+x)+(34+x)=100
82+3x=100
3x=18
x=6
Age of Usha =34+6=40
ANSWER:D #### D
QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
options: A)5 B)8 C)9 D)10 E)11
SOLUTION:Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5
Option A #### A
QUESTION:A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)120 m B)225 m C)300 m D)360 m E)280 m
SOLUTION:Speed = 54 x 5/18 m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/35 = 15
x + 300 = 525
x = 225 m.Answer: Option B #### B
QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg?
options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these
SOLUTION:Solution
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg
Answer D #### D
QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
options: A)11 days B)16 days C)13 days D)15 days E)19 days
SOLUTION:B
16 days
P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days. #### B
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
options: A)7 B)9 C)8 D)4 E)5
SOLUTION:25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 8
Answer:C #### C
QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr.
SOLUTION:Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=24 or x=12.
Rate upstream=12 km/hr,rate downstream=36 km/hr.
Hence,rate of stream=1/2(36-12)km/hr=12 km/hr.
Answer is B. #### B
QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8
SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in 5(5/11) min.
ANSWER:D #### D
QUESTION:In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ?
options: A)100 B)72 C)110 D)135 E)145
SOLUTION:Explanation :
Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x.
.'. 60% of x = 36 +5/6 *36
=>60/100 * x = 66
=>x = 110
Answer : C #### C
QUESTION:There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
options: A)Rs. 30 B)Rs. 34 C)Rs. 42 D)Rs. 48 E)Rs. 50
SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C #### C
QUESTION:Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have.
options: A)16.5 B)17.5 C)18.5 D)19.5 E)20.5
SOLUTION:Let Siri has x Rs, then Christine has 20+x Rs
Given x + (20+x)= 21
=> 2x= 1 or x= 0.5
So Christine and Siri has 20.5 and 0.5 Rs respectively.
ANSWER:E #### E
QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet?
options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge
SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location.
In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle.
Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate.
The correct answer is (E). #### E
QUESTION:Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
options: A)broke even, B)lost 4 cents C)gained 4 cents D)lost 10 cents E)gained 10 cents
SOLUTION:Solution:
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer: A #### A
QUESTION:What is the value of √36% ?
options: A)10% B)20% C)30% D)60% E)40%
SOLUTION:Explanation: br>√16%
=√36/√100
=6/10
=60/100=60%
correct answer is D)60% #### D
QUESTION:The missing term in the sequence 2, 3, 5, 7, 11, ... 17, 19 is
options: A)11 B)13 C)15 D)17 E)18
SOLUTION:Sequence is contain prime numbers.
Final sequence : 2,3,5,7,11,13,17,19
ANSWER:B #### B
QUESTION:The sum of the 1st and 3rd of 3consecutive odd integers is 131 less than three times the second integer. Find the three integers?
options: A)121 B)133 C)145 D)150 E)165
SOLUTION:Let x, x + 2 and x + 4 be three integers. The sum of the first x and third x + 4 is given by
x + (x + 4)
131 less than three times the second 3(x + 2) is given by
3(x + 2) - 131
"The sum of the first and third is 131 less than three times the second" gives
x + (x + 4) = 3(x + 2) - 131
Solve for x and find all three numbers
x = 129 , x + 2 = 131 , x + 4 = 133
As an exercise, check that the sum of the first and third is 131 less than three times
B #### B
QUESTION:Find the least number must be subtracted from 11070 so that remaining number is divisible by 22.
options: A)2 B)3 C)4 D)7 E)8
SOLUTION:On dividing 11070 by 22 we get the remainder 4, so 4 should be subtracted. Answer is A. #### A
QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ?
options: A)10 B)20 C)21 D)22 E)23
SOLUTION:Time taken by A to finish the work = XY/(Y-X)
= 10 x 20 / (20-10)
= 200/10
= 20 days
ANSWER : OPTION B #### B
QUESTION:A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
options: A)9:32 B)9:30 C)32:9 D)19:32 E)18:30
SOLUTION:Water:soap = 3:4
Soap:Salt=15:20
=> For 15 soap, salt = 20
=> For 4 Soap, salt = (20/15)*4 = 80/15=16/3
So, water:soap:salt = 3:4:16/3= 9:12:16
After open container, water:soap:salt =4.5:12:16
So, water:salt = 4.5:16 = 9:32
ANSWER:A #### A
QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
options: A)1.9 B)1.5 C)1.2 D)1.6 E)1.1
SOLUTION:72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer:B #### B
QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 2x+ 2y > 2z
III. yz > xz
IV. xy > y + z
options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only
SOLUTION:we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 2x+ 2y > 2z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B #### B
QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n =
options: A)3 B)2 C)0 D)-2 E)-3
SOLUTION:imo -2
(-17)^-2=
1/(1/49)=49
oops i meant 2
B #### B
QUESTION:If each data point in a certain set Q is increased by a factor of 20, what happens with the set's standard deviation?
options: A)Doesn't Change B)Decreases by Factor 20 C)Can't be determined D)Increases by 20 E)Increases by Factor 20
SOLUTION:Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 20, the standard deviation will increase proportionately, giving us answer choice E #### E
QUESTION:John is filling out the office space for his employees. There are 8 people in his office, and he must assign 8 employees to the following positions: 2 next to his cabin, 2 near the gate, 2 in center, and 2 near coffee machine. Only 2 employees are secretary and can sit next to his cabin, and they cannot sit anywhere else. The other employees can sit anywhere they like. How many different groupings are possible?
options: A)100 B)90 C)80 D)70 E)60
SOLUTION:Secretary can sit in 2C2 ways = 1
Near the gate we can have 6C2 combinations (2 secretaries are already having a place)
In the center we can have 4 C2 employees as 4 already have a place
Near coffee machine we can have 2C2 employees as all other place are taken
Number of selection = 2C2 * 6C2 * 4C2 * 2C2 = 90
Ans: B #### B
QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days
SOLUTION:B = 1/4 – 1/20 =0.2 days
ANSWER:E #### E
<<<Examples ends
QUESTION:A can do a piece of work in 4 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
options: A)22 days B)12 days C)67 days D)17 days E)18 days
SOLUTION:C = 1/2 - 1/6 - 1/4 = 1/12
=> 12 days
Answer:B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
options: A)10 B)11.3 C)13 D)14 E)15
SOLUTION:Speed of the first train = 120/9 = 13.3 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 13.3 + 8 = 21.3 m/sec.
Required time = (120 + 120)/21.3 = 11.3 sec.
Answer: Option B #### B
QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head?
options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8
SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {HHT,HHH,THH,HTH,TTT}
5/8
E #### E
QUESTION:. A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
options: A)338 B)2767 C)1023 D)1877 E)1722
SOLUTION:Explanation:
Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer:C #### C
QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000
SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000.
Answer: Option C #### C
QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
options: A)20% B)26% C)42% D)27% E)22%
SOLUTION:SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A #### A
QUESTION:A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5 hours, then the distance covered at 40 kmph is
options: A)130 km B)120km C)100km D)140km E)none of these
SOLUTION:Let the partial distance covered at 40 kmph be X
Let the another partial distance covered at 60 kmph be (250 - x)
Thus, x/40 - (250 - x)/60 = 5
or, x/40 + (250 - x)/60 = 5
or, (3x + 500 - 2x)//120 = 5
or 500 + x = 600
x=100
ANSWER:C #### C
QUESTION:If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage?
options: A)50% B)100% C)45% D)55% E)65%
SOLUTION:Let the C.P of each book be Re 1. Then,
S.P of 5 books= C.P of 10 books= Rs. 10
Now, C.P of 5 books= Rs.5, S.p of 5 books= Rs 10
Gain = Rs ( 10 -5 ) = Rs 5.
Gain% = ( 5/5× 100 ) % = 100%
Answer : B #### B
QUESTION:If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000?
options: A)$3500 B)$5000 C)$3150 D)$7200 E)$10000
SOLUTION:Saving = (45-30)% of 48000 = 7200.
Answer:D #### D
QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
options: A)Rs:567 B)Rs:518 C)Rs:519 D)Rs:500 E)Rs:520
SOLUTION:P - 340 = (P*4*8)/100
P = 500
Answer:D #### D
QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time?
options: A)70 min B)94 min C)110 min D)112 min E)120 min
SOLUTION:First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
And now we have 4 robots
So Total = (1) + (2) = 70 minutes
Answer - A #### A
QUESTION:If A:B is 3:4 and B:C is 4:5 then A:C is equal to
options: A)1:3 B)3:5 C)3:4 D)3:7 E)1:5
SOLUTION:The two ratios given are having the same number 4 for B in both the ratios.
Hence- A:B = 3:4 B:C = 4:5
=> A:C = 3:5
Answer B #### B
QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3?
options: A)1 B)2 C)3 D)5 E)0
SOLUTION:As per question => N=3P+2 for some integer p
hence 2N => 6Q + 4 => remainder => 1 for some integer Q
hence A #### A
QUESTION:In how many ways can 7 boys be seated in a circular order?
options: A)110 B)230 C)720 D)420 E)680
SOLUTION:Number of arrangements possible
=(7−1)!=6!=6x5x4x3x2x1=720
Answer: C #### C
QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
options: A)18% B)12% C)22% D)24% E)21
SOLUTION:1500 ---- 270
100 ---- ? => 18%
Answer:A #### A
QUESTION:By selling an article at Rs.600, a profit of 30% is made. Find its cost price?
options: A)400 B)267 C)287 D)480 E)811
SOLUTION:SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+50)]
= 600 * [100/150] = Rs.400
Answer: A #### A
QUESTION:A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
options: A)288 m B)256 m C)400 m D)278 m E)287 m
SOLUTION:Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60
= 65/3
x = 400 m.
Answer:C #### C
QUESTION:Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is?
options: A)6 km B)8 km C)9 km D)11 km E)12 km
SOLUTION:Let total distance =D=D
Distance travelled at 4 kmph speed =(23)D=(23)D
Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D
Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr
We know,
Time=DistanceSpeedTime=DistanceSpeed
Total time
2115=2/34D+1/35D2115=2/34D+1/35D
2115=2D12+D152115=2D12+D15
84=14D84=14D
D=6 km
Option A is correct #### A
QUESTION:If each side of the square is increased by 25% find the percentage change in its area?
options: A)89.45% B)56.25% C)89.98% D)54.48% E)45.0%
SOLUTION:let each side of the square be a. then area =a^2
new side=125a/100=5a/4
new area=(5a/4)^2=25a^2/16
increase in area=(25a^2/16-a^2)=9a^2/16
increased %=(9a^2/16*1/a^2*100)=56.25%
Answer is(B) #### B
QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides?
options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4
SOLUTION:XY=3
YZ=1+XY = 4
XZ=1+YZ=5
B is the correct option. #### B
QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE.
If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE?
options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards
SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question.
1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle.
2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus.
3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle.
4) From (1), we know that x = 202+y2−−−−−−−√202+y2.
5) From (3), we know x = 25 - y.
6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y
7) Solving for y, we get 4.5.
8) 25 - 4.5 = 20.5 = x
9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82.
The answer is B, 82 #### B
QUESTION:On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:
options: A)48759 B)51236 C)47619 D)6974 E)1235
SOLUTION:Explanation:
By hit and trial, we find that
47619 x 7 = 333333.
ANSWER:C #### C
QUESTION:A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum?
options: A)337 B)268 C)198 D)697 E)168
SOLUTION:1200 = P [1 + (12*6)/100]
P = 697'
Answer:D #### D
QUESTION:The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 50, and what number?
options: A)40 B)45 C)55 D)45 E)50
SOLUTION:a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -60 = 45
D #### D
QUESTION:If 1/2 of a pencil is blue, 1/8 of the remaining is red and the remaining 3/8 is white, what is the total length of the pencil?
options: A)5 B)3 C)1 D)4 E)2
SOLUTION:Blue is 1/2 but can also be written as 4/8
Red is 1/8
White is 3/8
4/8+1/8+3/8= 8/8=1
Answer is C) 1 #### C
QUESTION:A man swims downstream 40 km and upstream 56 km taking 8 hours each time, what is the speed of the man in still water?
options: A)6 B)24 C)8 D)12 E)44
SOLUTION:40 --- 8 DS = 5
? ---- 1
56 ---- 8 US = 7
? ---- 1 M = ?
M = (5 + 7)/2 = 6
Answer: A #### A
QUESTION:A train cross a 450 m bridge in 42 s and another bridge 650 m length in 50 s what is approximate speed of train in km/h?
options: A)90 Km /hr. B)25 Km /hr. C)30 Km /hr. D)20 Km /hr. E)None of these
SOLUTION:Explanation:
Let the length of the train be L.
Then,
=> (450 + L)/42 = (650+L)/50.
=> L= 600 m.
Now, speed = (450+600)/42 or (650+600)/50 = 25 m/s i.e. 25*(18/5) = 90 Km /hr.
ANSWER IS A #### A
QUESTION:The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km?
options: A)300 B)400 C)250 D)350 E)450
SOLUTION:50 kmph consumption is 1 lt/hr
so 400 km will take 8 hrs and the consumption is 8 lt for entire distance.
1 lt costs $30
so 8 lt costs $240
extra expenses for 1 hr - $20
8 hrs - $160
total expense - $240 + $160= $400
Answer : B #### B
QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2
SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2
= 62 m2.
answer :D #### D
QUESTION:If each side of a square is increased by 20%, find the percentage change in its area?
options: A)40% B)42% C)46% D)44% E)38%
SOLUTION:let each side of the square be a , then area = a x a
New side = 120a / 100 = 6a / 5
New area =(6a x 6a) / (5 x 5) = (36a²/25)
increased area== (36a²/25) - a²
Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44%
answer :D #### D
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)246 m B)240 m C)257 m D)577 m E)567 m
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36
= 15 ==> x + 300 = 540
==> x = 240 m.
Answer: B #### B
QUESTION:When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ?
options: A)11 B)44 C)24 D)25 E)22
SOLUTION:the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44
0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44.
Only option A-11 satisfies this
for remainder 11,
A=236 and B=25
Ans - D #### D
QUESTION:According to a survey, at least 60% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
options: A)15% B)20% C)25% D)0% E)35%
SOLUTION:It seems that something is wrong with your answer options.
1) minimum applesbananas:
[XXXXXXXXXXXXXX------] - apples
[-----XXXXXXXXXXXXXXX] - bananas
mimimum ab = 60 - (100-75) = 35%
2) minimum (applesbananas)cherries:
[XXXXXXXXX-----------] - applesbananas
[----XXXXXXXXXXXXXXXX] - cherries
mimimum ab = 35 - (100-80) =15%
A #### A
QUESTION:Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
options: A)16.80 × 4.50 + 4.4 B)1600 ÷ 40 + 16 × 2 C)5.5 × 8.4 + 34.6 D)1620 ÷ 20 – 1 E)1856.95 – 1680.65 – 96.3
SOLUTION:Others equal 80 whereas (c) equals 80.8.
Answer C #### C
QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B?
options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above
SOLUTION:et ratio of A and B be 6x & 7x
so net loss = 6x+7x= 7800
x=600
A=6x=6(600)=3600
B= 7x=7(600)=4200
so, B= 4200
ANSWER:A #### A
QUESTION:Of the 50 researchers in a workgroup, 30 percent will be assigned to Team A and the remaining 80 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
options: A) 15 B) 17 C) 20 D) 25 E) 30
SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
30 will be in team A
70 will be in team B
The larger diff is
70 want team A so diff is 70-30=40. At least 40 people will NOT get their wish, so for 50 researchers the same number is 20.
Answer choice C #### C
QUESTION:The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another member aged 39 years . The average age of
present committee is;
options: A)39 years B)38 years C)36 years D)35 years E)37 years
SOLUTION:Total age of the committee = 40*8 = 320,
Total age when a member is retired
and a new one was joined = 320-55 +39, =304
Average age of present committee = 304/8 = 38.
ANSWER:B #### B
QUESTION:Evaluate: |7 - 8(3 - 12)| - |5 - 11| = ?
options: A)40 B)50 C)73 D)70 E)80
SOLUTION:According to order of operations, inner brackets first. Hence
|7 - 8(3 - 12)| - |5 - 11| = |7 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |7 + 72| - |5 - 11|
= |79| - |-6|
= 79 - 6 = 73
correct answer C)73 #### C
QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)?
options: A)0 B)20 C)75 D)5 E)10
SOLUTION:Explanation :
Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0
Answer : A #### A
QUESTION:The probability that A speaks truth is 15/23 and that of B speaking truth is 17/29. What is the probability that they agree in stating the same fact?
options: A)182/395 B)129/289 C)197/353 D)479/667 E)None of these
SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 15/23 * 17/29 + 14/23 * 16/29
= 255/667 + 224/667 = 479/667
ANSWER:D #### D
QUESTION:16.02 × 0.1 = ?
options: A)0.1602 B)0.001602 C)1.6021 D)0.01602 E)None of these
SOLUTION:16.02 × 0.1 = 1.602
The answer is C. #### C
QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y
SOLUTION:The answer is B.
She runs x yards in 10x/y seconds =10x/60y minutes. #### B
QUESTION:The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income, what is the ratio of the savings of P, Q and R ?
options: A)15 : 8 : 2 B)19 : 7 : 9 C)7 : 15 : 10 D)12 : 9 : 17 E)None of these
SOLUTION:Explanation:
Let the incomes of P, Q, R be 6x, 8x, 11x and expenditure be 5y, 8y and 12y respectively.
Therefore, savings are : (6x – 5y), (8x – 8y) and (11x – 12y)
Now, 6x – 5y = 1/4(6x)
24x – 20y = 6x
18x = 20y
x/y = 20/18 = 10 / 9
Savings of P / Savings of Q = 6x – 5y / 8x – 8y
= [6(x/y) – 5] / [8(x/y) – 8]
= [(6 * 10/9) – 5] / [(8 * 10/9) – 8]
= 15/8
Savings of Q / Savings of R = 8x – 8y / 11x – 12y
= [8(x/y) – 8] / [11(x/y) – 12]
= (8 * 10/9) – 8 / (11* 10/9) – 12
= 8/2
Ratio of savings of P : Q : R = 15 : 8 : 2
ANSWER: A #### A
QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
options: A)3.25 B)3.6 C)4.2 D)4.4 E)6
SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours
Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours
in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours
Answer: option E #### E
QUESTION:The difference between a two-digit number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
options: A)4 B)9 C)3 D)Cannot be determined E)None of theses
SOLUTION:Let the two-digit number be 10x + y.
Then, (10x + y) – (10y + x) = 36
or x – y = 4
Answer A #### A
QUESTION:Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 35 as remainder
options: A)1235 B)1456 C)1567 D)1678 E)1631
SOLUTION:Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 35
5x = 1330
x = 266
Large number = 266+1365 = 1631
E #### E
QUESTION:The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is
options: A)3 B)5 C)6 D)8 E)9
SOLUTION:Sol.
By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6.
Answer C #### C
QUESTION:Ifaequals the sum of the even integers from 2 to 60, inclusive, andbequals the sum of the odd integers from 1 to 59, inclusive, what is the value of a - b ?
options: A)1 B)10 C)30 D)20 E)21
SOLUTION:This is a solution from Beatthegmat:
even numbers:
(60-2)/2 + 1 = 30 even integers.
(60+2)/2 = 31 is the average of the even set.
sum = avg*(#of elements) = 31*30 = 930 = a
odd numbers:
(59-1)/2 + 1 = 30 odd integers.
(59+1)/2 = 30 is the average of the odd set.
sum = avg*(#of elements) = 30*30 = 900 = b
a-b = 930 - 900 = 30. Answer : C #### C
QUESTION:Find the invalid no.from the following series 9, 16, 21, 28, 33, 37
options: A)13 B)18 C)40 D)37 E)25
SOLUTION:The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 37 is wrong.
Answer : D #### D
QUESTION:A shopkeeper purchased 85 kg of potatoes for Rs. 595 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent?
options: A)18 1/9 % B)18 9/3 % C)18 1/3 % D)14 2/7 % E)18 7/3 %
SOLUTION:C.P. of 1 kg = 595/85 = Rs. 7
S.P. of 1 kg = Rs. 8
Gain % = 1/7 * 100 = 100/7 = 14 2/7 %
Answer: D #### D
QUESTION:John bought a total of 20 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 20 mangoes and oranges that John originally purchased was 69 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?
options: A)4 B)5 C)6 D)7 E)8
SOLUTION:Let number of mangoes be x, number of oranges be 12-x
0.80x +(20-x)0.60/20 = 0.69
solving for x, we get x = 9 --> Mangoes 9, Oranges 11
Now, number of oranges to be returned be y
0.80*9 + (11-y)*0.60/20-y = 0.72
solving for y, y = 5
Ans: B #### B
QUESTION:A cube of edge 7 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:
options: A)1:25 B)1:49 C)1:52 D)1:522 E)None
SOLUTION:Sol.
Required ratio = 6 * 1 * 1 / 6 * 7 * 7 = 1/49 = 1:49.
Answer B #### B
QUESTION:A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
options: A)4:7 B)4:0 C)4:3 D)4:1 E)4:2
SOLUTION:12:9
= 4:3
Answer: C #### C
QUESTION:A ship sails out to a mark at the rate of 19 kmph. and sails back at the rate of 13 kmph. The average rate of sailing is ?
options: A)15 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None
SOLUTION:Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 19 x 13 ) / (19 +13 ) km/hr.
= 15 km/hr.
Correct Option: A #### A
QUESTION:The area of a triangle is with base 4m and height 5m?
options: A)20 m2 B)10 m2 C)82 m2 D)54 m2 E)28 m2
SOLUTION:1/2 * 4 * 5
= 10 m2
Answer:B #### B
QUESTION:Given that 268x74= 19632, find the value of 2.68x.74.
options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None
SOLUTION:Solution
Sum of decimals places =(2+2)
= 4.
Therefore, = 2.68×.74
= 1.9632
Answer A #### A
QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
options: A)33 1/7% B)33 2/3% C)33 1/3% D)37 1/3% E)23 1/3%
SOLUTION:675 ---- 225
100 ---- ? =>
=33 1/3%
Answer:C #### C
QUESTION:For which of the following values of s is (40+s)/s an integer?
options: A)3 B)4 C)9 D)11 E)40
SOLUTION:This problem has to be solved by checking the options
(40 + s)/s
For this entity to be an integer, 50 + s should be divisible by s
Option A: 43/3 - Not an Integer
Option B:44/4 - Not an Integer
Option C: 49/9 - Not an integer
Option D: 51/11 - Not an integer
Option E - 80/40- Integer
Correct Option: E #### E
QUESTION:By selling a watch for Rs.560/-, a man loses 20% what is that watch cost price
options: A)s. 700/- B)s. 800/- C)s. 880/- D)s. 900/- E)s. 990/-
SOLUTION:80 % ------> 560 (80 * 7 = 560)
100 % ------>700 (100 * 7 = 700)
Cost price = Rs. 700/-
A #### A
QUESTION:Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
options: A)17/65 B)17/29 C)17/21 D)P(EᴜP) =17/20 E)17/212
SOLUTION:n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D #### D
QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 35%?
options: A)600 B)887 C)256 D)654 E)675
SOLUTION:Cost price = Rs.500
profit = 35% of 500 = Rs.175
Selling price = Cost price + Profit
= 500 + 175 = 675
Answer: E #### E
QUESTION:The output of a factory was increased by 15% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?
options: A)20% B)27% C)30% D)32% E)79%
SOLUTION:The original output increases by 15% and then 20%.
Total % change = a + b + ab/100
Total % change = 15 + 20 + 15*20/100 = 38%
Now, you want to change it to 0, so,
0 = 38 + x + 38x/100
x = -38(100)/138 = 27% approximately
Answer is B #### B
QUESTION:10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
options: A)90 B)98 C)35 D)99 E)80
SOLUTION:Though 2*(10C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches.
Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches.
This continues like this and the total matches are 18+16+14...+2
18+16+...+2 = 2(9+8+...+1) = 2((9*10)/2) = 9*10 = 90.
ANSWER:A #### A
QUESTION:There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
options: A)A)3/7 B)B)5/8 C)C)6 D)D)6/7 E)E)5/12
SOLUTION:Let the two numbers be x and y.
60/100 * x + y = 5/4y
=> 3/5 x = 1/4 y => x/y = 5/12
E) #### E
QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph
SOLUTION:Speed downstream = 55 + 20
= 75 kmph
Speed upstream = 55 - 20
= 35 kmph
Answer: C #### C
<<<Examples ends
QUESTION:Find 30 % of 240
options: A)72 B)94 C)86 D)74 E)110
SOLUTION:We know that R % of m is equal to R/100 × m.
So, we have 30 % of 240
30/100 × 240
= 72
Answer:A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees?
options: A)A)182 B)B)208 C)C)220 D)D)224 E)E)302
SOLUTION:If x is the original number of employees, then after 13% reduction in employees number is .87x
but we are given .87x = 181
x = 208
So the original number of employees is 208
Correct Answer - B #### B
QUESTION:A sum is divided between A and B in the ratio of 1 : 2. A purchased a car from his part, which depreciates 14 2/7% per annum and B deposited his amount in a bank, which pays him 20% interest per annum compounded annually. By what percentage will the total sum of money increase after two years due to this investment pattern (approximately).
options: A)22.48% B)20.48% C)24.48% D)25.48% E)26.48%
SOLUTION:Let the total money=300
A's part=100
B's part=200
After 2 years A's part=73.46 (As it depreciates by 14.29% per annum)
After 2 years B's part=288 (using the compound interest formula, A=P(1+r/n)^nt), where
P=200,r=0.2,n=1,t=2)
So, After 2 years total amount=361.46
Therefore % increase in money=(361.46-300)*100/300=20.48%
ANSWER:B #### B
QUESTION:The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 16000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
options: A)Rs. 7000 B)Rs. 8000 C)Rs. 8500 D)Rs. 9000 E)None
SOLUTION:Answer
Average salary
= 8000 + 5000 + 16000 + 7000 + 9000 / 5
= Rs. 9000
Correct Option: D #### D
QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ?
options: A)1000 B)1100 C)1200 D)1300 E)1400
SOLUTION:let profit rate of b = x
acc to question profit rate of a becomes 5/3 x
and that of c= 1/3 x which is given as 10%
1/3 x= 10
therefore x=30
now b=30% , a=50%
now we will find out c's price-
11/10 * price = 2145
price = 1950
in similar way we will find out b's price as we know that profit is 30%
therefore 130/100 * price = 1950
so b 's price =1500
similarly for a ('profit is 50%)
150/100 * price = 1500
on solving it we get
a's price = 1000
ANSWER:A #### A
QUESTION:A certain basketball team that has played 2/3 of its games has a record of 18 wins and 2 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
options: A) 7 B) 6 C) 5 D) 4 E) 3
SOLUTION:18 wins, 2 losses - total 20 games played.
The team has played 2/3rd of all games so total number of games = 30
3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 2 games so it can lose another 5 at most.
Answer (C) #### C
QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9
SOLUTION:Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability B= 50/90 = 5/9
Correct answer E #### E
QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long?
options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec
SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec
time = (360+140)/25/2
= 500*2/25
=40sec
ANSWER:A #### A
QUESTION:If n is the product of three consecutive integers, and n is divisible by 6, which of the following is not necessarily a divisor of n ?
options: A)242 B)4 C)6.8 D)5 E)0.
SOLUTION:IF ONE NO. IS 6 THEN OTHER CONSEQUTIVE NO. ARE 4*5*6 =120 , 5*6*7=210 , 6*7*8 =336
NO NUMBER WILL NO BE DIVISOR OF N
E #### E
QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
options: A)3.25 B)3.6 C)4.2 D)4.4 E)6
SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours
Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours
in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours
Answer: option E #### E
QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is
options: A)35 B)37 C)38 D)41 E)42
SOLUTION:Explanation:
Let B's age = x years.
Then, As age = (x+ 8) years.
(x+8+10)=2(x—10)
hence x=38.
Present age of B = 38 years
Answer: Option C #### C
QUESTION:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
options: A) 6x B) 4x C) 5x/3 D) 3x/2 E) 3x/5
SOLUTION:Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<D<5x --> only option B fits.
Answer: B. #### B
QUESTION:The probability that a man will be alive for 10more yrs is 1/3 & the probability that his wife will alive for 10 more yrs is 5/8. The probability that none of them will be alive for 10 more yrs, is
options: A)1/8 B)1/4 C)2/3 D)3/4 E)2
SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/4
Ans.(B) #### B
QUESTION:In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ?
options: A)13/40 B)13/80 C)2/13 D)Data inadequate E)None
SOLUTION:Answer
Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp.
∴ 2/13 of total number of students took part in the camp.
Correct Option: C #### C
QUESTION:The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer?
options: A)1500 B)1600 C)1750 D)1900 E)2000
SOLUTION:Let the price of basic computer be C and the price of the printer be P: C+P=$2,500.
The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750.
Plug this value in the first equation: C+750=$2,500 --> C=$1,750
Answer: C. #### C
QUESTION:A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
options: A)30.98%loss B)20.98%loss C)20.97%loss D)20.68%loss E)20.98%loss
SOLUTION:81 ---- 17
100 ----- ? è
20.98%loss
Answer: B #### B
QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA
options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these
SOLUTION:Explanation:
Let A = 2x, B = 3x, C = 4x, then,
AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24
Answer: D #### D
QUESTION:A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)180 m B)200 m C)240 m D)320 m E)450 m
SOLUTION:Sol.
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x metres.
Then, x + 300 / 50 = 15 ⇔ x + 300 = 750 ⇔ x = 450 m.
Answer E #### E
QUESTION:Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
options: A)229 B)270 C)877 D)266 E)281
SOLUTION:Let xx be the total number of pages in the book, then she finished 23⋅x23⋅x pages.
Then she has x−23⋅x=13⋅xx−23⋅x=13⋅x pages left.
23⋅x−13⋅x=9023⋅x−13⋅x=90
13⋅x=9013⋅x=90
x=270x=270
So the book is 270 pages long.
Answer:B #### B
QUESTION:A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform?
options: A)45 B)47 C)49 D)51 E)53
SOLUTION:Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 14 * 10 = 140 m.
The time taken to pass the platform = (140 +370)/ 10 = 51 seconds
The answer is D. #### D
QUESTION:here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
options: A)2100 B)1800 C)1245 D)3210 E)4521
SOLUTION:5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Ans: B #### B
QUESTION:There are 5 different letters and 5 letter boxes of same size shape and colors. How many method are possible to post the letters?
options: A)50 B)51 C)52 D)53 E)54
SOLUTION:50000 ->1
41000 ->5
31100 ->10
32000 ->10
21110 ->10
22100 ->15
11111 ->1
1+5+10+10+10+30+1=52
ANSWER:C #### C
QUESTION:An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
options: A)267 B)180 C)287 D)177 E)911
SOLUTION:Angle traced by the hour hand in 6 hours
=(360/12)*6
Answer: B #### B
QUESTION:A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
options: A)8 B)12 C)15 D)21 E)27
SOLUTION:As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15
B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12
A+B=15+12=27
Answer: E. #### E
QUESTION:Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John’s weekly allowance?
options: A)$2.40 B)$3.00 C)$3.20 D)$3.60 E)$4.80
SOLUTION:Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$0.96
Therefore, X=$3.60. Answer D #### D
QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x?
options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined.
SOLUTION:A number x is multiplied with itself --> X^2
added to the product of 4 and x --> X^2+4X
If the result of these two operations is -4 --> X^2+4X=5
i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved.
(X-1)(X+5) = 0
Hence X=1. C=-5
IMO D #### D
QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ?
options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points
SOLUTION:A: B = 80 : 75, A : C = 80 : 65.
B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5
Therfore ,In a game of 60, B can give C 8 points.
Answer is E. #### E
QUESTION:Which of the following is equal to 3.14 x 10^6) ?
options: A)3.14 B)3140000 C)31400 D)314 E)314000
SOLUTION:= 3.14 x 10^6
= 3.14 x 1000000
= 3140000.
Answer is B. #### B
QUESTION:Find the greatest number that will divide 48, 210 and 136 leaving 4, 12 and 4 as remainders respectively
options: A)19 B)17 C)13 D)22 E)21
SOLUTION:Explanation:
Answer will be HCF of (48-4, 210-12, 136-4)
HCF of (44, 198, 132) = 22
Option D #### D
QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period?
options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3
SOLUTION:600 dollars in 2 years means 300 dollars in 1 year.
To get 2400 dollars' it will take 8 years.
To get 2400 in 3 years, we need 8/3 times money.
Answer is E. #### E
QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is
options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm
SOLUTION:Explanation:
Required Length = H.C.F of 700 cm, 385 cm and 1295 c
= 35 cm. Answer: C #### C
QUESTION:There are 6 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
options: A)1/9 B)2/9 C)3/5 D)4/9 E)2/3
SOLUTION:total 10 from take one.
10c1=10
red 6 from one
6c1=6
6/10= 3/5
ANSWER:C #### C
QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream?
options: A)15 B)17 C)19 D)18 E)16
SOLUTION:The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 57/3 = 19 kmph.
Answer:C #### C
QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5
SOLUTION:Rate of flow of water in second hour = 18 gallons per hour
Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour
Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons
Answer B #### B
QUESTION:Two pipe A and B fill a tank in 6 hours and 8 hours respectively.and C empty that tank in 12 hour.if all three pipe open together in empty tank then how much time it take to fill the tank?
options: A)19/3 B)23/2 C)24/5 D)18 E)16
SOLUTION:all three pipe resultant fill tank in 1 hour=[1/6+1/8-1/12]=5/24
total time taken to fill tank=24/5 hour
answer C #### C
QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600:
options: A)200 B)250 C)300 D)350 E)400
SOLUTION:X = Rs.5000/-
Y = Rs.15000/-
X share 1 part & Y share 3 parts
Total 4 parts -----> Rs.1600/-
----> 1 part -------> Rs.400/-
X share = 1 part -----> Rs.400/-
E #### E
QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.
options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter
SOLUTION:Explanation:
Speed = Distance/time = 300/18 = 50/3 m/sec
Let the length of the platform be x meters
then
Distance=Speed∗Timex+300=50/3 X 39
=>3(x+300)=1950=>x=350 meters
ANSWER IS D #### D
QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Tuesday, what was the expected day when both the brothers were to return home and when did Rohit Return?
options: A)Wednesday, Sunday B)Thursday, Monday C)Friday, Tuesday D)Monday, Friday E)none
SOLUTION:Rajat returned on Tuesday -i.e. 3 days earlier
so actual day to return home is Friday.
Rohit returned after days so Tuesday.
ANSWER:C #### C
QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit
SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1
[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1
[(5.4 + 2.4 + 1.8)/8] - [8/8]
+1.6/8
+20%
answer is D #### D
QUESTION:The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
options: A)58 B)70 C)63 D)65 E)72
SOLUTION:1/2bh=1/2(2a+1)(2a+6)
Now 4a-2=2a+6
2a=8 . a=4
Therefore,
A(0,0); B(0,14); C(9,14)
1/2*9*14=63
Answer: C #### C
QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight.
options: A)22 B)10 C)88 D)26 E)18
SOLUTION:M + D + I = 74 - - - (1)
(D + I) - M = 46 - - - (2)
I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3)
Adding (1) and (2) we get 2D + 2I = 120
Substituting the value of I in the above equation,
2D+2(2D5)=1202D+2(2D5)=120
⇒⇒ 14D = 600
⇒⇒ D = 300/7 = 42.8
Ans:B #### B
QUESTION:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue?
options: A)25/153 B)28/153 C)5/17 D)E=4/9 E)E=12/17
SOLUTION:P(at least one blue) = 1 - P(0 blue) = 1 - 10/18*9/17 = 12/17.
Answer: E. #### E
QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have?
options: A)10 B)16 C)8 D)11 E)14
SOLUTION:one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1080
180n - 360 = 1080
180n = 1440
n = 1440/180 = 8
ANSWER:C #### C
QUESTION:Due to 10% decrease in the price of sugar and John can buy 4kg more sugar in Rs100 , then find the CP of sugar?
options: A)s. 1(2/9) B)s. 2(7/9) C)s. 2(1/9) D)s. 3(2/7) E)s. 4(2/9)
SOLUTION:Here r = 10 % ,x = 100 and A = 4 kg
Actual price of sugar = 10*100/((100-10 )*4) = Rs. 2(7/9)
B #### B
QUESTION:The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ?
options: A)148 B)134 C)156 D)144 E)None
SOLUTION:Solution:
Ratio of Ducks and Frogs in Pond,
= 37 : 39.
Average of Ducks and Frogs in Pond,
= 132.
So, total number of Ducks and Frogs in the Pond,
= 2* 132 = 262.
Therefore,
Number of Frogs, = (262*39)/76 = 134.
Answer: Option B #### B
QUESTION:In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
options: A)32 B)16 C)64 D)80 E)16 or 48
SOLUTION:Let total number be x
No in the interior = (x/8)^2
No outside = 16
So : x - (x/8)^2=16
x^2-64x+16*64=0
(x-32)^2=0
x=32
A #### A
QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble?
options: A)134 B)167 C)125 D)113 E)111
SOLUTION:C
lb : reverse the calculations:
So 48.75 ÷ 0.75 = 65,
65 ÷ 0.8 = 81.25 and
81.25 ÷ 0.65 = 125. #### C
QUESTION:Calculate the rate on a principal of Rs.1500 which yields a simple interest of Rs. 220.50 in 3 Years?
options: A)6.9% B)2.9% C)9.9% D)5.9% E)4.9%
SOLUTION:220.50 = (1500*3*R)/100
R = 4.9%
Answer: E #### E
QUESTION:The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 1000 years is:
options: A)587 x 10^13 miles B)999× 1238 miles C)346 × 1012 miles D)247 × 1012 miles E)587 × 1012 miles
SOLUTION:The distance of the light travels in one years is:
5,870,000,000,000 = 587 * 10 ^10
The distance of the light travels in 1000 years is:
= 587 * 10^10 x 10 ^3 = 587 x 10^13 miles
Answer :A #### A
QUESTION:Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window?
options: A)a 100 B)b 112 C)c 90 D)d 120 E)e 30
SOLUTION:D
David's position is fixed. Now we need to arrange all others around David.
There are 5x4x3x2x1= 120 ways to arrange five people. #### D
QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was
options: A)960 B)980 C)900 D)970 E)1000
SOLUTION:Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 1000
Answer: E) Rs 1000 #### E
QUESTION:If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
options: A)9 B)8 C)7 D)6 E)5
SOLUTION:0.[u]225[/u = 0.225225225.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E #### E
QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
options: A)150 B)152 C)154 D)158 E)144
SOLUTION:D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158 #### D
QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled
options: A)50% B)40% C)33.5% D)37.5% E)None of these
SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8
∴ required% = 3A⁄ (8 × A) × 100 = 37.50%
Answer D #### D
QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
options: A)109 B)119 C)129 D)139 E)149
SOLUTION:45 + 23 + 15 = 83%
100 – 83 = 17%
700 * 17/100 = 119
The answer is B. #### B
QUESTION:What is the sum of all the numbers which divides 100 ?
options: A)408 B)102 C)816 D)916 E)416
SOLUTION:You first have to know all the divisor of 100. They are 2,4,5,10,20,25,50 and 100. If you add all these numbers together, you get 408.
Final Answer:
A #### A
QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
options: A)80% B)20% C)40% D)50% E)None of these
SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84
Number of students failed = 140 - 84 = 56.
Required percentage = 28/56 * 100 = 50%.
ANSWER:D #### D
QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
options: A)180 B)787 C)178 D)179 E)172
SOLUTION:Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers
= (S + T)/2 = 180.
Answer:A #### A
QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
options: A)18/35 B)18/38 C)18/34 D)18/31 E)18/30
SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35.
Answer:A #### A
QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
options: A)Rs.10528 B)Rs.10521 C)Rs.10511 D)Rs.10411 E)Rs.10500
SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7
= Rs.10500
Answer: E #### E
QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS:
options: A)15 B)16 C)18 D)25 E)NONE OF THESE
SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4
SUPPOSE TANYA TAKES X DAYS TO DO THE WORK;
5:4::20:X, X=(4x20/5), X=16 DAYS.
CORRECT OPTION: B #### B
QUESTION:Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
options: A)228gallons B)267gallons C)120gallons D)767gallons E)167gallons
SOLUTION:Explanation:
Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying]
Volume of {\color{Black} \frac{1}{40}} part = 3 gallons
Volume of whole = (3 x 40) gallons = 120 gallons.
Answer: C #### C
QUESTION:The greatest common factor of positive integers m and n is 9. What is the greatest common factor of (2m^2, 2n^2)?
options: A)9 B)81 C)162 D)324 E)405
SOLUTION:m = 9j and n = 9k, where the greatest common factor of j and k is 1.
2m^2 = 2*9*9*j^2 and 2n^2 = 2*9*9*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*9*9 = 162
The answer is C. #### C
QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
options: A)600 B)500 C)575 D)655 E)675
SOLUTION:Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
So answer is E. #### E
QUESTION:Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different.
options: A)z=3x B)x=3z C)y=2x D)x=2y E)y=3x
SOLUTION:Rovert Travelled for x,y and for z min.
Total Time : x + y + z
Which is equal to : 3y
Equating both sides we get
x+y+z = 3y
=> x+z =2y ........ Eqn 1
Looking out at options
D Says x =2y
Using it in Eqn 1
2y + z = 2y
=> Z = 0 mins, Which I guess is not possible.
The Ans isD #### D
<<<Examples ends
QUESTION:A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 3 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
options: A)1/5 B)1/2 C)2/3 D)4/5 E)6/5
SOLUTION:Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B
FOR THE FIRST BUCKET ...
Red color - 2
Blue color - 2
FOR THE SECOND BUCKET
Red color - 3
Blue color -2
In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :
Scenario I - He picks Red color from List A and Blue color from List B
Scenario II - He picks Blue color from List A and Red color from List B
Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5
Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...
Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...
We get 1/5 + 3/10 = 2/3 (C) #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A committee of three students has to be formed. There are six candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
options: A)3 B)4 C)5 D)6 E)8
SOLUTION:Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE.
D #### D
QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed?
options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph
SOLUTION:829/7
= 118 kmph
Answer: C #### C
QUESTION:If x and y are different integers and x^2 = xy, which of the following must be true ?
I. y = 0
II. x = 0
III. x = y
options: A)I only B)II only C)III only D)I and III only E)II, and III
SOLUTION:Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer E #### E
QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was?
options: A)16 years B)14 years C)18 years D)19 years E)15 years
SOLUTION:Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5)
= 14 years.
Answer: B #### B
QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
options: A)10 m B)16 m C)245 m D)19 m E)235 m
SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30
= 25/2 => 2(140 + x) = 750 => x
= 235 m.
Answer: E #### E
QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 13.7
II. 12.3
III. 9.3
options: A)I only B)I and II only C)II only D)III only E)I and III only
SOLUTION:Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
12.3 and 13.7 lies in the range of 2SD from mean
Answer: Option D #### D
QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9?
options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21
SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15
E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2
probability = 2/15
Answer is A #### A
QUESTION:which of the following is a prime number ?
options: A)17 B)18 C)15 D)20 E)25
SOLUTION:Clearly, 17 is a prime number.
Option A #### A
QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
options: A)15 B)30 C)36 D)72 E)46
SOLUTION:Explanation:
Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have : (2x - 16) = (x + 8) or x = 24.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72.
Answer: D #### D
QUESTION:Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail?
options: A)3/4 B)1/4 C)3/8 D)1/2 E)1/8
SOLUTION:Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting 3 heads
Then E = {HHH,HTH,THH,HHT}
P(E) = n(E)/n(S) =4/8 = 1/2
Answer is D #### D
QUESTION:In how many ways can a group of 4 men and 2 women be made out of a total of 6 men and 4 women?
options: A)63 B)67 C)70 D)90 E)80
SOLUTION:We need to select 4 men from 6 men and 2 women from 4 women. Number of ways to do this
= 6C4 × 4C2
90
D) #### D
QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 66900. What is his profit percent?
options: A)22 B)77 C)18 D)21.6 E)88
SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 66900
Profit(%) = (66900 - 55000)/55000 * 100 = 21.6%
Answer: D #### D
QUESTION:A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
options: A)50 kmph B)58 kmph C)62 kmph D)65 kmph E)75 kmph
SOLUTION:Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 50) kmph = 62 kmph.
Answer : C. #### C
QUESTION:In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter?
options: A)15 B)25 C)30 D)45 E)60
SOLUTION:This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...
We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats.
Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as...
15X/7X
When we add the 16 cats and factor in the 'ending ratio', we have an equation....
15X/(7X+16) = 15/11
Here we have 1 variable and 1 equation, so we can solve for X....
(15X)(11) = (7X+16)(15)
(X)(11) = (7X+16)(1)
11X = 7X + 16
4X = 16
X = 4
With this X, we can figure out the initial number of dogs and cats...
Initial dogs = 15X = 15(4) = 60
Final Answer: D #### D
QUESTION:If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 5.
II. x is an integer multiple of 3
III. x is an integer multiple of 6
options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only
SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6.
Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.
Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even
Answer E #### E
QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
options: A)10987 B)11755 C)17576 D)19775 E)21899
SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C #### C
QUESTION:Consider two statements
Statement 1 => If R is an integer and R=2p+1 where p is not an integer.
Statement 2 => If S is an integer and S=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of R and S respectively
options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined
SOLUTION:answer will be E
R = integer
R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even R would odd
if n odd R would be even
ANSWER IS E #### E
QUESTION:16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work?
options: A)26.7 days B)77 days C)20 days D)88 days E)44 days
SOLUTION:16 * 25 = 15 * x => x
= 26.7 days
Answer: A #### A
QUESTION:4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 weavers in 10 days?
options: A)10 B)15 C)20 D)25 E)30
SOLUTION:1 weaver can weave 1 mat in 4 days.
10 weavers can weave 10 mats in 4 days.
10 weavers can weave 25 mats in 10 days.
The answer is D. #### D
QUESTION:When a 192 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ?
options: A)52 B)68 C)62 D)67 E)69
SOLUTION:Answer
No. of pieces = Total length / Length of each piece
= 192/3.2
= 60
Option: D #### D
QUESTION:How many numbers between 100 and 600 are divisible by 2, 3, and 7 together?
options: A)112 B)77 C)267 D)12 E)99
SOLUTION:Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 600
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 600:
600/42 = 14.28
Hence, 42*14 = 588 is the last number divisible by 42 within 600
Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12
ANSWER: D #### D
QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase?
options: A)$32 B)$50 C)$320 D)$400 E)$500
SOLUTION:Property tax as a percentage of its assessed value = 8%
Increase in assessed value of the property = 24000 - 20000 = 4,000 $
Increase in property tax = (8/100)* 4000 = 320 $
Answer C #### C
QUESTION:The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits M of the larger integer?
options: A)M=2 B)M=5 C)M=8 D)10 E)11
SOLUTION:Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A). #### A
QUESTION:n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
options: A)3 B)2 C)1 D)0 E)None of these
SOLUTION:Let n=4q+3.
2n=8q+6=4(2q+1)+2
Thus, when 2n is divided by 4, the remainder is 2.
Correct Option: B #### B
QUESTION:In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,-5) and (t,-7). What is the least possible value of the slope of line L?
options: A)6 B)-1 C)-2 D)-6 E)-10
SOLUTION:We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,-5). hence, x= p and Y=-5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (-7+5)/(4-2) = -1
IMO option B is correct answer. #### B
QUESTION:A retailer buys 80 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ?
options: A)110 B)115 C)112 D)118 E)120
SOLUTION:let the market price of each pen be $1
then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20
profit %=((43.20*100)/36) %=120%
Answer E)120 #### E
QUESTION:The average of 35 numbers is 25. If each number is multiplied by 5, find the new average?
options: A)125 B)772 C)821 D)912 E)121
SOLUTION:Sum of the 35 numbers = 35 * 25 = 875
If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.
Thus, the new average = 25 * 5 = 125.
Answer:A #### A
QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers?
options: A)1 B)5 C)7 D)8 E)9
SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6
y = mx + b => 12 2/3 = -22*5/6 + b => b = 31
y = -5x/6 + 31
Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point.
A #### A
QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides?
options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4
SOLUTION:XY=3
YZ=1+XY = 4
XZ=1+YZ=5
B is the correct option. #### B
QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3?
options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10
SOLUTION:arrangement = 5!/3!=20
Probability of getting all 3 balls=
3 from 5=5c3
1 from 3 red ball,1 green,1 yellow
(3c1*1c1*1c1)/5c3 =3/10
ANSWER:A #### A
QUESTION:If $0.80 is the commission for sales of $2,000, what percent of the sales amount is the commission?
options: A)4% B)0.4% C)0.04% D)0.004% E)0.0004%
SOLUTION:% of sales amount of commission
= (Commission/Total Value) *100
= (0.8/2000) * 100
= 0.04%
The answer is C. #### C
QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12
SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A #### A
QUESTION:9886 + x = 13200, then x is ?
options: A)3327 B)3237 C)3337 D)2337 E)None of these
SOLUTION:Answer
x = 13200 - 9886 = 3314
Option: E #### E
QUESTION:Evaluate 30!/28!
options: A)720 B)600 C)870 D)910 E)650
SOLUTION:we have 30!/28! = 30*29*28!/28! = 30*29 = 870
Answer is C #### C
QUESTION:If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is
options: A)40 B)49 C)80 D)88 E)90
SOLUTION:Sol.
Let the numbers be x and y.
Then, (x+y) = 22 and x2 + y2 = 386.
Now, 2xy = (x+y)2 - (x2 + y2)
= (22)2 - 386= 484 - 386= 98
xy = 49.
Answer B #### B
QUESTION:10, 20, 12, 24, 16, 32, ?
options: A)20 B)21 C)22 D)23 E)24
SOLUTION:E
24
This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E
QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549
SOLUTION:A+B+C = 2600
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 2600 = Rs.1200
Answer: A #### A
QUESTION:Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary?
options: A)RS.3500 B)Rs.1500 C)Rs.4500 D)Rs.2500 E)Nill
SOLUTION:Answer: Option D
Let's anil's salary be Rs. 100.
Money spent on Rent = 40% of 100 = Rs. 40.
Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18.
Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40
anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60
for 33.6 ---> 100 ; 840 ---> ?
Required salary = 840/33.6 * 100 = Rs. 2500 #### D
QUESTION:5216 × 51 = ?
options: A)266015 B)266014 C)266016 D)266116 E)266226
SOLUTION:Normal way of multiplication may take time. Here is one alternative.
5216×51=(5216×50)+5216=(5216×1002)+5216=5216002+5216=260800+5216=266016
Answer is C. #### C
QUESTION:The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes.
options: A)$0.94 B)$0.96 C)$0.99 D)$1.00 E)$1.20
SOLUTION:Assume the manager bought 100 tomatoes.
Cost Price = 80
Given: 10% are damaged --> Available tomatoes to sell = 90
90 * x - 80 = 0.12 * 80
90x - 80 = 9.6
90x = 89.6
x = 89.6/90 = 0.995
x is slightly under 0.9955 = 0.99
Answer: C #### C
QUESTION:Which of the following CANNOT be a value of 8/(x–8)?
options: A)-1 B)-1/2 C)0 D)2 E)8
SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation.
If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0.
The answer is C. #### C
QUESTION:Reena took a loan of 1500 with simple interest for as many years as the rate of interest. If she paid 735 as interest at the end of the loan period, what was the rate of interest?
options: A)3.6 B)7 C)18 D)Cannot be determined E)None
SOLUTION:Explanation: Let rate = R% and time = R years.
Then, (1500 x R x R)/100 = 735
15R² = 735
R² = 49
R = 7.
Answer: Option B #### B
QUESTION:If a man walks to his office at 5/4 of his usual rate, he reaches office 30 minutes early than usual. What is his usual time to reach office.
options: A)2 hrs B)2 1⁄2 hrs C)1 hr 50 min D)2 hrs 15 min E)None of these
SOLUTION:usual time × (4⁄5 - 1) = -30⁄60
⇒ usual time = 1⁄2 × 5 = 21⁄2 hrs
Answer B #### B
QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three?
options: A)14 B)16 C)18 D)24 E)34
SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
ANSWER:A #### A
QUESTION:Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and B is closed after 3 minutes, how much further time would it take for A to fill the bucket?
options: A)5min. 50sec. B)5min. 30 sec. C)6 min 36 sec. D)6mins. 32 sec. E)6 min. 15 sec.
SOLUTION:Explanation:
Part filled in 3 minutes =
3∗(1/12+1/15)=3∗9/60=9/20
Remaining part =1−9/20=11/20
=>1/12:11/20=1:X
=>X=6.6 mins.
=>X=6.6 mins.
So it will take further 6 mins 36 seconds to fill the bucket.
Option C #### C
QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages.
options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12
SOLUTION:Explanation:
Let the present ages of A and B be 'a' and 'b' respectively.
3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1)
a-b = 5 -------(2) Solving (1) and (2) we get b=8
Substituting b = 8 in second equation, we get a= 13. Answer : C
=> 2a = 32 => a = 16.
Answer: C #### C
QUESTION:In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 40 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
options: A) 1000 B) 625 C) 1,250 D) 2,500 E) 10,000
SOLUTION:total fish = x
percentage of second catch = (2/40)*100 = 5%
so, x * 5% = 50
x = 1000 ans.A #### A
QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
options: A)12% B)19% C)15% D)14% E)22%
SOLUTION:Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:A #### A
QUESTION:Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24
options: A)22 B)62 C)28 D)16 E)11
SOLUTION:Answer:B #### B
QUESTION:The present worth of Rs.676 due in 2 years at 4% per annum compound interest is
options: A)Rs.150.50 B)Rs.154.75 C)Rs.156.25 D)Rs.625 E)None
SOLUTION:Solution
Present Worth = Rs.[676/(1+4/100)²]
= Rs.(676x25/26x25/26)
= Rs.625
Answer D #### D
QUESTION:Average age of students of an adult school is 42 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
options: A)1200 B)120 C)360 D)200 E)None of these
SOLUTION:Explanation :
Let the original no. of students be x.
According to situation, 42x + 120*32 = (x + 120)36 ⇒ x = 80
So, Required no. of students after joining the new students
= x + 120 = 200.
Answer : D #### D
QUESTION:A sum of money at simple interest amounts to $ 980 in 3 years and to $1024 in 4 years. The sum is:
options: A)$153 B)$848 C)$398 D)$549 E)$675
SOLUTION:B
$848
S.I. for 1 year = $(1024 - 980) = $44.
S.I. for 3 years = $(44 x 3) = $132.
Principal = $(980 - 132) = $848. #### B
QUESTION:Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
options: A)60% B)50% C)25% D)20% E)10%
SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 55 - {both} + 40
{both} = 20%.
Answer: D. #### D
QUESTION:A boat can move upstream at 20 kmph and downstream at 34 kmph, then the speed of the current is?
options: A)7 B)6 C)8 D)4 E)2
SOLUTION:US = 20
DS = 34
M = (34 - 20)/2 = 7 Answer:A #### A
QUESTION:If 2x = 3y = 20, then 12xy = ?
options: A) 1,200 B) 800 C) 120 D) 40 E) 20
SOLUTION:2x = 20;x=10
3y = 20;y=20/3
Multiply: 12xy=12*10*20/3=800.
Answer: B. #### B
QUESTION:Let the number which when multiplied by 11 is increased by 300.
options: A)14 B)20 C)26 D)28 E)30
SOLUTION:Solution
Let the number be x .
Then, 11x - x = 300
‹=›10x = 300
x ‹=› 30.
Answer E #### E
QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents?
options: A)24 B)18 C)32 D)16 E)20
SOLUTION:0.10(x)+0.35(20-x)=2.5
0.10x+7-0.35x=2.5
so x=18
ans is B #### B
QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
options: A)40% B)45% C)57% D)58% E)60%
SOLUTION:tot no of votes = (1136+7636+11628) = 20400
req = > (11628/20400 * 100) = > 57%
ANSWER C #### C
QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides?
options: A)3 B)6 C)5 D)9 E)1
SOLUTION:S = (1 + 2 + 7)/2
= 5 Answer:C #### C
QUESTION:If (5^15)(9^8)=3(15^x), what is the value of x?
options: A) 7 B) 9 C) 11 D) 13 E) 15
SOLUTION:(5^15)(9^8)=3(15^x)
=> 5^15 * 3^16 = 3 * 3^x * 5^x
=> 5^15 * 3^16 = 3^(x+1) * 5^x
Value of x = 15
Answer E #### E
QUESTION:The speeds of 3 trains in the ratio 10:15:20. The ratio between time taken by them to travel the same distance is?
options: A)6:4:3 B)1:2:3 C)4:8:9 D)6:5:2 E)4:8:7
SOLUTION:Ratio of time taken is = 1/10 : 1/15 : 1/20 = 6:4:3
Answer is A #### A
QUESTION:8k8
+ k88
--------
1,6w6
If k and w represent non-zero digits within the integers above, what is w?
options: A)6 B)7 C)8 D)9 E)17
SOLUTION:8k8
k88
--------
16w6
Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and w=6.
Answer: A. #### A
QUESTION:The average successfull Search time for sequential search on n items is
options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1
SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison.
Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons.
Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons.
so we can write total search time will be: (1+2+3+........+n)
average search time will be (1+2+3+........+n)/n
NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2
ANSWER: C #### C
QUESTION:In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 210 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
options: A)40 ml B)70 ml C)20 ml D)20/3 ml E)10 ml
SOLUTION:There are 0.3*100=30 ml of element X in the initial solution.
We need X to be 1/3rd of 210 ml in the resulting solution, so 70 ml. Thus out of 110 ml of solution added, 40 must be X (in order it to become 70 ml) ans the remaining 70 must be Y.
Answer: B #### B
<<<Examples ends
QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
options: A)35 min B)30 min C)25 min D)20 min E)40 min
SOLUTION:Explanation:
Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20
ANSWER IS D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices.
options: A)220. B)205. C)250 D)105 E)225
SOLUTION:different ways..
1) EASIEST approach..
lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220...
Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15..
total = 220-15 = 205
ANSWER:B #### B
QUESTION:Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
options: A)40 to 100 B)80 to 140 C)160 to 260 D)220 to 260 E)220 to 300
SOLUTION:260-X+X+300-X+GT60 = 400
=>X = GT 620-400
=> X = GT 220
=> X >= 220 (Here GT means Greater than)
So Min value of X is 220 coming to options D/E
X's maximum value cannot exceed 260 as per the venn diagramsince 'W' circle cannot accomodate 'X' More than 260
ANSWER:D #### D
QUESTION:In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.64.50 per Kg?
options: A)3 : 1 B)3 : 2 C)4 : 3 D)5 : 3 E)None
SOLUTION:Required ratio = 750 : 250 = 3 : 1
Answer A #### A
QUESTION:A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 60% have red flags, what percentage of children have flags of both the colors?
options: A)5% B)10% C)15% D)20% E)It can not be determined
SOLUTION:Solution: let the total number of flags be 100(even number)
let the total number of 'blue' flags alone be 'a'
let the total number of 'red' flags alone be 'b'
let the total number of 'both' flags be 'c'
We have given,
total number of blue flags = 60% = 60 = a+c
total number of red flags=55%=55=b+c
total number of flags = a+b+c=100 (since all the flags have been utilized)
So, substituting for c in the third equation, we have,
60-c+c+60-c=100
c=20
Option D. #### D
QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
options: A)8 B)9 C)7 D)62 E)2
SOLUTION:2x * x = 128 => x= 8
Answer: A #### A
QUESTION:A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
options: A)675 B)680 C)685 D)690 E)695
SOLUTION:Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec.
Length of the train = 75 * 9 = 675 m.
Answer: Option A #### A
QUESTION:In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ?
options: A)3990 B)1540 C)1995 D)3672 E)None of these
SOLUTION:In order that two books on French are never together, we must place all books as under
X E X E X E X E X E .....X E X
where E denotes the position of an English book and X that of a French book.
Since there are 21 books on English, the number of places marked X are therefore, 22.
Now, 19 places out of 22 can be chosen in 22C19 = 22C3 = (22x21x20)/(3x2x1) = 1540 ways
Answer B. #### B
QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:
options: A)90 B)106 C)110 D)120 E)130
SOLUTION:sax Letlheo g alnumberofworkers hex
x workers can do the wor - 100 days
(x — 10) workers can do the work in 110 days
4 100x 1u1x— 10)
1100 Q x 110
C #### C
QUESTION:Which of the following is equal to 1(4/5)%?
options: A)0.012/100 B)0.12/100 C)1.2/100 D)1.8/100 E)12/10
SOLUTION:This notation may be confusing for some, since it looks like we're multiplying 1 and 4/5
How about adding a space:Which of the following is equal to (1 4/5)%
(1 4/5)% = 1.8% = 1.8/100
Answer:
D #### D
QUESTION:The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is
options: A)35.22 B)36.12 C)36.22 D)36.42 E)None
SOLUTION:Solution
Correct sum = (36x50+44-23)
= 1821.
∴ Correct mean = 1821 / 50
= 36.42.
Answer D #### D
QUESTION:X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits?
options: A)X-Y B)Y-X +100 C)100X-Y D)X+Y-100 E)100-XY
SOLUTION:Using the simple formula
100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour
So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values.
Hence Answer D #### D
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)150 m B)200 m C)240 m D)400 m E)150 m
SOLUTION:Answer: Option C
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m. #### C
QUESTION:7+2+2^2+2^3+2^4+2^5=？
options: A)(2^3-1)(2^3+1) B)2^6+5 C)2^5-1 D)2^5+1 E)2^5-2
SOLUTION:From 7+2+2^2+2^3+2^4+2^5=69,
2^6+5=69
the correct answer is B. #### B
QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen?
options: A)6 B)24 C)36 D)66 E)72
SOLUTION:Try using the formula for combinations:
n!/r!(n-r)!
12!/2!(12-2)!
12!/2!*10!
12*11/2*1
=66
ANSWER:D #### D
QUESTION:A scooter costs 30,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years?
options: A)10,000 B)12,500 C)12,800 D)12,000 E)15,360
SOLUTION:After first year, the value of the scooter = 24,000
After second year, the value of scooter = 19,200
After third year, the value of scooter = 15,360
Answer E #### E
QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work?
options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs
SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work ..
Therefore, Y will do the remaining 1/10 th work alone..
As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job...
ans 10
E #### E
QUESTION:A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase?
options: A)10% B)12% C)14% D)16% E)18%
SOLUTION:Let x be the amount of money paid for the first purchase.
The second time, the customer paid 0.8(1.1x)=0.88x.
The difference is 12%.
The answer is B. #### B
QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
options: A)14700 B)14500 C)14900 D)14300 E)14000
SOLUTION:Total amount invested = 50000
Assume that investment of C =x.
Then investment of B =5000+x,
Investment of A =4000+5000+x=9000+x
x+5000+x+9000+x=50000
⇒3x+14000=50000
⇒3x=50000–14000=36000
⇒x=36000/3=12000
Investment of C =x=12000
Investment of B =5000+x=17000
Investment of A =9000+x=21000
Ratio of the investment of A, B and C
=21000:17000:12000
=21:17:12
Share of A = Total profit ×21/50
=35000×21/50=700×21=14700
Answer is A. #### A
QUESTION:If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD?
options: A) 62 B) 55 C) 48 D) 31 E) 25
SOLUTION:I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square.
25 is a perfect square.
Ans:E #### E
QUESTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
options: A)2443200 B)3643200 C)5443200 D)1443200 E)2163200
SOLUTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216
Choosing the digit for p - 9 ways;
Choosing the digit for q - 8 ways;
Choosing the digit for r - 7ways;
Choosing the digit for s - 6ways;
Choosing the digit for t - 5ways;
# of permutations of 3 digits in ppqrst - 6!/2!
Total: 9*8*7*6*5*6!/2!=5443200.
Answer: C. #### C
QUESTION:If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ?
options: A)16 B)1.6 C)0.16 D)0.016 E)None of these
SOLUTION:Explanation :
(204/12.75) = 16
⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10)
⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B #### B
QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
options: A)20% B)40% C)50% D)60% E)70%
SOLUTION:70 + 55 + 35 = 160%
The number is 60% above 100% because 60% of the counties were counted twice.
The answer is D. #### D
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
options: A)22 B)25 C)66 D)77 E)91
SOLUTION:800 --- 200
100 --- ? => 25%
Answer: B #### B
QUESTION:If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?
options: A)38 B)27 C)24 D)19 E)17
SOLUTION:Explanation:
Let t be his usual time to reach his office and v be his usual speed.
v = d/t ……….(d is the distance Ajay travels while going to his office)
vt = d
At v1 = 4v/5 ; t1 = t + 6
4v/5 = d/(t + 6)
4v/5* (t + 6) = d
4v/5* (t + 6) = vt
On solving we get,
t = 24 minutes
ANSWER:C #### C
QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is:
options: A)15 B)18 C)19 D)22 E)23
SOLUTION:explanation:
60-6= 54 ,190-10= 180
Highest number that divides 54 and 180 is HCF of numbers
HCF of 54 nad 180= 18
Answer:B #### B
QUESTION:70,76, 74,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74.
Answer: C. #### C
QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 82 unique alphanumeric case sensitive characters.
options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6)
SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password
= 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways )
=82^4(1+ 82)
=82^4 * 83
Answer B #### B
QUESTION:A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
options: A)10 B)20 C)50 D)30 E)40
SOLUTION:Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 15 - 2.5 = 12.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 12.5 - 2.5 = 10 km/hr
Answer is A. #### A
QUESTION:The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
options: A)1:3 B)2:5 C)3:2 D)9:4 E)4:2
SOLUTION:Explanation:
Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
Answer: Option B #### B
QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
options: A)4 B)16 C)8 D)1 E)2
SOLUTION:Explanation:
Let the required number of mats be x
More mat-weavers, more mats (direct proportion)
More days, more mats (direct proportion)
Hence we can write as
(mat-weavers) 4:8
(days) 4:8}::4:x
⇒4×4×x=8×8×4
⇒x=2×2×4=16
Answer: Option B #### B
QUESTION:List R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?
options: A)12 B)16 C)20 D)24 E)28
SOLUTION:The middle number is 40.
Let the smallest number be x. Then the largest number is 2x+20.
To make x as small as possible, let's make the remaining numbers as large as possible.
So the second largest = the largest = 2x+20.
The second smallest should be equal to the median.
The numbers are x, 40, 40, 2x+20, 2x+20.
x + 40 + 40 + 2x + 20 + 2x + 20 = 5*40 = 200
5x = 80
x = 16
The answer is B. #### B
QUESTION:The positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
options: A)I only B)II only C)III only D)I and II only E)II and III only
SOLUTION:Let q = 10% then l = 100/11 %
let b = 100 then a = 110
after increasing a by l and decreasing b yq we get c= 108
therefore c<a
C it is answer #### C
QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate?
options: A)576 B)425 C)215 D)321 E)None of these
SOLUTION:Explanation :
In a circle, 5 boys can be arranged in 4! ways
Given that the boys and the girls alternate.
Hence there are 4 places for girls which can be arranged in 4! ways
Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A
QUESTION:If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Yoe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Yoe?
options: A)15 B)60 C)75 D)90 E)105
SOLUTION:This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Yoe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins
So answer 30+60= 90 mins.D #### D
QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases?
options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc
SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips
The answer is C. #### C
QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables w are there in the warehouse?
options: A)6 B)8 C)10 D)15 E)30
SOLUTION:Total number of ways to choose 2 chairs from 5 w= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A #### A
QUESTION:Janet has to pay back her bank loan over 10 months following the below sequence.
$50, $55, $65, $80, $85, $95, $110, $115, $125, ?
How much will she pay back on the tenth month?
options: A)$155 B)$140 C)$135 D)$125 E)$130
SOLUTION:The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 10th Month is $140
Ans B #### B
QUESTION:Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?
options: A)24. B)28. C)36. D)42. E)48
SOLUTION:Diameter of tube= 5 inches
Height of wooden tube= 15 inches
Two tubes can stand in 31 inches height
Two tubes can fit in 11 inches length
Two tubes can fit in 10 inches width
So, one box can hold 8 tubes
Three boxes can hold= 8*3= 24 tubes
A is the answer #### A
QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
options: A)90. B)45. C)50. D)40. E)25.
SOLUTION:STREET-CAT DOMESTIC-Cat
70 130
(25gray+45other) 85gray+45other
Answer:B #### B
QUESTION:For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b - 4| + |ab + b| = ?
options: A)a) ab - 4 B)b) 2b - ab - 4 C)c) ab + 4 D)d) ab - 2b + 4 E)e) 4 - ab
SOLUTION:|a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b+4
Since ab is Positive and b is Negative so |ab - b| = ab + b
i.e. |b - 4| + |ab - b| = -b+4 + ab + b =ab + 4
Answer: Option C #### C
QUESTION:The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?
options: A)33 1/3% B)33 1/8% C)33 6/3% D)33 8/3% E)31 1/3%
SOLUTION:100
75
-------
75 ------- 25
100 ------ ? => 33 1/3%
Answer: A #### A
QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten?
options: A)15 B)18 C)21 D)23 E)29
SOLUTION:There are two conditions:
1. Angel got at least one score of each of 1, 2, 3, and 4.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18.
Answer: B. #### B
QUESTION:A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes?
options: A)35:1 B)Either ;35:1 C)Either 70;35:1 D)Either 55;45:1 E)Either 65;35:5
SOLUTION:Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B) #### B
QUESTION:If the a radio is sold for Rs 490 and sold for Rs 465.50.find loss%.
options: A)4% B)5% C)6% D)3% E)5.5%
SOLUTION:sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Answer is B. #### B
QUESTION:For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?
options: A)8/5 B)5/2 C)3 D)33/25 E)4
SOLUTION:Let monthly salary for each of the 11 months except December was x, then
11x*1/10 + Nx*1/3 = 1/8(11x + Nx);
11/10 + N/3 = 1/8(11 + N)
33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66
N = 66/50=33/25
Answer: D. #### D
QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire?
options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters
SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 120,000 m : C is the circumference
C = 5 meters
correct answer C #### C
QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces?
options: A)12 B)8 C)6 D)10 E)16
SOLUTION:The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge.
There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube.
4 + 4 + 4 = 12.
Answer A #### A
QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
options: A)56 B)28 C)45 D)24 E)45
SOLUTION:D
24
Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x <-> 27 x x = 36 x 18
x = (36 x 18)/27
x = 24 #### D
QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)?
options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5
SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57)
4.5/(4.5 - 2) = 9/5 (1.8)
3.5/(3.5 - 2) = 7/3 (~2.33)
2.5/(2.5-2) = 5
1.5/(1.5 - 2) = -3
Thus, the answer is D. #### D
QUESTION:In a box of 9 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
options: A)2/9 B)3/10 C)4/11 D)5/12 E)6/13
SOLUTION:# defective pens = 3
# good pens = 6
Probability of the 1st pen being good = 6/9
Probability of the 2nd pen being good = 5/8
Total probability = 6/9 * 5/8 = 5/12
The answer is D. #### D
QUESTION:The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
options: A)4 years B)8 years C)6 years D)5 years E)1 years
SOLUTION:Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20 => x = 4.
Age of youngest child = x = 4 years.
Answer: A #### A
QUESTION:A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time W it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?
options: A) 0.8(80 – y) B) 0.8 + 0.0025y C) 80/y – 1.25 D) 80/1.25y E) 80 – 0.25y
SOLUTION:This may be a case of bad numberpicking but it worked for me.
80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.
80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <=> 1/12,5 weeks per house * 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks.
Which means finishing all houses at normal rate W=> 2*4 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks.
7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9. #### B
QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec
SOLUTION:D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer: C #### C
QUESTION:Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have.
options: A)16.5 B)17.5 C)18.5 D)19.5 E)20.5
SOLUTION:Let Siri has x Rs, then Christine has 20+x Rs
Given x + (20+x)= 21
=> 2x= 1 or x= 0.5
So Christine and Siri has 20.5 and 0.5 Rs respectively.
ANSWER:E #### E
QUESTION:The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes.
options: A)$0.94 B)$0.96 C)$0.99 D)$1.00 E)$1.20
SOLUTION:Assume the manager bought 100 tomatoes.
Cost Price = 80
Given: 10% are damaged --> Available tomatoes to sell = 90
90 * x - 80 = 0.12 * 80
90x - 80 = 9.6
90x = 89.6
x = 89.6/90 = 0.995
x is slightly under 0.9955 = 0.99
Answer: C #### C
QUESTION:Ravi and sunil are partners in a business. Ravi invests Rs.12,000 for 4 months and Sunil invested Rs.10000 for 5 months then after one year ratio of their profits will be
options: A)1:3 B)2:3 C)24:25 D)20:22 E)3:4
SOLUTION:=(12000*4):(10000*5)
=48000:50000
=24:25
ANSWER:C #### C
QUESTION:Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is
options: A)Rs.1550 B)Rs.1650 C)Rs.1750 D)Rs.2000 E)None
SOLUTION:Solution
C.I. =Rs[4000x(1+10/100)²-4000]
Rs.(4000x11/10x11/10-4000) = Rs.940.
Sum =Rs. [420x100 /3x8]
= Rs.1750.
Answer C #### C
QUESTION:What is the number of integers from 1 to 100 (inclusive) that are divisible by neither 5 nor by 6?
options: A)35 B)47 C)58 D)26 E)34
SOLUTION:In 100 consecutive numbers, number of multiples of 5 = 100/5 = 20 (Ignore decimals)
In 100 consecutive numbers, number of multiples of 6 = 100/6 = 16
Number of multiples of 5*6 i.e. 30 = 100/30 = 3
Number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - (29 + 16 - 3) {Using the concept of sets here) = 58
Answer is C #### C
QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
options: A)1200 B)1723 C)1129 D)2613 E)1372
SOLUTION:A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 150= 3k + 150 => 2k = 300 => k = 150
The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A
QUESTION:The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and three-fourths of the females in the class?
options: A)218 B)226 C)234 D)242 E)250
SOLUTION:1/2*2/5 + 3/4*3/5 = 4/20 + 9/20 = 13/20
The number of degrees is 13/20 * 360 = 234 degrees
The answer is C. #### C
QUESTION:If 9^y = 3^14, what is y?
options: A)2 B)3 C)4 D)5 E)7
SOLUTION:9^y = 3^2y = 3^14
2y=14
y = 7
The answer is E. #### E
QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount?
options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these
SOLUTION:Explanation :
F = Rs. 2360
TD = Rs. 360
PW = F - TD = 2360 - 360 = Rs. 2000
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 2000 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2360 for unexpired time
=360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B
QUESTION:The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
options: A)1677 B)2523 C)1683 D)3363 E)3567
SOLUTION:L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683. Answer: Option 'C' #### C
QUESTION:The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
options: A)2 years B)5 years C)9 years D)4 years E)1 years
SOLUTION:28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer:D #### D
<<<Examples ends
QUESTION:If y is an integer, then the least possible value of |23 - 4y| is
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:We know that 4y is a multiple of 4, so let’s first look at the multiples of 4 closest to 23. We have “20” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 4y = 20, y is 5 and when 4y = 24, y is 5. Let’s start with letting y = 4.
|23-4(5)|
|23-20|
|3| = 3
Next, let’s let y equal 5.
|23-4(6)|
|23-24|
|-1| = 1
We see that the smallest possible value of |23-4y| is 1.
Answer A. #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:6x + 2y = -4
4x + y = 1
In the system of equations above, what is the value of x?
options: A)5 B)4 C)3 D)2 E)1
SOLUTION:6x + 2y = -4 can be written as 3x + y = -2
Let's subtract the second equation from this equation.
-x = -3
x = 3
The answer is C. #### C
QUESTION:In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-9, 1), (1, 1), (1, -8) and (-9, -8)?
options: A)72 B)180 C)70 D)90 E)140
SOLUTION:Length of side 1= 9+1=10
Length of side 2= 8+1= 9
Area of rectangle= 10*9= 90
D is the answer #### D
QUESTION:Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3.
options: A)131 B)197 C)207 D)219 E)227
SOLUTION:Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3.
Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1) = 131.
ANSWER:A #### A
QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?
options: A)4 B)6 C)10 D)12 E)24
SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5∗150=90
2nd Question : four fifths of the remainder answered the second question correctly so 4/5∗(150−90)=4/5∗60=48
total students who answered at least one Q correct =90+48=138
so students who answered BOTH incorrectly = 150−138=12
ANSWER:D #### D
QUESTION:If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer?
I. w + t + 2
II. w^2 + 2wt + t^2
III. w^2 + t^2
options: A)None B)I only C)II only D)III only E)I, II, and III
SOLUTION:w^2–t^2 is an odd integer means that either w is even and t is odd or w is odd and t is even.
Check all options:
I. w + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. w^2 + 2wt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. w^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A. #### A
QUESTION:the banker's discount on a bill due 4 months hence at 15% is Rs.420. what is the true discount?
options: A)41 B)400 C)390 D)380 E)480
SOLUTION:TD= (BD * 100)/(100+TR)= (420 * 100)/100+((4/12)*15)= (420 * 100)/100+((1/3)*15)
=(420 * 100)/100+5= (84 * 100)/21 = 4*100=400
correct answer: (B) #### B
QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
options: A)6 days B)4 days C)8 days D)5 days E)1 days
SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4
=> 4 days
Answer: B #### B
QUESTION:Excluding stoppages, the speed of a train is 55 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour?
options: A)82 B)16 C)12 D)82 E)18
SOLUTION:Explanation:
T = 15/55 * 60 = 16
Answer: Option B #### B
QUESTION:The age of Somu is one-third his father's. 8 years back he was one-fifth of his father's age. What is his persent age ?
options: A)11 B)13 C)14 D)16 E)10
SOLUTION:Explanation :
Let Somu's age be x and that of his father be 3x.
So, x - 8 = 3x - 8/5 = x = 16
Answer : Option D #### D
QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:
options: A)276 B)299 C)322 D)345 E)395
SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12).
Larger number = (23 x 12) = 276.
Answer: Option A #### A
QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly?
options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20
SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/5*1/4 = 9/10.
Answer: D. #### D
QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 450. Find the total worth of the stock?
options: A)20029 B)22500 C)20289 D)20027 E)20026
SOLUTION:Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 450 => x = 22500
Answer: B #### B
QUESTION:If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?
options: A)4:3 B)4:0 C)4:5 D)4:7 E)4:2
SOLUTION:Explanation:
a1:a2 = 4:3
d1:d2 = 4:3
Answer: Option A #### A
QUESTION:A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
options: A)6 B)4 C)8 D)2 E)3
SOLUTION:M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9
= 4
Answer: B #### B
QUESTION:Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have.
options: A)16.5 B)17.5 C)18.5 D)19.5 E)20.5
SOLUTION:Let Siri has x Rs, then Christine has 20+x Rs
Given x + (20+x)= 21
=> 2x= 1 or x= 0.5
So Christine and Siri has 20.5 and 0.5 Rs respectively.
ANSWER:E #### E
QUESTION:The sub-duplicate ratio of 25:49 is
options: A)4:3 B)5:7 C)6:4 D)1:4 E)2:3
SOLUTION:root(25):root(49)=5:7
ANSWER:B #### B
QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone?
options: A)4 2/3 B)7 C)9 D)24 E)21
SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 6 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/7+6*1/x=1
5x+42=7x
2x=42
x=21 days.
Ans:E #### E
QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600:
options: A)200 B)250 C)300 D)350 E)400
SOLUTION:X = Rs.5000/-
Y = Rs.15000/-
X share 1 part & Y share 3 parts
Total 4 parts -----> Rs.1600/-
----> 1 part -------> Rs.400/-
X share = 1 part -----> Rs.400/-
E #### E
QUESTION:A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?
options: A)10.21 days B)10.23 days C)18.25 days D)10.25 days E)40.25 days
SOLUTION:Explanation:
A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work.
=> In one day A came complete 1/9th of the task(x/9)
=> In one day B can complete 1/12th of the job.(x/12)
First day x/9th work will be done next day x/12th and so on:
Together A and B can do x/9 + x/12 work.
=>(x/9) + (x/12) = 7/36th work done
In 10 days 35/36th of the work will be done.
On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work.
So, 1/36th work will be done in 1/4 days.
=>10.25 days
ANSWER: D #### D
QUESTION:The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly
options: A)24.64 B)24.69 C)24.62 D)24.6 E)24.61
SOLUTION:Explanation:
For 1st year S.I =C.I.
Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200
i.e S.I on the principal for 1 year is Rs.200
Principle = = Rs.2500
Amount for 2 years, compounded half-yearly
C.I = Rs.424.64
Also,
Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64
Answer:A #### A
QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda
spends 20% more time painting the house than Angela, each receives a payment
of m dollars when the work is completed. If Angela decides to pay Linda n
dollars so that they would have received the same compensation per hour
worked, what is n in terms of m?
options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m
SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100)
According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs.
so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12*100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11
answer E #### E
QUESTION:In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
options: A)50% B)40% C)20% D)30% E)10%
SOLUTION:Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 10) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/10) * 100 ---> 10%
Answer : E #### E
QUESTION:What is the total surface area in square meters of a rectangular solid whose length is 8 meters, width is 7 meters, and depth is 4 meters?
options: A)132 m2 B)145 m2 C)165 m2 D)152 m2 E)120 m2
SOLUTION:Surface Area of a cuboid = 2(lb+bh+lh) = 2(8*7+7*4+8*4)=2(56+28+32)=2*116=132 m2
Answer : A #### A
QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three?
options: A)14 B)16 C)18 D)24 E)25
SOLUTION:Explanation:
Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
ANSWER IS A #### A
QUESTION:40, 45, 50, 50, 60, 75, 75, 100, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5.
1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.
Answer B. #### B
QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance?
options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr
SOLUTION:Total distance traveled = 100+200+300+100 = 700km
Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs
Average speed = 700/16.67 = 42km/hr approximately ;
Answer is B #### B
QUESTION:Ayesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
options: A)6 B)40 C)50 D)10 E)20
SOLUTION:Mother's age when Ayesha's brother was born = 42 years.
Father's age when Ayesha's brother was born = (58 + 4) years = 62 years.
Required difference = (62 - 42) years = 20 years.
Answer:E #### E
QUESTION:Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related)
options: A)100 B)200 C)300 D)90 E)80
SOLUTION:Well, the pattern looked REALLY familiar to me, like it's a binary progression.
And it is...but with a twist.
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence).
BUT, if you convert 8 to base 8, you get 10.
And if you convert 32 to base 8, you get 40.
Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8.
If this is true, then you next number would be:
2^7 = 128
That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A #### A
QUESTION:How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 26%?
options: A)100 ml B)60 ml C)120 ml D)130 ml E)150 ml
SOLUTION:we can also go by answer choices
Tke 100 ml for eg
400 (old)+100 (new concentr)ml
500*26/100 = 130 ml (30ml is de old concentration +100 ml (newly added)
Answer D #### D
QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
options: A)5 B)4 C)6 D)8 E)3
SOLUTION:65*(90/100)*((100-x)/100) = 56.16
x = 4%.Answer:B #### B
QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
options: A)5 B)6 C)9 D)7 E)3
SOLUTION:7 * 8 : 9 * x = 8:9
=> x= 7
Answer: D #### D
QUESTION:At what time between 4 & 5 will the hands of a watch point in opposite directions?
options: A)50 min past 4 B)42 5/11 min past 4 C)43 min past 4 D)40 min past 4 E)50 4/11 min past 4
SOLUTION:At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30min. spaces apart.
Minute hand will have to gain 5 min. spaces.
55min spaces are gained in 60 min.
5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min.
Required time = 54 6/11 min. past 4.
Answer is E #### E
QUESTION:Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.?
options: A)8 B)12 C)14 D)16 E)18
SOLUTION:Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+34
3x + 6 = x + 34
2x = 28
\inline \therefore x = 14
\inline \therefore Middle number = x + 2 = 14+2 = 16
D #### D
QUESTION:P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
options: A)1:8 B)1:6 C)2:1 D)1:1 E)1:7
SOLUTION:Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1:1
Answer:D #### D
QUESTION:If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is?
options: A)A)15 B)B)10 C)C)14 D)D)12 E)E)11
SOLUTION:2 * 22/7 * 14 * x = 880 => x = 10
ANSWER:B #### B
QUESTION:Thin rectangular slab of potato was cut into two pieces for an osmosis lab. One piece is 50mm greater than the other. If the original uncut slab is 600mm, what is the length of the other piece of the potato after it is cut.
options: A)550 B)275 C)50 D)300 E)250
SOLUTION:piece one as p1, and piece two as p2.
p2+50=p1 as eq.a
p1+p2=600 as eq.b
substitute eq. a into eq.b, resulting in (p2+50) + p2=600mm.
Group like terms, p2+p2=600-50
(2*p2/2)=550/2 solves to p2= 275.
Ansewr is B. #### B
QUESTION:Two persons A and B can complete a piece of work in 30 days and 60 days respectively. If they work together, what part of the work will be completed in 10 days?
options: A)1/8 B)1/3 C)1/6 D)1/2 E)5/3
SOLUTION:A's one day's work = 1/30
B's one day's work = 1/60
(A + B)'s one day's work = 1/30 + 1/60 = 1/20
The part of the work completed in 10 days = 10 (1/20) = 1/2.
Answer:D #### D
QUESTION:5020−(502÷100.4)=?
options: A)15 B)20 C)5015 D)25 E)35
SOLUTION:Explanation:
=5020−(502/1004×10)
=5020−5=5015
Option C #### C
QUESTION:A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
options: A)49 kmph B)50 kmph C)51 kmph D)52 kmph E)54 kmph
SOLUTION:Explanation:
Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec.
[(25/2) x (18/5)] km/hr = 45 km/hr.
Let the speed of the train be 'x' km/hr.
Then, relative speed = (x - 4) km/hr.
x - 4 = 45 => x = 49 km/hr.
ANSWER IS A #### A
QUESTION:In the city of San Durango, 50 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 30 owned rabbits, and 20 owned exactly two of the three types of pet, how many people owned all three?
options: A)2 B)4 C)8 D)5 E)12
SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR
50 = 20 + 30 + 30 - (20) - 2x
x = 5
So, answer will be D #### D
QUESTION:The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
options: A)100 kg B)102.5 kg C)85 kg D)Data inadequate E)None of these
SOLUTION:Explanation:
Total weight increased = (10 x 3.5) kg = 35 kg.
Weight of new person = (65 + 35) kg = 100 kg.
Answer: A #### A
QUESTION:Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
options: A)5/7 B)5/3 C)5/1 D)5/6 E)5/2
SOLUTION:P(at least one graduate) = 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer: D #### D
QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed?
options: A)104 B)130 C)298 D)269 E)213
SOLUTION:520/4 = 130 kmph
Answer:B #### B
QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is
options: A)5 B)10 C)11 D)2 E)3
SOLUTION:Explanation:
Number of words which can be formed = 3! - 1 = 6 - 1 = 5.
Answer: A #### A
QUESTION:Find a a prime number the options below.
options: A)78 B)80 C)81 D)82 E)83
SOLUTION:Clearly, 83 is a prime number.
E #### E
QUESTION:What is the are of an equilateral triangle of side 4 cm?
options: A)2√3 B)3√3 C)5√3 D)4√3 E)8√3
SOLUTION:Area of an equilateral triangle = √3/4 S2
If S = 4, Area of triangle = √3/4 * 4 * 4
= 4√3 cm2;
Answer:D #### D
QUESTION:Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg. How much amount did he pay to the shopkeeper?
options: A)A)1040 B)B)1045 C)C)1055 D)D)1190 E)E)1075
SOLUTION:Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 70 × 9 = 630.
Total cost he has to pay = 560 + 630 = 1190.
D) #### D
QUESTION:Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket
to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
options: A)$8 B)$14 C)$5 D)$15 E)$0
SOLUTION:1/5 x $60 = $12 for sandwich
1/6 x $60 = $10 for museum
1/2 x $60 = $30 for book
$12 + $10 + $30 = $52 spent
$60 - $52 = $8 left over
correct answer A #### A
QUESTION:how many square are there between 2001....2300 I don't remember the exact series.
options: A)1 B)4 C)2 D)3 E)5
SOLUTION:series was from 2001 to 2300
45^2=2025
46^2=2116
47^2=2209
48^2=2304 (so exclude 48)
so ans is 3 (45,46 and 47)
ANSWER:D #### D
QUESTION:What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each?
options: A)$3.36 B)$6.85 C)$8.46 D)$10.08 E)$12.46
SOLUTION:Answer = E
2 * 2.49 + 4 * 1.87
= 2 (2.50 - 0.01) + 4 (2.00 - 0.13)
= 5 + 8 - 0.02 - 0.52
= 13 - 0.54
= 12.46 #### E
QUESTION:When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?
options: A)$1,600 B)$1,850 C)$2,250 D)$2,400 E)$2,750
SOLUTION:Let the value of the item be $x, then 0.07(x−1,000)=87.5--> x−1,000=1,250x−1,000=1,250 --> x=2,250.
Answer: C. #### C
QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is?
options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m
SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
E #### E
QUESTION:Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3?
options: A)2/5 B)2/7 C)33/83 D)51/250 E)100/249
SOLUTION:SOLUTION
The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250.
Answer: D #### D
QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water
options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr
SOLUTION:still in water=1/2(98+10)km/hr
=54km/hr
correct option is :B #### B
QUESTION:What is the remainder when 103 * 505 * 607 is divided by 9
options: A)6 B)18 C)2 D)4 E)7
SOLUTION:103/9==> Remainder=4
505/9==> Remainder=1
607/9==> Remainder=4
=4*4*1=16/9==> Remainder=7
Answer: E #### E
QUESTION:v, w, x, y, and z are five positive integers for which v≤w≤x≤y≤z. If the average (arithmetic mean) of the five numbers is 30 and their median is 25, which is the smallest possible value of z?
options: A)30 B)35 C)37 D)38 E)40
SOLUTION:sum=150
mid value = 25
minimize 'z'. So, 25 25 25 37 38
answer: D #### D
QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate?
options: A)Cannot be determined B)43 C)3 D)6 E)10
SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position.
Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A
QUESTION:A man buys s cycle for $100 and sells it at a loss of 10%. What is the selling price of the cycle?
options: A)$50 B)$60 C)$70 D)$80 E)$90
SOLUTION:S.P. = 90% of the $100 = 90/100 * 100 = $90
Answer is E #### E
QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n?
options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years
SOLUTION:Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $700.
Therefore, the Simple Interest earned = 700 - 100 = $600.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 600 = (100 * n * 8) / 100
Or 8n = 600
Or n = 75 years.
correct choice is (E) #### E
QUESTION:If 4a = 16b and 8b = 13c, Find a:b:c?
options: A)52:13:8 B)13:7:52 C)7:13:52 D)7:13:54 E)None of these
SOLUTION:Explanation:
(4a = 16b ==> a/b = 16/4)
and (8b = 13c ==> b/c = 13/8)
==> a:b = 16:4 and b:c = 13:8
a:b:c = 52:13:8
Answer: Option A #### A
QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A - B is also a Even number.
(3) A^B is also a prime number.
options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3.
SOLUTION:Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A - B is also a Even number. : True
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans : C #### C
QUESTION:3640 ÷ 14 × 16 + 340 = ?
options: A)0.7 B)3525 C)4480 D)None of these E)Cannot be determined
SOLUTION:Solution
Given exp. = 260 × 16 + 340 = 4160 + 340 = 4500.
Answer D #### D
QUESTION:Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die.
options: A)1/2 B)1/6 C)0 D)5/6 E)1
SOLUTION:Determine if E and F are independent.
P(E|F) = the probability of event E occurring given that event F has already occurred
P(E|F) ≠ P(E) as P(E) is changed if it is given that F occurs.
Consequently, P(E∩F) ≠ P(E)P(F) since the events are not independent. As a result, P(E∩F) ≠ 1/4 = P(E)P(F)
We must use the more complex formula for finding the intersection of E and F:
P(E∩F) = P(F)P(E|F)
P(F) = the probability of event F occurring
The probability of rolling a 1, 2, or 3 is 3/6 = 1/2
P(E|F) = the probability of event E occurring given that event F has already occurred
If event F already occurred, we are limited to the numbers 1, 2, or 3. Within this range of 3 possible numbers, only one number--namely, 2--is an even number. Therefore, P(E|F) = 1/3
P(E∩F) = P(F)P(E|F) = (1/2) * (1/3) = 1/6
Answer B #### B
QUESTION:A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives
options: A)Rs. 8400 B)Rs. 11,900 C)Rs. 13,600 D)Rs. 14,700 E)NONE
SOLUTION:Solution: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000.
=> 3x = 36000.
=> x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
So A's share = Rs. (35000 x 21/50) = Rs. 14,700.
Answer: Option D #### D
<<<Examples ends
QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?
options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5
SOLUTION:Explanation:
Let the capacity of 1 bucket = x.
Then, capacity of tank = 25x.
New capacity of bucket = 2/5 x.
Required no of buckets = 25x / (2x /5) = 62.5
ANSWER IS B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
options: A)3:5 B)3:9 C)3:2 D)2:2 E)3:8
SOLUTION:The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r1^2 . h1/r2^2. h2 => 1/15
= (1)^2h1/(2)^2h2
=> h1/h2 = 3/5
i.e. h1 : h2 = 3:5
Answer: A #### A
QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many W digits does this integer consists of?
options: A)150 B)339 C)342 D)359 E)362
SOLUTION:Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer W= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C #### C
QUESTION:A circular well with a diameter of 6 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out?
options: A)678.6 m3 B)36 m3 C)40 m3 D)44 m3 E)None
SOLUTION:Solution
Volume = πr2h
‹=› (22 /7 ×3×3×24)m3
‹=›678.6 m3.
Answer A #### A
QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value W of 100th term?
options: A)126 B)192 C)232 D)252 E)342
SOLUTION:(1~99) 19, (100~199) 19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer W is 342. The correct answer is E. #### E
QUESTION:Which of the following is equal to the value of 2^7 + 2^7 + 3^7 + 3^7 + 3^7 ?
options: A)2^8 + 3^8 B)2^6 + 3^8 C)2^8 + 3^6 D)2^9 + 3^9 E)2^5 + 3^5
SOLUTION:2^7 + 2^7 + 3^7 + 3^7 + 3^7
= 2 (2^7) + 3 (3^7)
= 2^1 (2^7) + 3^1 (3^7)
= 2^(1+7) + 3^(1+7)
= 2^8 + 3^8
Ans: A #### A
QUESTION:Convert 50miles into yards?
options: A)25630 yards B)35200 yards C)88000 yards D)42560 yards E)41520 yards
SOLUTION:1 mile = 1760 yards
50 miles = 50*1760 = 88000 yards
Answer is C #### C
QUESTION:Maddie has 15 apples, if she give 8 to mike, how many does she have left?
options: A)1 B)7 C)3 D)4 E)5
SOLUTION:15-8=7
B. 7 #### B
QUESTION:Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
options: A)5/5 B)5/9 C)3/4 D)5/7 E)5/2
SOLUTION:In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27
The probability = 27/36 = 3/4.
Answer: C #### C
QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners.
Conclusions:
1) 80% of the team consists of spinners.
2) The opening batsmen were spinners.
options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow
SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow.
D #### D
QUESTION:Which of the following is equal to 3.14 x 10^6) ?
options: A)3.14 B)3140000 C)31400 D)314 E)314000
SOLUTION:= 3.14 x 10^6
= 3.14 x 1000000
= 3140000.
Answer is B. #### B
QUESTION:A beats B by 50m in a race of 500m ,then B beats by C by 25m in a race of 500m.Find the
distance by which A beats C in a race of 400?
options: A)55m B)56m C)57m D)58m E)59m
SOLUTION:A beats B in 500m race by 50m
so,for every 10 m race A beat B by 1m..
So,in 400 m race A beat B by 40m
In a case of B & C,
B beats C by 25m in 500m race..
So,B beats C by 1m in 20 m race
Now,in a 400m race B beats C by 18m..
In a 400m race,
A beats B by 40m & B beats C by 18m..
So,A beats C by 58m
ANSWER:D #### D
QUESTION:If the tens digit of positive integer x is 6 and the tens digit of positive integer y is 6, how many possible values of the tens digit of 2(x+y) can there be?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 60 + p and 60 + q respectively.
2(60+p+60+q)= 240 + 2(p + q).
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 40 up to 76.
There can be 4 possibilities for the tens digit.
The answer is C. #### C
QUESTION:Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on?
options: A)3. B)4. C)5. D)6. E)7.
SOLUTION:Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 4 = 5x + 2
6x - 4 = 5x + 2
x = 6
Answer: D #### D
QUESTION:1395 x 1395
options: A)1946025 B)1981709 C)18362619 D)2031719 E)None of these
SOLUTION:1395 x 1395 = (1398)2
= (1400 - 2)2
= (1400)2 + (5)2 - (5 x 1400 x 5)
= 1946025.
Answer: Option A #### A
QUESTION:A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?
options: A)$20,200 B)$20,500 C)$20,800 D)$21,000 E)$21,400
SOLUTION:average = 2(19000)+(21000)+3(22000) / 6 = $20,833
The answer is C. #### C
QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
options: A)2000 B)2781 C)2278 D)2081 E)2721
SOLUTION:Explanation:
(10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A #### A
QUESTION:Reena took a loan of 1500 with simple interest for as many years as the rate of interest. If she paid 735 as interest at the end of the loan period, what was the rate of interest?
options: A)3.6 B)7 C)18 D)Cannot be determined E)None
SOLUTION:Explanation: Let rate = R% and time = R years.
Then, (1500 x R x R)/100 = 735
15R² = 735
R² = 49
R = 7.
Answer: Option B #### B
QUESTION:Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount?
options: A)$1200 B)$1400 C)$1600 D)$1800 E)$2000
SOLUTION:0.7(x-600)=0.6(x-400)
0.1x=420-240
x=1800
The answer is D. #### D
QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
options: A)33/99 B)33/91 C)36/91 D)33/97 E)33/33
SOLUTION:Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= 33/91
Answer: B #### B
QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state?
options: A)8200 B)7500 C)7000 D)8000 E)8400
SOLUTION:Equal number of candidates appeared in each state.
In state A, 6% candidates got selected.
In state B, 7% candidates got selected.
Given that 80 more candidates got selected in state B than A.
Therefore, 1% of candidates appeared in each state =80
Answer: Option D
= 100% of candidates appeared in each state
=80×100=8000
i.e., number of candidates appeared from each state = 8000 #### D
QUESTION:There are 5 boxes in a cargo. The weight of the 1st box is 200 KG, the weight of the 2nd box is 20% higher than the third box, whose weight is 25% higher than the 1st box weight. The 4th box which weighs 350 KG is 30% lighter than the 5th box. Find the difference in average weight of the 4 heaviest boxes and the four lightest boxes.
options: A)22 B)75 C)25 D)70 E)11
SOLUTION:weight of 1st box=200
weight of 3rd box=(125/100)*200=250
weight of 2nd box=(120/100)*250=300
weight of 4th box =350
weight of 5th box=(10/7)*350=500
average of 4 highest weighted boxes=(500+350+300+250)/4=350
average of 4 lightest boxes=(350+300+250+200)/4=275
therefore difference=350-275=75
Answer:B #### B
QUESTION:if log 5 = 0.69897, the number of digits in 5128 is
options: A)90 B)39 C)88 D)28 E)11
SOLUTION:Explanation:
log(5128) = 128log(5) = 128 × 0.69897 ≈ 89.46
ie, its characteristic = 89
Hence, number of digits in 2128 = 89+1 = 90
Answer: Option A #### A
QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:First, reach to the point of getting the equation W: x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D
QUESTION:A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job?
options: A)6 B)8 C)3 D)4 E)0
SOLUTION:Explanation:
Use formula For a work Members × days = constant
8 × 3 = 4 × a
a = 6
so answer is 6 days
Answer: A #### A
QUESTION:What is the units digit of 3333^(333)*3333^(222)?
options: A)0 B)2 C)4 D)6 E)8
SOLUTION:Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits.
Here's another way to organize the information.
We're given [(2222)^333][(3333)^222]
We can 'combine' some of the pieces and rewrite this product as....
([(2222)(3333)]^222) [(2222)^111]
(2222)(3333) = a big number that ends in a 6
Taking a number that ends in a 6 and raising it to a power creates a nice pattern:
6^1 = 6
6^2 = 36
6^3 = 216
Etc.
Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6.
2^111 requires us to figure out thecycleof the units digit...
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....).
111 = 27 sets of 4 with a remainder of 3....
This means that 2^111 = a big number that ends in an 8
So we have to multiply a big number that ends in a 6 and a big number that ends in an 8.
(6)(8) = 48, so the final product will be a gigantic number that ends in an 6.
Final Answer:
D #### D
QUESTION:A customer pays 40 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
options: A)50 B)40 C)70 D)60 E)20
SOLUTION:Let x be the original price.
x - 20 = 40
x - 20 + 20 = 40 + 20
x + 0 = 60
x = 60
Answer is D #### D
QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
options: A)2388 B)2380 C)2888 D)2663 E)2922
SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer: B #### B
QUESTION:If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q
options: A)1 B)3 C)5 D)7 E)9
SOLUTION:3/7 = 0.428571... (a repeating pattern one digit long)
B #### B
QUESTION:What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”?
options: A)5 B)7 C)49 D)20 E)25
SOLUTION:The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum).
C #### C
QUESTION:Divide $ 1162 among A, B, C in the ratio 35 : 28 : 20.
options: A)490,490,490 B)360,392,460 C)490,382,280 D)260,160,60 E)492,390,280
SOLUTION:Sum of ratio terms = (35 + 28 + 20) = 83.
A's share = $ (1162 x (35/83))= $ 490; B's share = $ (1162 x(28/83))= $. 392;
C's share = $ (1162 x (20/83))= $ 280.
Option C #### C
QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo
options: A)61 B)62 C)63 D)64 E)65
SOLUTION:4C1+4C2+4C3+4C4=15.
If their positions also takes into consideration then the ans will be 64
ANSWER:D #### D
QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
options: A)Rs. 1900 B)Rs. 2660 C)Rs. 2800 D)Rs. 2840 E)Rs. 3000
SOLUTION:Explanation:
For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
B's share = Rs.(7030 X 14/37)=Rs. 2660.
ANSWER IS B #### B
QUESTION:In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 45 percent of the vote. How many additional votes would James have needed to win the election?
options: A)901 B)989 C)990 D)891 E)1,001
SOLUTION:James = (0.5/100)*2000 = 10
Votes to win = (45/100)*Total Votes +1 = (45/100)*2000 +1 = 901
Remaining Voted needed to win election = 901 - 10 = 891
Answer: option D #### D
QUESTION:The ratio of the incomes of A and B is 5:4 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $1600 then the income of A is?
options: A)$1500 B)$4000 C)$2000 D)$2500 E)$3200
SOLUTION:Let the income of A and B be $5x and $4x
Let their expenditures be $3y and $2y
5x-3y = 1600-------1)
4x-2y = 1600-------2)
From 1) and 2)
x = 800
A's income = 5x = 5*800 = $4000
Answer is B #### B
QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres?
options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these
SOLUTION:Explanation:
As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute
To climb 26 metres, the time required is:
The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes
Also, the last 5 metres it climbs in another 1 minute
Hence, total time required = 14 + 1 = 15 minutes
ANSWER C #### C
QUESTION:If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10?
options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5
SOLUTION:92p × 5p+w + 11w × 6pw--1=B #### B
QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ?
options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None
SOLUTION:Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.9 - 19 x 15) kg
= 13 kg.
Correct Option: D #### D
QUESTION:The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z?
options: A)35 B)33 C)28 D)21 E)15
SOLUTION:The smallest possible product is 33 which is 3*11.
All other products are too big.
The answer is B. #### B
QUESTION:A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water?
options: A)32 kmph B)34 kmph C)30 kmph D)50 kmph E)65 kmph
SOLUTION:US = 45
DS = 55
M = (45 + 55)/2 = 50
Answer:D #### D
QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1200 per sq. metre.
options: A)Rs. 15000 B)Rs. 15550 C)Rs. 24750 D)Rs. 16500 E)None of these
SOLUTION:Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1200 × 20.625) = 24750. Answer C #### C
QUESTION:In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
options: A)2.5 sec B)4.25 sec C)3.75 sec D)12.5 sec E)6 sec
SOLUTION:Speed = 144 * 5/18 = 40 m/sec
Time taken = 150/40 = 3.75 sec.
ANSWER:C #### C
QUESTION:Two pipes A and B can fill a cistern in 20 and 40 minutes respectively, and a third pipe C can empty it in 80 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
options: A)19 1/7 min B)15 1/7 min C)17 1/7 min D)7 1/7 min E)16 min
SOLUTION:1/20 + 1/40 - 1/80 = 5/80
80/5 = 16
ANSWER:E #### E
QUESTION:The sum of two consecutive number is 109. Which is the larger number?
options: A)42 B)43 C)44 D)45 E)55
SOLUTION:Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=109
2x+1=109
2x=108
x=54
Therefore larger number is x+1=55
ANSWER:E #### E
QUESTION:Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
options: A)2a2 – ab + 3b2 B)(a – b)(2a – 3b) + 4ab C)(a – b)2 + (a2 + ab + 2b2) D)(a + b)2 + (a2 + 2b2 – 3ab) E)(a + b)(a – b) + (2a2 – ab + 4b2)
SOLUTION:The other parts are equal to 34.
Answer E #### E
QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
options: A)112 B)50 C)77 D)14 E)12
SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer: B #### B
QUESTION:What is the principal sum?
I. The sum amounts to Rs. 720 in 4 years at S.I.
II. The sum amounts to Rs. 810 in 7 years at S.I.
III. The rate of interest is 10% p.a.
options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above
SOLUTION:Explanation:
Clearly, any of the three will give us the answer
Answer: E #### E
QUESTION:If n = 2.0767 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n?
options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0047 E) 0.0033
SOLUTION:n*=2.08
n*-n=2.08-2.0767
0.0033
Answer: E #### E
QUESTION:The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A
options: A)A)11 B)B)12 C)C)13 D)D)14 E)E)15
SOLUTION:Explanation:
Given that A+B = 11 + B + C
=> A – C = 11 + B – B = 11
=> C is younger than A by 11 years
Answer: Option A #### A
QUESTION:When positive integer F is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when F is divided by B?
options: A) 13 B) 14 C) 15 D) 16 E) 17
SOLUTION:the remainder will be obtained from the decimal part when F is divided by B i.e. 0.35
0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this
PS: for B-14 F=174 and B=40 #### B
QUESTION:A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
options: A)6.4 days B)4.4 days C)5.4 days D)8.4 days E)2.4 days
SOLUTION:A
6.4 days
1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300
So, all three together will complete the work in 300/47 = 6.4 days.- #### A
QUESTION:It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
options: A)142 B)144 C)3680 D)3280 E)3680
SOLUTION:Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th .
Now, number of even places = 3.
Number of girls to occupy the even places = 3.
Even places can be filled = P (3, 3) ways.
Number of boys = 4.
The remaining 4 places can be filled by 4 boys = P (4, 4) ways
By the fundamental principle of counting:
The required number of seating arrangements
P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144
ANSWER:B #### B
QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ?
options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these
SOLUTION:Explanation:
Part filled by A in 1 hour = 1/6
Part filled by B in 1 hour = 1/18
Part filled by C in 1 hour = 1/36
Part filled by (A+B+C) in 1 hour =
1/6+1/18+1/36=9/36
So all pipes will fill the tank in 4 hours.
Option C #### C
QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women?
options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35
SOLUTION:METHOD- 1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A #### A
QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28
SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 70 students =
800 + 3000 = 3800
Average marks of all the students = 3800/70 = 54.28
ANSWER:B #### B
QUESTION:A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
options: A)13 8/3 days B)13 1/3 days C)13 6/3 days D)63 1/3 days E)13 5/3 days
SOLUTION:5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer:B #### B
QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots?
options: A)4/M B)4M C)900M D)M/900 E)M/4
SOLUTION:The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours.
The answer is E. #### E
QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7?
options: A)1 B)2 C)3 D)5 E)6
SOLUTION:As per question => N=7P+2 for some integer p
hence 5N => 35Q + 10 => remainder =>10 for some integer Q
Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3
hence C #### C
QUESTION:A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed T of the train.
options: A)a) 45 B)b) 33 C)c) 48 D)d) 55 E)e) 61
SOLUTION:Let y be the balance distance to be covered and x be the former speed.
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late
so, y/(3x/4) - y/x = 35/60
4y/3x - y/x = 7/12
y/x(4/3-1)=7/12
y/x*1/3=7/12
y/x=7/4
4y-7x=0 ........ 1
Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late
so, (y-24)/(3x/4) - (y-24)/x = 25/60
4(y-24)/3x - (y-24)/x = 5/12
(y-24)/x (4/3-1) = 5/12
(y-24)/x *1/3 = 5/12
(y-24)*12 = 3x*5
(y-24)*4 = 5x
4y-5x = 96 ....... 2
eq2 - eq1
2x=96
x=48=T
Ans = C #### C
QUESTION:If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight?
options: A)80 B)86 C)92 D)98 E)104
SOLUTION:L+K = 160 and so K = 160-L
L+10 = 1.5K = 1.5(160-L)
2.5L = 230
L = 92
The answer is C. #### C
QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
options: A)897 B)164,850 C)164,749 D)149,700 E)156,720
SOLUTION:Explanatory Answer
Step 1: Identify the series
The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.
The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107.
The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.
It is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2).
So, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3.
Step 2: Compute the sum
Sum of an Arithmetic Progression (AP) = [first term + last term/2]n
We know the first term: 101
We know the last term: 998.
The only unknown is the number of terms, n.
In an A.P., the nth term an = a1 + (n - 1)*d
In this case, therefore, 998 = 101 + (n - 1)* 3
Or 897 = (n - 1) * 3
(n - 1) = 299 or n = 300.
Sum of the AP will therefore, be [101+998/2]∗300 = 164,850
Choice B is the correct answer. #### B
QUESTION:(3x + 2) (2x - 1) = ax^2 + kx + n . What is the value of a - n + k ?
options: A)5 B)8 C)9 D)10 E)11
SOLUTION:Expanding we have 6x^2 - 3x + 4x -2
6x^2 + x - 2
Taking coefficients, a = 6, k= 1, n = -2
Therefore a - n + k = 6 - (-2) +1 = 8 + 1 = 9
The answer is C. #### C
QUESTION:there are 15 cars and 16 trucks? which is greater15 or 16?
options: A)15 B)14 C)12 D)17 E)16
SOLUTION:E #### E
QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years?
options: A)2500 B)2800 C)3500 D)3600 E)2050
SOLUTION:P = 4032
R = 20%
Required population of town = P/(1 + R/100)^T
= 4032/(1 + 20/100)^2
= 4032/(6/5)^2
= 2800(approximately)
Answer is B #### B
QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
options: A)5 B)8 C)9 D)10 E)11
SOLUTION:Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5
Option A #### A
<<<Examples ends
QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice?
options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7
SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2*(1/2)^2 = 2/4 =0.5.
The answer is, therefore, (A). #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3?
options: A)1 B)2 C)3 D)5 E)0
SOLUTION:As per question => N=3P+2 for some integer p
hence 2N => 6Q + 4 => remainder => 1 for some integer Q
hence A #### A
QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
options: A)Rs.486 B)Rs.455 C)Rs.487 D)Rs.480 E)Rs.489
SOLUTION:SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125]
= Rs.480
Answer: D #### D
QUESTION:A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
options: A)240 B)250 C)260 D)230 E)220
SOLUTION:Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 36
=> 300+L = 15×36 = 540
=> L = 540-300 = 240 meter
Answer is A. #### A
QUESTION:The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
options: A)308 sq cm B)220 sq cm C)440 sq cm D)132 sq cm E)138 sq cm
SOLUTION:r = 7 h = 3
2πr(h + r) = 2 * 22/7 * 7(10) = 440
ANSWER:C #### C
QUESTION:If x and y are different prime numbers, each greater than 10, which of the following must be true? I. x+y is an even integer II. xy is an odd integer III. (x/y) is not an integer
options: A)III only B)I only C)II only D)I,II only E)I,II and III
SOLUTION:Given: x and y are different prime numbers, both greater than 10
Statement I: x+y is an even integer
Since x and y are prime numbers greater than 10, they will be odd
Therefore sum will be even.
Correct
Statement II: xy is an odd integer
Since x and y are prime numbers greater than 10, they will be odd
Therefore multiplication will be odd.
Correct
Statement III: (x/y) is not an integer
Since x and y are prime integers, therefore they will not have any common factor apart from 1
Hence (x/y) will not be an integer
Correct
Hence all three statements I, II and III are correct
Answer : E #### E
QUESTION:How many even multiples of 55 are there between 549 and 1101?
options: A)5 B)6 C)9 D)10 E)11
SOLUTION:550 = 10*55
1100 = 20*55
The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B. #### B
QUESTION:If pq = p^3 + q^2 – 2pq, for what value of q is pq equal to p^3 for all values of p?
options: A)-2 B)-1 C)0 D)1 E)2
SOLUTION:C
p3 + q2 – 2pq = p3
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI
C #### C
QUESTION:If 9^y = 3^14, what is y?
options: A)2 B)3 C)4 D)5 E)7
SOLUTION:9^y = 3^2y = 3^14
2y=14
y = 7
The answer is E. #### E
QUESTION:Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive?
options: A)$444 B)$445 C)$446 D)$447 E)$448
SOLUTION:A+B+C = 1200
Given ratio 10:12:13
Let us say the shares of A,B,C deducting 10,20,15 be a,b,c
a+b+c = 1200-45= 1155 = 35K
c share = (1155X13)/35 = 429
C = chandran share = 429+15 = 444
Option A #### A
QUESTION:A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A?
options: A)Rs.240 B)Rs.340 C)Rs.260 D)Rs.280 E)Rs.440
SOLUTION:LCM = 180
Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c
= (180/15)/(180/15 +180/20 + 180/45)
= (12/25) * 500
= Rs.240
ANSWER:A #### A
QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
options: A)16 B)24 C)32 D)28 E)54
SOLUTION:after 7 girls left remaining 7 girls
now boys 14 are twice as many as remaining girls.
initially boys=14 and girls=14.
ANSWER:D #### D
QUESTION:Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?
options: A)2000 B)3000 C)4000 D)1000 E)5000
SOLUTION:Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
Answer:B #### B
QUESTION:A train crosses a platform in 15 sec, same train crosses another platform of length 250 m in 20 sec. If the speed of the train is 15 m/sec then find the length of the platform?
options: A)277m B)180m C)165m D)278m E)175m
SOLUTION:Length of the train be ‘X’
(X + 250)/20 = 15
X = 50m
Let the length of the platform be y
(y + 50)/15 = (50 + 250)/20
4y + 200 = 900
X = 1750m
Answer: E #### E
QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
options: A)5 B)9 C)4 D)1 E)3
SOLUTION:US = 25
DS = 35
M = (35 - 25)/2
= 5
Answer: A #### A
QUESTION:Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 30~ ?
options: A)1 B)0 C)2 D)8 E)31
SOLUTION:n~ = (n-1)!
so 30~ = (30-1)! = 29!
when 29!/30 we have 16*2 inside 29!
hence 30 gets cancelled and we get remainder as 0
B #### B
QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money?
options: A)1489 B)6845 C)2598 D)1875 E)2600
SOLUTION:P = 75(100/20)5 => P = 1875
Answer: D #### D
QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
options: A)12 B)14 C)15 D)19 E)10
SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15. Answer:C #### C
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
options: A)2287 B)27 C)299 D)287 E)150
SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
Answer: E #### E
QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
options: A)60 B)80 C)100 D)120 E)140
SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 160 books were paperbacks, the dealer would earn a profit of $320.
Since the actual profit was $400, the dealer must have sold 80 hardbacks.
Then the number of paperbacks sold was 160-80 = 80.
The answer is B. #### B
QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?
options: A)3 B)4 C)6 D)9 E)12
SOLUTION:yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:
A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?
So for a job to be done in 2 hours R = 1/2
R_a(Rate of Machine R) = 1/36
R_s(Rate of Machine S) = 1/36
Lets say x machines are used to attain the desired rate, thus
x/36+x/36 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)
(x+x)/36 = 1/2
2x/36 = 1/2
x = 9.
QA = 9 (ANSWER D) #### D
QUESTION:The length of the room is 3m and width is 3m. Find the cost of paving the floor by slabs at the rate of Rs.300 per sq meter?
options: A)1800 B)1500 C)1700 D)1600 E)1540
SOLUTION:l=3m w=3m
area of the floor = 3 x 3 = 9 sq m
cost of paving = 200 x 9 = Rs. 1800
Answer: A #### A
QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m?
options: A)1350 B)1357 C)2025 D)2052 E)2122
SOLUTION:Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 3 = Rs.2025
Answer:C #### C
QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55
SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;
A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents.
Answer: C. #### C
QUESTION:If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend?
options: A)$30.60 B)$72.60 C)$70.60 D)$40.60 E)$50.60
SOLUTION:The tip is 20% of what he paid for lunch. Hence
tip = 20% of 60.50 = (20/100)*60.50 = $12.1
Total spent
60.50 + 12.1 = $72.6
correct answer B #### B
QUESTION:Sandy bought 65 books for $1480 from one shop and 55 books for $920 from another shop. What is the average price that Sandy paid per book?
options: A)$38 B)$18 C)$99 D)$27 E)$20
SOLUTION:average price per book = (1480 + 920) / (65 + 55) = 2400 / 120 = $20
The answer is E. #### E
QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 7.
options: A)150 B)152 C)154 D)158 E)160
SOLUTION:D = d * Q + R
D = 17 * 9 + 7
D = 153 + 7
D = 160
ANSWER E #### E
QUESTION:The sum of four consecutive even numbers is 292. What would be the smallest number?
options: A)74 B)76 C)70 D)68 E)65
SOLUTION:Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
ANSWER:C #### C
QUESTION:What is the decimal equivalent of (1/2)^2?
options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5
SOLUTION:(1/2)² = (1/2)(1/2)= 1/4
APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25
D #### D
QUESTION:If y exceeds x by 25%, then x is less than y by?
options: A)20% B)16 3/3% C)16 2/3% D)12 2/3% E)16 1/3%
SOLUTION:X=100 y=125
125------25
100-------? => 20%
Answer:A #### A
QUESTION:A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.15 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
options: A)1276 B)1200 C)2832 D)1800 E)1236
SOLUTION:Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 15 = 1800
Answer: Option D #### D
QUESTION:If an amount of Rs 41,910 is distributed equally
amongst 22 persons, how much amount would each
person get?
options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None
SOLUTION:Required amount =41910/22 = Rs 1905
Answer A #### A
QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km
SOLUTION:Explanation:
Speed in still water = 6 kmph
Speed of the current = 1 kmph
Speed downstream = (6+1) = 7 kmph
Speed upstream = (6-1) = 5 kmph
Let the required distance be x km
Total time taken = 1 hour
⇒ x/7+x/5=1
⇒5x+7x=35
⇒12x=35
⇒x=2.9 km
Answer: Option C #### C
QUESTION:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of t feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?
options: A)5,280(x/t) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280
SOLUTION:In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet.
The number of revolutions = distance/circumference = 5,280x/t.
Answer: A. #### A
QUESTION:One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel?
options: A)400 B)450 C)500 D)550 E)600
SOLUTION:The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour.
The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours.
The answer is A. #### A
QUESTION:1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:1/5 , 1/2 , 1/3
1/5*2 , 1/2*2 ,1/3*2
1/5*3 , 1/2*3 ,1/3*3
1/5*4 , 1/2*4 ,1/3*4
so
1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,2
ANSWER:B #### B
QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
options: A)10hours B)12hours C)8hours D)5hours E)15hours
SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10
The leak will empty the tank in 10hours
Answer is A #### A
QUESTION:How many digits are required to number a book containing 260 pages?
options: A)784 B)672 C)492 D)372 E)300
SOLUTION:9 pages from 1 to 9 will require 9 digits.
90 pages from 10 to 99 will require 90*2=180 digits.
260-(90+9)=161 pages will require 161*3=483 digits.
The total number of digits is 9+180+483=672.
The answer is B. #### B
QUESTION:Three (rather lazy) men A, B and C working together can do a work in 5 days. They start the work together and A works for 1 day and takes rest on the second day, B works for 2 days and takes rest on the next two days and C works for 2 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)
options: A)7 days B)8 days C)9 days D)10 days E)11 days
SOLUTION:Total work is 3*5 = 15 units.
A does 1 day of work every 2 days.
B does 2 days of work every 4 days.
C does 2 days of work every 5 days.
Test the options.
In 7 days:
A will do 1*3 + 1 = 4 units (3 complete cycles and 1 day of work).
B will do 2*1+ 2= 4 units (1 complete cycle, 2 days of work, and 1 day of rest).
C will do 2*1 + 2 =4 units (1 complete cycle and 2 days of work).
Total = 4 + 4 + 4 = 12 units.
In 8 days:
A will do 1*4 = 4 units (4 complete cycles).
B will do 2*2= 4 units (2 complete cycles).
C will do 2*1 + 2 =4 units (1 complete cycle, 2 days of work, and 1 day of rest).
Total = 4 + 4 + 4 = 12 units.
In 9 days:
A will do 1*4 + 1 = 5 units (4 complete cycles and 1 day of work).
B will do 2*2+ 1 = 4 units (2 complete cycles and 1 day of work).
C will do 2*1 + 2 = 4 units (1 complete cycle, 2 days of work, and two days of rest).
Total = 5 + 5 + 4 = 14 units.
In 10 days:
A will do 1*5 = 5 units (5 complete cycles).
B will do 2*2+ 2= 6 units (2 complete cycle and 2 days of work).
C will do 2*2 =4 units (2 complete cycles).
Total = 5 + 6 + 4 = 15 units.
Therefore, the answer is D. #### D
QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)20, 35, 48 E)None of these
SOLUTION:Let the present ages are 4x, 7x, 9x.
=> (4x-8) + (7x-8) + (9x-8) = 56
=> 20x = 80
=> x = 4
So their present ages are: 16,28,36
ANSWER:B #### B
QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
options: A)19 B)19.7 C)19.9 D)21.7 E)22.8
SOLUTION:Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B) #### B
QUESTION:Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many straight lines can be formed by joining them ?
options: A)124 B)144 C)134 D)142 E)143
SOLUTION:The number of straight lines formed joining the 18 points, taking 2 at a time = 18C2=153. Number of straight lines formed by joining the 5 points, taking 2 at a time =5C2=10. But 5 collinear point, when joined pairwise give only one line. Required number of straight lines =153-10+1 =144. Answer :B #### B
QUESTION:The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria
options: A)10 B)12 C)14 D)16 E)18
SOLUTION:The question basically asks how many minutes it takes for a population to increase by factor 50(50,000 / 1,000 = 50).
Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:
2^x >= 50, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^6 = 64, i.e. the population has to double 6 times.
Since it takes the population 2 minutes to double once it takes 6*2 minutes = 12 minutes to double nine times.
Thus, solution B = 12 is correct. #### B
QUESTION:Find the product of the localvalue and absolutevalue of 4 in 20468?
options: A)1000 B)1100 C)1200 D)1300 E)1600
SOLUTION:Local value of 4 = 4 x 100 = 400
Place value of 4 = 4
There fore = 4 x 400 = 1600
E #### E
QUESTION:The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
options: A)1:3 B)2:5 C)3:2 D)9:4 E)4:2
SOLUTION:Explanation:
Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
Answer: Option B #### B
QUESTION:A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
options: A)1/10 B)1/8 C)1/6 D)1/5 E)1/4
SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 5*3*2=30.
P(dispensing one of each color)=30/120=1/4.
The answer is E. #### E
QUESTION:Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds?
options: A)186 B)130 C)180 D)181 E)120
SOLUTION:LCM of 9, 12, 15 and 18 is
180
LCM=180
ANSWER:C #### C
QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg?
options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42
SOLUTION:1000*(25/100) = 250 ---- 5
? ---- 1
=> Rs.50
Answer: A #### A
QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996?
options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3
SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A
QUESTION:Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 12% vinegar, dressing P comprises what percentage of the new dressing?
options: A)50% B)40% C)30% D)20% E)10%
SOLUTION:Let x be the percentage of dressing P in the new dressing.
0.3x + 0.1(1-x) = 0.12
0.2x = 0.02
x = 0.1 = 10%
The answer is E. #### E
QUESTION:Tough and Tricky questions: Work/Rate Problems.
If it takes 80 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?
options: A)40/3 B)11 C)7 D)8 E)9/7
SOLUTION:80 Workers = 3 hours then,
1 Worker = 3*80 Hours
30 Workers = (3*80) /(30) = 8 Answer.D #### D
QUESTION:The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
options: A)15% B)32% C)44% D)62% E)80%
SOLUTION:Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 .
So overall increase is from 100 to 144 is 44%
Answer C #### C
QUESTION:If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12.
options: A)6 B)1 C)3 D)8 E)7
SOLUTION:Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3
If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3
When divided by 12, it must leave a remainder of 3.
The answer is C. #### C
QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ?
options: A)95 B)110 C)20 D)None of these E)Cannot be determined
SOLUTION:Solution
2/5of 350 - 4/7of 210 = 20.
Answer C #### C
QUESTION:In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
options: A)-4/3 B)1/4 C)-4 D)3/4 E)4/3
SOLUTION:The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A. #### A
QUESTION:In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters?
options: A)125.5 meters B)126.5 meters C)127.5 meters D)128.5 meters E)None of these
SOLUTION:Explanation:
When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters.
Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters.
So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C.
So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters.
Answer: C #### C
QUESTION:31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 12 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
options: A)A)11 B)B)23 C)C)24 D)D)29 E)D)36
SOLUTION:lets solve by creating equation..
W = 31..
Total = 50..
Not W = 50 -31= 19..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..
so who won Nobel but not Wolf = x+3 = 11..
But people who won BOTH W and N = 12..
so total who won N = 11+12 = 23..
B #### B
QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered?
options: A)60% B)28% C)30% D)56% E)73%
SOLUTION:Let C.P. be Rs. 100.
Then, S.P. = Rs. 121.60
Let marked price be Rs. x. Then, 95/100 x = 121.60
x = 12160/95 = Rs. 128
Now, S.P. = Rs. 128, C.P. = Rs. 100
Profit % = 28%.
Answer: B #### B
QUESTION:A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform?
options: A)45 B)47 C)49 D)51 E)53
SOLUTION:Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 14 * 10 = 140 m.
The time taken to pass the platform = (140 +370)/ 10 = 51 seconds
The answer is D. #### D
QUESTION:A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago?
options: A) 8 B) 10 C) 12 D) 14 E) 7
SOLUTION:Let's say
Age of Richard isR
Age of David isD
Age of Scott isS
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 7 years ago?
i.e. D-7 = 14-7 = 7 years
Answer: Option
E #### E
QUESTION:In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,-5) and (t,-7). What is the least possible value of the slope of line L?
options: A)6 B)-1 C)-2 D)-6 E)-10
SOLUTION:We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,-5). hence, x= p and Y=-5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (-7+5)/(4-2) = -1
IMO option B is correct answer. #### B
QUESTION:The average of first ten prime numbers which are odd is?
options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5
SOLUTION:Sum of first 10 prime no. which are odd = 158
Average = 158/10
= 15.8
Answer:D #### D
QUESTION:Which of the following must be divisible by 4, given that y is a positive integer?
options: A)(y−1)*y*(y+3) B)y^2*(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3)
SOLUTION:option A) (y−1)*y*(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A
QUESTION:Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 55% nuts, what percent of the combined mixture is dried fruit?
options: A)8.5% B)11.7% C)14.2% D)17.6% E)20.5%
SOLUTION:55% is 25%-points above 30% and 5%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 1:5.
1/6*70% = 11.7%
The answer is B. #### B
QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage.
options: A)4 B)2 C)1 D)3 E)None of them
SOLUTION:cost price=rs27.50, sp=rs 28.50
gain=rs(28.50 –27.50)=rs1.10
so gain%={(1.10/27.50)*100}=4%
Answer is A. #### A
<<<Examples ends
QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
options: A)1000 B)817 C)278 D)268 E)280
SOLUTION:2 * 22/7 * 1.75 * x
= 11000
x = 1000
Answer: A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1
SOLUTION:1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: C #### C
QUESTION:The sale price sarees listed for Rs.528 after successive discount is 20% and 10% is?
options: A)288 B)277 C)380 D)290 E)262
SOLUTION:528*(80/100)*(90/100)
= 380
Answer: C #### C
QUESTION:Calculate the circumference of a circular field whose radius is 6 centimeters.
options: A)2 π cm B)1 π cm C)15 π cm D)12 π cm E)19 π cm
SOLUTION:Circumference C is given by
C = 2πr = 2π*6 = 12 π cm
Answer: D #### D
QUESTION:A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
options: A)$4,040 B)$4,120 C)$1,960 D)$4,920 E)$1,400
SOLUTION:In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost.
Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $5,000-$880=$4,120.
Answer: B. #### B
QUESTION:What is the remainder when 25472 is divided by 2?
options: A)3 B)1 C)8 D)7 E)0
SOLUTION:If the digit in unit place is even, the number will be divisible by 2.
2 is an even number,so the number is divisible by 2
ANSWER:0 #### E
QUESTION:Two trains leave the same train station at 6:00 am and 6:45 am and they travel at 100 kph and 125 kph respectively. How many kilometers from the train station will the two trains be together?
options: A)300 B)325 C)350 D)375 E)400
SOLUTION:At 6:45, the first train is 75 km ahead.
The second train gains 25 km each hour.
The time it takes the second train to catch the first train is 75 / 25 = 3 hours.
In this time, the second train travels 3*125=375 km.
The answer is D. #### D
QUESTION:x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b?
options: A)24 B)21 C)20 D)17 E)15
SOLUTION:Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20.
Answer: C. #### C
QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers?
options: A) 3 B) 7 C) 5 D) 9 E) 12
SOLUTION:If x=6 and y=4, then x^2-y^2=20and 20 is divisible only by 5 from the options, thus it must be correct.
Answer: C. #### C
QUESTION:How many words can be formed by using all letters of the word “BIHAR”
options: A)452 B)320 C)365 D)456 E)120
SOLUTION:The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
Ans: E #### E
QUESTION:By selling an umbrella for Rs. 300, a shop keeper gains 200%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
options: A)50 B)25 C)400 D)200 E)150
SOLUTION:Marked price = Rs. 300
C.P. = 100/300 * 300 = Rs. 100
Sale price = 90% of Rs. 300 = Rs. 270
Required gain % = 200/100 * 100 = 200%.
Answer:D #### D
QUESTION:The population of a town is 10000. It increases annually at the rate of 25% p.a. What will be its population after 2 years?
options: A)14000 B)14400 C)14500 D)15625 E)14700
SOLUTION:Formula :
10000 × 125/100 × 125/100 = 15625
Answer : D #### D
QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
options: A)299 B)267 C)269 D)400 E)276
SOLUTION:2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D #### D
QUESTION:A factory produces 6000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
options: A)4436 toys B)1500 toys C)6113 toys D)2354 toys E)1375 toys
SOLUTION:To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
6000 /4 = 1500 toys
correct answer B #### B
QUESTION:For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is?
options: A)between 2 and 20 B)between 10 and 20 C)between 20 and 30 D)between 30 and 40 E)greater than 40
SOLUTION:SOL:
Lets consider h(100):
=> 2*4*6*8.........*98*100
=> (2*1) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50)
=> (2^50) * (1*2*3*4........*49*50)
=> h(100) = (2^50) * (50!)
We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100).
But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50;
ANSWER:E #### E
QUESTION:If Susan can paint a house in 4 hours, and Jeff can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
options: A)2.4 hr B)2.6 hr C)3.0 hr D)5.0 hr E)5.2 hr
SOLUTION:If Susan can paint the house in 4 hours, then in 1 hour she can paint 1/4 of the house.
If Jeff can paint the house in 6 hours, then in 1 hour he can paint 1/6 of the house.
Let x = number of hours it would take them together to paint the house so,
1/4 + 1/6 = 1/x
x=12/5 or 2.4 hours
Answer: A #### A
QUESTION:Kate and her boyfriend Ben, completed the painting of their new apartment together in 6 days.If they were to work separately, how long will it take each of them to complete it, if Ben can complete the painting 5 days earlier than Kate.
options: A)6 and 11 B)5 and 10 C)10 and 15 D)8 and 13 E)6 and 10
SOLUTION:Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job.
Answers E, A and C are illogical, since the individual times must both be greater than 10 days.
so we can TEST the values for Answers B and D.
Using the values for Answers C and D...
Answer C: (10)(15)/(10+15) = 150/25 = 6 This is a match
Final Answer:
C #### C
QUESTION:A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 63 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?
options: A)14 B)45 C)54 D)65 E)81
SOLUTION:Just check the answers and reverse the numbers until you get 63.
81 - 18 = 63
Answer E #### E
QUESTION:There are between 100 and 110 marbles in a collection of cards. If they are counted out 3 at a time, there are 1 left over, but if they are counted out 4 at a time, there is 4 left over. How many marbles are in the collection?
options: A) 100 B) 103 C) 106 D) 108 E) 109
SOLUTION:Let number of cards = x
If the cards are counted 3 at a time , there are 2 left over-
x = 3p+1
x can take values 100 , 104 , 109
If the cards are counted 4 at a time , there is 1 left over
x= 4q+4
x can take values 100 , 108
Therefore , x = 100
Answer A #### A
QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 4 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
options: A)1.6 B)1 C)0.4 D)0.16 E)0.016
SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*16*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 160/10,000 = 16/1000 = 0.016 ft
The answer is E. #### E
QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8?
I. x^2
II. y^2
III. xy
options: A)I only B)II only C)III only D)I and II only E)I, II and III
SOLUTION:4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is C #### C
QUESTION:Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Let x be the number of shelves.
11x - 30 = 7(x-1) + 5
4x = 28
x = 7
The answer is C. #### C
QUESTION:Shreyas bought an article and sold it for 112% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42750/-?
options: A)Rs.24600 B)Rs.38169 C)Rs.38989 D)Rs.23200 E)None of these
SOLUTION:Explanation:
112% of CP = Rs.42750
:. CP = Rs.42750x100/112 = Rs.38169.
Answer: Option B #### B
QUESTION:In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ?
options: A)100 B)72 C)110 D)135 E)145
SOLUTION:Explanation :
Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x.
.'. 60% of x = 36 +5/6 *36
=>60/100 * x = 66
=>x = 110
Answer : C #### C
QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94
SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 96, there are 47 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (47 + 12)/94
= 59/94
= 5/8
Ans is E #### E
QUESTION:Rahul went to a shop and bought things worth Rs. 28, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
options: A)Rs 15 B)Rs 12.10 C)Rs 22.70 D)Rs 26.80 E)None of these
SOLUTION:Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 28 - 5 - 0.30
=22.70
Answer : C #### C
QUESTION:4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there.
options: A)6! x 7P4 B)6! x 9P4 C)6! x 5P4 D)6! x 3P4 E)6! x 2P4
SOLUTION:Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways.
So total ways are 6! x 7P4
Answer:A #### A
QUESTION:We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $390. How many math books did we buy?
options: A)57 B)60 C)63 D)66 E)69
SOLUTION:M + H = 90
H = 90 - M
4M + 5H = 390
4M + 5*(90 - M) = 390
M = 60
The answer is B. #### B
QUESTION:A sum is divided between A and B in the ratio of 1 : 2. A purchased a car from his part, which depreciates 14 2/7% per annum and B deposited his amount in a bank, which pays him 20% interest per annum compounded annually. By what percentage will the total sum of money increase after two years due to this investment pattern (approximately).
options: A)22.48% B)20.48% C)24.48% D)25.48% E)26.48%
SOLUTION:Let the total money=300
A's part=100
B's part=200
After 2 years A's part=73.46 (As it depreciates by 14.29% per annum)
After 2 years B's part=288 (using the compound interest formula, A=P(1+r/n)^nt), where
P=200,r=0.2,n=1,t=2)
So, After 2 years total amount=361.46
Therefore % increase in money=(361.46-300)*100/300=20.48%
ANSWER:B #### B
QUESTION:A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ?
options: A)650 meter B)555 meter C)500 meter D)458 meter E)None of these
SOLUTION:Explanation:
Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
=>800+x=65/3∗60
=>800+x=20∗65=1300
=>x=1300−800=500
So the length of the tunnel is 500 meters.
Option C #### C
QUESTION:A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10?
options: A) 0 B) 1 C) 2 D) 3 E) 5
SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since{Neither}=0(allare even or multiple of 5) then:
18 = 6 + 12 - {Both} + 0;
{Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: A. #### A
QUESTION:What is the tens digit of 7^1415?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
1415= 4*353 + 3
The ten's digit will be 4 .
Answer E #### E
QUESTION:What is the sum of all four digit integers formed using the digits 3 ,4 ,5 and 6 (repetition is allowed)
options: A)1279874 B)1279872 C)1279875 D)1279876 E)1279870
SOLUTION:n = 4 * 4 * 4 * 4 = 256
<x> = (6666 + 3333) / 2 = 4999.5
Sum = number of integers x average value
n * <x> = 256 * 4999.5 = 1279872
answer = B #### B
QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
options: A)2 cm B)7 cm C)1 cm D)4 cm E)9 cm
SOLUTION:Explanation:
Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h = 9 cm
Answer: Option E #### E
QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
options: A)1.7 B)1.4 C)1.1 D)1.5 E)1.2
SOLUTION:M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D #### D
QUESTION:How many numbers amongst the numbers 5 to 30 are there which are exactly divisible by 6 but not by 4?
options: A)Nil B)1 C)2 D)3 E)More than 3
SOLUTION:6,12,18,24,30 are divisible by 6.
12, 24 are divisible by 4 also.
So there are 3 numbers exactly divisible by 6 but not by 4
ANSWER:D #### D
QUESTION:Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.
options: A)5113 B)5117 C)5120 D)8119 E)10115
SOLUTION:Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, D,E The answer to be C
Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year.
If x = initial number of trees = 5120
Year 1 = 5/4x
Year 2 = (5/4)(5/4)x
Year 3 = (5/4)(5/4)(5/4)x
Year 4 = (5/4)(5/4)(5/4)(5/4)x
Only for Answer D: (5/4)(5/4)(5/4)(5/4) 5120 = 12500
Hence, correct answer = C #### C
QUESTION:John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?
options: A)1/16 B)5/16 C)3/8 D)1/2 E)1/4
SOLUTION:John will run farther if he runs at 5 mph and Amanda runs at 4 mph.
P(John runs farther) = 1/4 * 1/4 = 1/16
The answer is A. #### A
QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
options: A)12 B)18 C)22 D)24 E)none of these
SOLUTION:Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x 27 * x = 36 * 18
x = (36 * 18)/27
x = 24.
Answer is D. #### D
QUESTION:A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
options: A)A)300 B)B)350 C)C)450 D)D)470 E)E)500
SOLUTION:Explanation:
10 * 150 = 1500
4 * 100 + 5 * 150 = 1150
1500 – 1150 =350
B #### B
QUESTION:A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum?
options: A)337 B)268 C)198 D)697 E)168
SOLUTION:1200 = P [1 + (12*6)/100]
P = 697'
Answer:D #### D
QUESTION:If
1 = 6
2 = 12
3 = 18
4 = 24
5 = 30
6 = 36
Then 24 = ?
Hint: Its a logic Riddle not a mathematical riddle
options: A)1 B)2 C)4 D)6 E)8
SOLUTION:C
24
As stated
4=24 => 24=4
Answer is C #### C
QUESTION:A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
options: A)227 B)400 C)230 D)288 E)271
SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 42 = 50/3
3(x + 300) = 2100 è x = 400m.
Answer: B #### B
QUESTION:Which number is the odd one out?
159
248
951
357
122
582
options: A)951 B)246 C)325 D)147 E)852
SOLUTION:A
951
In the rest there is the same difference between each digit, eg: 9(–4) 5 (–4)1 #### A
QUESTION:What is the median from the below series 90, 93, 93, 88, 95, 88, 97, 87, and 98
options: A)80 B)85 C)93 D)97 E)100
SOLUTION:Ordering the data from least to greatest, we get:
87, 88, 88, 90, 93, 93, 95, 96, 98
The median quiz score was 93. (Four quiz scores were higher than 93 and four were lower.)
C #### C
QUESTION:A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?
options: A)15002 B)15001 C)15000 D)15007 E)15009
SOLUTION:Principal = (100 * 5400) / (12 * 3) = Rs. 15000.Answer:C #### C
QUESTION:How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest?
options: A)2.35 years B)4.25 years C)7 years D)1.25 years E)2 years
SOLUTION:Explanation:
Time = (100 x 60)/(400 x 12) years
= 1.25 years.
Answer: D #### D
QUESTION:Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 192, what is the area of the side face of the box?
options: A)13 B)16 C)18 D)29 E)32
SOLUTION:Lets suppose length= l, breadth= b, depth= d
Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l)
top face area= w*d
side face area= w*d = 1.5 d*l (w=1.5l)
Volume = l*w*d= 192
l*1.5l*2l= 192
l=4
Side face area= l*d= l*2l= 4*2*4
=32
E is the answer #### E
QUESTION:Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ?
options: A)500 B)600 C)450 D)550 E)None of these
SOLUTION:Explanation:
Let the lent at 5% be 'A'
(A x 5 x 1)/100 + [(1500 - A)x 6 x 1]/100 = 85
5A/100 + 90 – 6A/100 = 85
A/100 = 5
=> A = 500
ANSWER IS A #### A
QUESTION:The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000?
options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796.
SOLUTION:30,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option B fulfills the condition and hence is the answer #### B
QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
options: A)10 B)12 C)16 D)18 E)21
SOLUTION:Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B #### B
QUESTION:There are 136 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
options: A)15 B)11 C)12 D)13 E)14
SOLUTION:IMO 15
Take each answer choice and substract it from 136 and the divided this with 11. A #### A
QUESTION:Find the value of x. (47% of 1442 - 36% of 1412) + 66 = x?
options: A)1 B)2 C)3 D)6 E)5
SOLUTION:D) 6 #### D
QUESTION:What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
options: A)$788 B)$812 C)$864 D)$878 E)$912
SOLUTION:After one year: 1.2 * $500
After two years: (1.2)^2 * $500
After three years: (1.2)^3 * $500 = $864
The answer is C. #### C
QUESTION:Find the odd man out
2, 5, 10, 17, 26, 37, 50, 64
options: A)50 B)26 C)64 D)27 E)17
SOLUTION:Difference is series of ODD numbers
2+3 = 5
5+5 =10
10+7=17
17+9=26
26+11=37
37+13=50
50+15=65
ANSWER:C #### C
QUESTION:During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.6 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?
options: A)$2.5 B)$2.55 C)$1.51 D)$3.25 E)$3.0
SOLUTION:finding the Harmonic mean here.
HM = 4/(1/12 + 1/14 + 1/16 + 1/21) = 15.1
C #### C
QUESTION:For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y?
options: A)14 B)12 C)10 D)16 E)18
SOLUTION:we know that : x > 1, y > 1, and x + 3y < 1000,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 =1024 (it exceeds 920, so, x can't be 2^10)
so, max value that X can take is 2^9 , for which has length of integer is 9.
now, since x =512 ,x+3y<920
so, 3y<408
==> y<136
so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7
for 2^7 has length of integer is 7.
SO, combined together : 9+7 = 16.
D #### D
QUESTION:Walking 4/3 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
options: A)22 B)16 C)27 D)28 E)20
SOLUTION:Speed Ratio = 1:4/3 = 3:4
Time Ratio = 4:3
1 -------- 4
4 --------- ? 16 m.Answer:B #### B
QUESTION:A single discount equivalent to the discount series of 10%, 10% and 5% is?
options: A)23.05 B)31.95 C)21.65 D)23.45 E)23.15
SOLUTION:100*(90/100)*(90/100)*(95/100) = 76.95
100 - 76.95 = 23.05
Answer: A #### A
QUESTION:How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible?
options: A)4C3+4 B)4C3+9 C)4C3+2 D)4C3 E)4C3+6
SOLUTION:So 4C3 for abcd - 4 choices
3 more for dd(b,c or a)
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 4C3+9
Ans : B #### B
QUESTION:At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A).
At what time will car B pass car A?
options: A)12 pm B)1 pm C)2 pm D)3 pm E)4 pm
SOLUTION:After t hours the distances D1 traveled by car A is given by
D1 = 40 t
Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by
D2 = 60 (t-1)
When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives
40 t = 60 (t-1)
Solve the above equation for t to find
t = 3 hours
Car B passes car A at
9 + 3 = 12 pm
Answer A #### A
QUESTION:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
options: A)1/15 B)4/5 C)4/15 D)1/5 E)2/5
SOLUTION:tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x)
hence 1/5
D #### D
QUESTION:A no. x when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
options: A)1 B)4 C)9 D)11 E)13
SOLUTION:221 + 43 = 264/17 = 9 (Remainder)
C #### C
QUESTION:If 5^29 * 4^15 = 2 * 10^n, what is the value of n?
options: A)11 B)21 C)22 D)29 E)32
SOLUTION:My attempt:
5^(29) * 4^(15) = 2*10^p
5^(29) * 2 ^ (30) = 2 * (2*5)^p
5^(29) * 2 ^ (30) = 2 * 2^(p) * 5^(p)
5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p)
=> (p+1) = 30
=> p = 29
Answer: 29 (D) #### D
QUESTION:A shop owner sells 56 apples and gains SP of 16 apples. Find the gain %?
options: A)30% B)40% C)50% D)56% E)78%
SOLUTION:Gain=16 apples
Total 56 apples
CP 56-16=40
(16/40)*100
=40%
Ans B #### B
<<<Examples ends
QUESTION:A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?
options: A)3/4 B)1 C)4/3 D)2 E)7/2
SOLUTION:This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k.
{{k + 4}/4} = k
k + 4 = 4k
4 = 3k
k = 4/3
Answer = C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
options: A)13/109 B)13/162 C)13/111 D)13/102 E)13/112
SOLUTION:Let S be the sample space.
Then, n(S) = \inline {\color{Black}52C_{2} }=(52 x 51)/(2 x 1) = 1326.
Let E = event of getting 1 spade and 1 heart.
n(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = \inline {\color{Black}13C_{1}\times 13C_{1} } = 169.
P(E) = n(E)/n(S) = 169/1326 = 13/102.
Answer: D) 13/102 #### D
QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
options: A)19% B)11% C)18% D)218% E)14%
SOLUTION:Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer:C #### C
QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 5: 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
options: A)A)1:5 B)B)1:1 C)C)1:8 D)D)1:9 E)E)1:3
SOLUTION:Number of men in the colony = 5/7 * 70 = 50.
Number of women in the colony = 2/7 * 70 = 20.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 50 - 10 = 40.
Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4.
Answer:A #### A
QUESTION:If x is a sum of all even integers on the interval 13...55 and y is their number, what is the GCD (x, y)?
options: A) 1 B) 21 C) 26 D) 52 E) 1014
SOLUTION:x = 14 + 16 + ... + 54 = (largest + smallest)/2 *(# of terms) = (14 + 54)/2*21= 34*21.
GCD of 21 and 34*21 is 21
Answer: B. #### B
QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show?
options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30
SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour.
The two clocks show 2:00 at 2 0'clock
At 3:00 -
Clock B is at 3:00
Clock A is at 3:20 (1 hour + gains 20 minutes)
AT 4:00 -
Clock B is at 4:00
Clock A is at 4:40 (2 hours + gains 40 minutes)
In 4 hours the clock A gains 4*20=80 minutes or 1 hour 20 minutes
If clock A is at 7:20 the clock B is at 6:00
Answer is B #### B
QUESTION:Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics?
options: A)7/12 B)4/9 C)5/9 D)1/4 E)2/3
SOLUTION:Lets pick smart numbers. Total number of students: 12
Biology (1/2): 6
Chemistry (1/3): 4
Physics (1/6): 2
After leaving school
Biology: 4
Chemistry: 4
Physics: 1
New Total number of students: 9
Biology and Physics: 5
Answer 5/9 or C #### C
QUESTION:If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is:
options: A)8 B)9 C)12 D)14 E)13
SOLUTION:Let the numbers be x and y
Then x2-y2=39
And x-y=3
We get x+y=13
Solving x-y=3, x+y=13
X=8, y=5
Larger number 8
ANSWER A 8 #### A
QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
options: A)25 B)34 C)50 D)67 E)50
SOLUTION:Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 6 oz can = 300 oz/6 oz = 50
Answer E, 50 cans #### E
QUESTION:The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y?
options: A)7/9 B)14/9 C)7/18 D)11/13 E)It Cannot Be Determined
SOLUTION:Ratio = 7k/9k = 7/9, 14/18, etc.
v and y are increased by 4 --> (7k + 4)/(9k + 4)
New ratio can be 11/13, 18/22, etc.
Answer: E #### E
QUESTION:One computer can upload 100 megabytes worth of data in 4 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 20 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?
options: A) 6 B) 2.5 C) 9 D) 11 E) 13
SOLUTION:Since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4*5=20 seconds it can upload 5*100=500 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-500=800 megabytes worth of data. The second computer can upload 100 megabytes of data in 2.5 seconds.
Answer: B. #### B
QUESTION:The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
options: A)39 B)41 C)42 D)43 E)44
SOLUTION:Total age of mother and 6 children = avg x n = 9 x (6+1)= 63
If mother is excluded new average is (9 - 5) = 4
so for 6 children = 6 x 4 =24
so mother's age is 63 - 24 =39
Answer: Option A #### A
QUESTION:If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n?
options: A)10 B)12 C)15 D)18 E)20
SOLUTION:There are 10 numbers divisible by 2
There are 5 numbers divisible by 4
There are 2 numbers divisible by 8
There is 1 number divisible by 16.
Hence the total number of 2’s in 20! are 10+5+2+1=18
ANSWER:D #### D
QUESTION:What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5?
options: A)1 B)3 C)2 D)4 E)5
SOLUTION:Only the unit's digit of the product will decide the remainder when divided by 5.
Hence, 1*4*3= will give units digit as 2
So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2.
Option C #### C
QUESTION:Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm.
options: A)25 B)45 C)35 D)15 E)40
SOLUTION:Required length = H.C.F. of 495 cm, 900 cm and 1665 cm.
495 = 32 x 5 x 11, 900 = 22 x 32 x 52, 1665 = 32 x 5 x 37.
Therefore, H.C.F. = 32 x 5 = 45.
Hence, required length = 45 cm.
Answer is B. #### B
QUESTION:Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?
options: A)20% B)17% C)4.0% D)3.3% E)2.8%
SOLUTION:20/6 =3.33
Answer : D #### D
QUESTION:A man has some hens and cows. If the number of heads be 44 and the number of feet equals 140, then the number of hens will be:
options: A)22 B)23 C)18 D)26 E)28
SOLUTION:let hens be x and cows be y
now,
feet: x*2+y*4=140
heads: x*1+y*1=44
implies, 2x+4y=140 and x+y=44
solving these two equations, we get x=18 and y=26
Therefore, hens are 26.
ANSWER:C #### C
QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides?
options: A)3 B)6 C)5 D)9 E)1
SOLUTION:S = (1 + 2 + 7)/2
= 5 Answer:C #### C
QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15
SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B
QUESTION:When a merchant imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $94.50, what was the total value of the item?
options: A)$2,350 B)$2,850 C)$3,250 D)$3,400 E)$3,750
SOLUTION:Let x be the value in excess of $1,000.
0.07x = 94.5
x = $1,350
The total value was $1,350 + $1,000 = $2,350.
The answer is A. #### A
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
options: A)14 B)67 C)56 D)89 E)34
SOLUTION:Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer:A #### A
QUESTION:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts?
options: A)6 B)14 C)19 D)20 E)81
SOLUTION:< 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100
Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5;
TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14;
Interns who areNot Tired S= 5 + 14 = 19.
Answer: C. #### C
QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/4 meter, and then if the cable were cut at each mark, how many different size length of cable would result?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:In this particular example length (10 meter) is just extraneous information.
The location of the marks for 1/3 meter would be 4/12, 8/12, 12/12, etc...
The location of the marks for 1/4 meter would be 3/12, 6/12, 9/12, 12/12, etc...
The distances between marks are 3/12, 1/12, and 2/12.
The answer is C. #### C
QUESTION:A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.
options: A)23 days B)25 days C)21 days D)26 days E)29 days
SOLUTION:C
21 days
WC = 2:1
2x + x = 1/7
x = 1/21 => 21 days #### C
QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?
options: A)11 B)12 C)13 D)14 E)15
SOLUTION:Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q × (130/100) = 1/23
=> q = 100/(23×130) = 10/(23×13)
Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13
=> P and Q together can do the work in 13 days
Answer is C. #### C
QUESTION:In how many ways can 6 boys and 3 girls be arranged at a table if 3 girls are never together?
options: A)47520 B)45620 C)47888 D)42156 E)43210
SOLUTION:Total ways of arranging 10 person in a circle = 9! = 51840 ways
If we consider three women as one, then we have 6+1=7 persons. Arranging these seven persons in circle will take = 6! = 720 ways
And three women can arrange themselves in 3! ways
Total ways in which three women sit together in circle = 6!*3! = 4320 ways
Total ways in which three women doesn’t sit together in circle = 9! - 6!*3! = 51840 - 4320 = 47520 ways
A #### A
QUESTION:Three numbers are in the ratio 5 : 6 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 49. Find the third number?
options: A)A)54 B)B)75 C)C)48 D)D)42 E)E)63
SOLUTION:Let the numbers be 5x, 6x, 8x.
Largest number = 8x.
Smallest number = 5x.
Third number = 6x.
8x + 5x = 6x + 49
7x = 49 =>x=7
6x=42=> third number is 42.
Answer:D #### D
QUESTION:In a group of 3 boys and 2 girls can be formed out of a total of 4 boys and4 girls?
options: A)20 B)22 C)24 D)26 E)29
SOLUTION:Solution: Total number of ways = (select 3 boys from group of 4 boys) * (2 girls from group of 4 girls)
=> (4c3) * (4c2) = 24
C #### C
QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years.
options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these
SOLUTION:Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗4/100) /(P∗R∗12/100)]
=4PR /12PR=1:3
Option C #### C
QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 10 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
options: A)15 litres B)10 litres C)30 litres D)20 litres E)8 litres
SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+10)=4/5
20x=4(3x+10)
8x=40
x=5
Quantity of alcohol = (4 x 5) litres = 20 litres.
Answer is D. #### D
QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9
SOLUTION:72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B #### B
QUESTION:An enterprising businessman earns an income of Re 5 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 10th day of business, he earns an income of:
options: A)21 B)22 C)20 D)45 E)30
SOLUTION:2nd day he earns = 3(2 – 5)
3rd day he earns = 3(3 – 5)
On 20th day he earns 3(20 -5) = 45 rupees
ANSWER:D #### D
QUESTION:The average of 11 numbers is 11. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
options: A)10.4 B)11.5 C)81.5 D)11.5 E)21.5
SOLUTION:Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 11 x 11] = 10.4.
Answer: A #### A
QUESTION:If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil?
options: A)9 B)5 C)7 D)8 E)4
SOLUTION:Let the total length be xm
Then black part =x/8cm
The remaining part=(x-x/8)cm=7x/8cm
White part=(1/2 *7x/8)=7x/16 cm
Remaining part=(7x/8-7x/16)=7x/16cm
7x/16=7/2
x=8cm
Answer is D. #### D
QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2!
SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 boys are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 boys do not sit together would be: 7!-3!5!.
Answer: D). #### D
QUESTION:A fill pipe can fill 1/3 of cistern in 20 minutes in how many minutes, it can fill 3/4 of the cistern?
options: A)15 min B)45 min C)25 min D)40 min E)50 min
SOLUTION:1/3 of the cistern can fill in 20 min
3/4 of the cistern can fill in = 20*3*3/4 = 45min
Answer is B #### B
QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs?
options: A)362880 B)340009 C)250909 D)345008 E)1000
SOLUTION:number of ways =9! = 362880
Answer is A #### A
QUESTION:A day-trader plans to invest a total of $23,600 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment?
options: A)$2,800 B)$4,000 C)$3,500 D)$3,800 E)$3,900
SOLUTION:We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice).
Total of 14 minimized investments = (14)(1400) = $???600
The 15th investment + $???600 = $23,600
So, the HUNDREDS DIGITS of the 15th investment must be 0
Answer: B #### B
QUESTION:If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is?
options: A)6 B)12 C)24 D)36 E)48
SOLUTION:Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B #### B
QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0
SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B , if you put x = -5, you get -ve value for y co-ordinate.
Answer must be (B) #### B
QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly?
options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20
SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/5*1/4 = 9/10.
Answer: D. #### D
QUESTION:If n = 20! + 19, then n is divisible by which of the following?
I. 15
II. 17
III. 19
options: A)I only B)II only C)III only D)I and II E)II and III
SOLUTION:19 divides 20! so 19 also divides 20! + 19.
15 and 17 divide 20! so they do not divide 20! + 19.
The answer is C. #### C
QUESTION:The average of runs of a cricket player of 10 innings was 40. How many runs must he make in his next innings so as to increase his average of runs by 4?
options: A)87 B)16 C)10 D)84 E)17
SOLUTION:Average after 11 innings = 44
Required number of runs
= (44* 11) - (40* 10) = 484- 400
= 84.
Answer: D #### D
QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Going down = 16 m
Going Up = 8 --> Total = 24
Going down = 8 --> Total = 32
Going Up = 4 --> Total = 36
Going down = 4 --> Total = 40
Going up = 2 --> Total = 42
Going down = 2 --> Total = 44
Going up = 1 --> Total = 45
Going down = 1 --> Total = 46
Going up = 0.5 --> Total = 46.5 (Caught)
No of going downs = 5 ..
ANSWER:A #### A
QUESTION:Find the ratio between whole surfaces of a sphere and a hemisphere?
options: A)4:3 B)3:4 C)3:2 D)5:2 E)4:6
SOLUTION:4 πr2 : 3 πr2 => 4:3
ANSWER A #### A
QUESTION:Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail?
options: A)3/4 B)1/4 C)3/8 D)1/2 E)1/8
SOLUTION:Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting 3 heads
Then E = {HHH,HTH,THH,HHT}
P(E) = n(E)/n(S) =4/8 = 1/2
Answer is D #### D
QUESTION:In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60?
options: A)2.82 B)7.82 C)5.82 D)12.82 E)8.82
SOLUTION:In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65
In 85 points B give 15 since 80-65=15
In 50 points B gives=50*15/85=8.82
ANSWER:E #### E
QUESTION:A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food.
options: A)$400 B)$1400 C)$3400 D)$2400 E)$4400
SOLUTION:Part of salary left =1-(2/5+3/10+1/8)
=7/40
Let the monthly salary be $x
Then (7/40) of x=1400
X=8000
Expenditure on food=$2400
Option D #### D
QUESTION:A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
options: A)18:11 B)18:13 C)23:12 D)11:9 E)11:10
SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only.
A : B
8000*18 : (8000*8) + (4000*10)
144000 : 104000
A:B = 18:13
ANSWER:B #### B
QUESTION:The breadth of a rectangular hall is two-thirds of its length. If the area of the hall is 2400 sq metres, what is the length in metres?
options: A)120 B)80 C)60 D)40 E)None of these
SOLUTION:Let the length of the rectangular hall be ‘x’ m, then the breadth of the rectangular hall = 2x⁄3 m.
Area of hall = 2x⁄3 × x = 2x2⁄3
or, 2x2⁄3 = 2400 or x = 60 m
Answer C #### C
QUESTION:A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join?
options: A)4 months B)5 months C)6 months D)7 months E)8 months
SOLUTION:Explanation:
Assume that C was there in the business for x months
A:B:C
=40000×12:60000×10:120000 × x
=40×12:60×10:120x
=40:5×10:10 x
=8:10:2x
=4:5:x
C's share =375000 x/ 9+x=375000 x/9+x
⇒375000 x/9+x=150000
⇒375x9+x=150
⇒15x=6(9+x)
⇒5x=18+2x
⇒3x=18
⇒x=6
It means C was there in the business for 6 months. Given that B joined the business after 2 months. Hence C joined 4 months after B joined.
Answer: Option A #### A
QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
options: A)2200 B)1897 C)8799 D)2000 E)2782
SOLUTION:P(11/10)4 - P(6/5)2 = 482
P = 2000
Answer: D #### D
QUESTION:In a stack of cards, 11 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 5/6 . What is the number of cards in the stack?
options: A)10 B)11 C)12 D)15 E)18
SOLUTION:This question can be solved by TESTing THE ANSWERS.
Answer C: 12 total cards
With 12 total cards, and 11 blue cards, the probability of pulling two blue cards is...
(11/12)(10/11) = 110/132 ~= 5/6
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
C #### C
QUESTION:A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price?
options: A)$1200 B)$1300 C)$1000 D)$1700 E)$1050
SOLUTION:C
$1000
90%
104%
--------
14% ---- 140
100% ---- ? => $1000 #### C
QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
options: A)10 hours B)17 hours C)19 hours D)16 hours E)27 hours
SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A #### A
QUESTION:0.9*0.007= _________
options: A)0.063 B)0.0063 C)0.63 D)0.00063 E)63
SOLUTION:9*7=63
Sum of decimal places= 4
So, 0.9*0.007= 0.0063
ANSWER:B #### B
QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number?
options: A)10 B)60 C)30 D)40 E)50
SOLUTION:Explanation:
6:7
6x + 10 : 7x + 10 = 7 : 8
8[6x + 10] = 7[7x + 10]
48x + 80 = 49x + 70
49x - 48x = 80 - 70
x = 10
Then smallest number is = 6
6x = 60
Answer: Option B #### B
QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the
rest at 5 kmph. Find the total distance.
options: A)4 km B)5 km C)6 km D)7 km E)8 km
SOLUTION:time=distance/speed
let total distance travelled be x in 84/60 hrs
2/3 rd of x travelled in 4 km/hr
1/3 rd of distance travelled in 5 km/hr
2x/(3*4)+x/(3*5)=84/60
x=6 km
ANSWER:C #### C
QUESTION:A coin is tossed 6 times. What is the probability of getting exactly 5 heads?
options: A)3/8 B)3/16 C)5/16 D)3/32 E)7/64
SOLUTION:The number of possible outcomes is 2^6 = 64
There are 6 ways to get exactly 5 heads.
P(exactly 5 heads) = 6/64 = 3/32
The answer is D. #### D
QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
options: A)600 B)500 C)575 D)655 E)675
SOLUTION:Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
So answer is E. #### E
QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit.
options: A)1200 B)1400 C)2660 D)1600 E)1800
SOLUTION:A is a working member and for that, he receive 5% of the profit
= 5% of 7400 = 5*7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = 6500*6 : 8400*5 : 10000*3
= 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20
= 13 : 14 : 10
Share of B in the profit = 7030 * (14/37) = 190*14 = 2660
Answer is C #### C
QUESTION:The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number
options: A)400 B)256 C)120 D)490 E)None of these
SOLUTION:Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 14 * 5040
x = (14*5040)/144 = 490
Option D #### D
QUESTION:How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2.
options: A)4:3 B)4:7 C)4:9 D)4:2 E)4:1
SOLUTION:Explanation:
No explanation is available for this question!
ANSWER: A #### A
QUESTION:Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 4 = f(3x – 6)
options: A)3 B)4 C)6 D)7 E)13
SOLUTION:Answer = A = 3
f(x) = 3x – 5
2*[f(x)] – 4 = f(3x – 6)
2(3x-5) -4 = 3 (3x-6) - 5
6x - 14 = 9x - 23
x = 3 #### A
QUESTION:Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 50 people bought tickets to the concert, what was the total revenue from ticket sales?
options: A)$600 B)$740 C)$860 D)$980 E)$1,140
SOLUTION:Price of 1 ticket = 20$
Revenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )
= 10 * 12 = 120
Revenue generated from sales of next 20 tickets = 20 *(85/100 * 20 )
=20*17 = 340
Revenue generated from sales of last 20 tickets = 20 * 20
= 400
Revenue generated from sales of 50 tickets = 120 + 340 + 400
= 860 $
Answer C #### C
<<<Examples ends
QUESTION:A started a bussiness with a sum of Rs. 14000. After 4 months, B entered with an amount of Rs. 12000 and A added another 2,000 in the business. After 6 months, C entered with Rs. 20000 and 'B' withdrew Rs. 2000 from the business. What will be C's share of profit out of a total profit of Rs. 94000 at the end of 2 years.
options: A)Rs. 376000 B)Rs. 204000 C)Rs. 36000 D)Rs. 18000 E)Rs. 260000
SOLUTION:Investments--
A=14000x4+16000x20=376000
B=12000x2+10000x18=204000
C=20000x18=360000
So C's Share = 94000xC/(A+B+C)=36000
ANSWER:C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple?
options: A)225 B)228 C)230 D)231 E)235
SOLUTION:CP = 140*2+150*3+160*4+170*1=1540
SP = 1.5*1540=2310
Total no.of kgs=2+3+4+1=10
SP per kg=2310/10=231
ANSWER:D #### D
QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had?
options: A)23 B)24 C)25 D)26 E)27
SOLUTION:Explanation :
If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible
number of books = 15,17,19,21,23,25,27,29
If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible
number of books = 17,20,23,26,29
If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible
number of books = 15,19,23,27
Hence ,the common number is only 23 so it will be answer.
Answer : A #### A
QUESTION:The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
options: A)8m. B)6m. C)4m. D)2m. E)5m.
SOLUTION:Explanation:
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: Option D #### D
QUESTION:In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr?
options: A)2.0 sec B)2.8 sec C)7.5 sec D)2.3 sec E)1.5 sec
SOLUTION:Speed = 144 * 5/18
= 40 m/sec
Time taken = 80/40
= 2.0 sec.
Answer:A #### A
QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers.
options: A)28 B)30 C)32 D)34 E)36
SOLUTION:Given:
Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6)
Average = Sum of Quantities/Number of Quantities
= [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27
Simplifying we get, x = 24
Therefore,
Largest number = (x + 6) = (24 + 6) = 30
Smallest number = 24
ANSWER IS B #### B
QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her
options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger
SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1997 has to be the ring finger
Answer is (D) #### D
QUESTION:A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
options: A)8 B)9 C)10 D)20 E)30
SOLUTION:x ------- 6
(x + 10) ---- 3
x * 6 = (x + 10)3
x = 10
ANSWER:C #### C
QUESTION:Replace the ? by the correct Mathematics symbol to make the expression true 15 ? 3 ? 3 ? 5 = 20
options: A)15 ÷ 3 x 3 - 5 = 20 B)15 + 3 ÷ 3 + 5 = 20 C)15 x 3 + 3 + 5 = 20 D)15 x 3 ÷ 3 + 6 = 20 E)15 x 3 ÷ 3 + 5 = 20
SOLUTION:Answer : E #### E
QUESTION:The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A?
options: A)81 B)65 C)75 D)89 E)90
SOLUTION:A + B + C = 3 *70 = 210
A + B + C + D = 4 * 70 = 280 ---- (i)
So, D = 70& E = 70 + 3 = 73
B + C + D +E =68 * 4 = 272 --- (ii)
From Eq. (i) & (ii)
A-E = 280 –272 = 8
A = E +8 = 73 + 8 = 81
Answer : A #### A
QUESTION:Worker A takes 12 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
options: A)40 days B)40/9 days C)39/9 days D)30/9 days E)20/3 days
SOLUTION:A's one hour work = 1/12.
B's one hour work = 1/15.
(A+B)'s one hour work = 1/12+1/15 = 9/60 = 3/20.
Both A & B can finish the work in 20/3 days
E #### E
QUESTION:A shop owner has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 years. How much sale must she have in the 6th year so that she gets an average sale of Rs. 6500?
options: A)5000 B)5500 C)4991 D)5600 E)5700
SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991
C #### C
QUESTION:A student got twice as many sums wrong as he got right. If he attempted 27 sums in all, how many did he solve correctly ?
options: A)12 B)16 C)18 D)9 E)12
SOLUTION:Explanation:
Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 27 3x = 27 x = 9.
Answer:D #### D
QUESTION:A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,200 sedans in Anytown, how many motorcycles are there?
options: A)1260 B)2100 C)3600 D)3200 E)5200
SOLUTION:Let the total number of trucks = 3x
total number of sedans = 7x
total number of motorcycles = 2x
total number of sedans = 11200
=> 7x = 11200
=> x = 1600
total number of motorcycles =2x = 2*1600
=3200
Answer D #### D
QUESTION:A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not green?
options: A)15/28 B)1/4 C)9/16 D)1/32 E)1/16
SOLUTION:The question asks they will both be not green. Considering that these are draws without replacement there are following possibilities :
draw 1, draw 2
===== =====
1) Not green, green;
2) green, Not green;
3) green, green;
4) Not green, not green;
The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are green
P(4) = 6/8*5/7=15/28
1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28
A #### A
QUESTION:A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day at 1 mile faster than 2nd day for same hours. How many miles in total did she walk?
options: A)63 B)44 C)58 D)60 E)62
SOLUTION:First day - 18 miles with 3 miles per hours then total - 6 hours for that day
Second day - 4 miles per hour and 5 hours - 20 miles
Third day - 5 miles per hour and 5 hours - 25 miles
Total 18+20+25 = 63
Answer: option A. #### A
QUESTION:A grocery shop has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
options: A)4857 B)4184 C)4012 D)4991 E)5291
SOLUTION:Let the sale in the sixth month =x
Then
(6435+6927+6855+7230+6562+x)/6 =6500
=>6435+6927+6855+7230+6562+x =6×6500
=> 34009+x=39000
=> x=39000−34009
=4991
ANSWER:D #### D
QUESTION:8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged?
options: A)A.1296 B)B.1850 C)C.2880 D)D.3546 E)E.4200
SOLUTION:Glue milk and water bottlestogether: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: C. #### C
QUESTION:x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median W of x, y, and z?
I. 9
II. 10
III. 11
options: A)I only B)II only C)III only D)I and II only E)I and III only
SOLUTION:Average gives us an idea that 3 nos. are close to 10.
so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.
Let us see options.
If 9 has to be median W.
1st term has to less than 9 or equal to 9. (also maintain z-x = 3)
9 9 12 --> satisfies all conditions so 9 can be a median value.
If 11 has to be a median
3rd term has to be 11 or more than 11. (also maintain z-x = 3)
8 11 11 -->satisfies all conditions so 9 can be a median value.
Now for 10 to be median.
z+ x = 20 and z-x = 3, we wont have integer values of z.
10 cannot be a median
E is the answer. #### E
QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
options: A)No profit, no loss B)5% C)8% D)10% E)11%
SOLUTION:Explanation:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =80/100X100%=5%
ANSWER IS B #### B
QUESTION:An escalator moves towards the top level at the rate of 7 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length.
options: A)5sec B)25sec C)20sec D)15sec E)10sec
SOLUTION:Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 180/ (7+2) = 20sec
Answer : C #### C
QUESTION:Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have?
options: A)5 B)10 C)30 D)40 E)50
SOLUTION:Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)*100% = 60%
Now by Alligation Rule:
A . ......... B
20% . . . 80%
. . 60% . .
(80-60) . (60-20)
=20 : =40
Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration)
So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%)
So as per above ration Qty B mixed will be 50 gallons.
Qty of water in mixture B = 20% of 50 = 10 gallons.
ANSWER:B #### B
QUESTION:The speed of a car is 50 km in the first hour and 60 km in the second hour. What is the average speed of the car?
options: A)79 kmph B)85 kmph C)55 kmph D)23 kmph E)14 kmph
SOLUTION:S = (55 + 60)/2
= 55 kmph
Answer:C #### C
QUESTION:An seller earns an income of Re 3 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 15th day of business, he earns an income of:
options: A)19 B)22 C)25 D)20 E)36
SOLUTION:2nd day he earns = 3(2 – 3)
3rd day he earns = 3(3 – 3)
On 15th day he earns 3(15 -3) = 36 rupees
ANSWER:E #### E
QUESTION:The average of first 11 prime numbers is?
options: A)14.55 B)11.11 C)12.11 D)13.11 E)14.11
SOLUTION:Sum of 11 prime no. = 160
Average = 160/11 = 14.55
ANSWER: A #### A
QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was
options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000
SOLUTION:A+B=20000
total profit=5000
5000-2000=3000
3000;2000=3:2
then 3*20000/5=12000
ANSWER:E #### E
QUESTION:A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes?
options: A)35:1 B)Either ;35:1 C)Either 70;35:1 D)Either 55;45:1 E)Either 65;35:5
SOLUTION:Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B) #### B
QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
options: A)110 B)115 C)120 D)125 E)130
SOLUTION:Let number of notes of each denomination be x.
Then x + 5x + 10x = 640
16x = 640
x = 40.
Hence, total number of notes = 3x = 120
ANSWER :C #### C
QUESTION:If 7^t is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of t?
options: A)12 B)13 C)14 D)15 E)16
SOLUTION:So the question just means that we have to find all the multiples t of 7 between 1 to 100
So there are 14 multiples of 7 ( 7 - 98)
But 49 and 98 contain two 7's as factors
so we have to add 14 + 2 = 16
E #### E
QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2490 ?
options: A)Rs. 832 B)Rs. 830 C)Rs. 822 D)Rs. 812 E)Rs. 810
SOLUTION:Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830.
Answer: B #### B
QUESTION:If the sides of a triangle are 26 cm, 24 cm and 20 cm, what is its area?
options: A)120 B)772 C)288 D)266 E)240
SOLUTION:The triangle with sides 26 cm, 24 cm and 20 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 20 = 240 cm2
Answer: E #### E
QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
options: A)8% B)7% C)10% D)6% E)9%
SOLUTION:Explanation:
Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol,
such that Benson buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Benson spends additional 15% on petrol,
amount spent by Benson = 100× (100+15)/100 = Rs.115
Hence Quantity of petrol that he can purchase = 115/125 Litre
Quantity of petrol reduced = (1−115/125) Litre
Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8%
Answer: Option A #### A
QUESTION:You have been given a physical balance and 7 weights of 40, 42, 36, 33, 47, 52 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 169 kgs.
options: A)163 B)166 C)162 D)164 E)165
SOLUTION:67 + 52 + 47 = 166
Answer: E #### E
QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by:
I. 12 II. 24 III. 48
options: A)I B)I & III C)II D)II & III E)III
SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24.
So answer is III
Answer : E #### E
QUESTION:Adding 30% of x to x is equivalent to multiplying x by which of the following?
options: A)12.5 B)1.05 C)1.15 D)1.3 E)1.25
SOLUTION:130x/100= 1.3*x
ANSWER:D #### D
QUESTION:Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number?
options: A)7 B)9 C)11 D)13 E)15
SOLUTION:Let the three numbers be x, x+2, and x+4.
3x = 2(x+4) + 3
x = 11 and then the third number is x+4 = 15.
The answer is E. #### E
QUESTION:A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?
options: A)126 Kmph B)136 Kmph C)172 Kmph D)128 Kmph E)19 Kmph
SOLUTION:Length = Speed * time
Speed = L/T
S = 700/20
S = 35 M/Sec
Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 126 Kmph
Answer: A #### A
QUESTION:A set of 11 positive integers has an average of 20. Which of the following is the greatest possible value for the median of this set?
options: A)25 B)30 C)35 D)45 E)46
SOLUTION:for the median to bé max , we should take all the values below meadian to be the lowest and the remaining values to be the same..
here 1 is the lowest value(positive int) số thẻ lowest 5 int will equal 5..
remaining 6= 20*11-5=215..
therefore each valueof these 6 int =215/6=35
ans C #### C
QUESTION:In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
options: A)3:16. B)2:3. C)4:9 D)3:4. E)2:5.
SOLUTION:1st statement : ratio of pants
Store A : Store B
10x : 30x
X:3X
Price :
4y:3y
Total revenue
4xy : 9xy
4:9
Answer : C #### C
QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have?
options: A)9 B)12 C)18 D)28 E)36
SOLUTION:Lets take an example: find the number of factors of 100
try to represent 100 in least possible prime numbers
100= 2^2 * 5^2=p^a*q^b
no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9
similarly find the number of factors of p^3 * q^6--->a=3,b=6
(3+1)(6+1)=28 Ans D. #### D
QUESTION:A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent?
options: A)70% B)45% C)48% D)30% E)40%
SOLUTION:Explanation:
840 ---- 380
100 ---- ? => 45%
Answer: B #### B
QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 82 unique alphanumeric case sensitive characters.
options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6)
SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password
= 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways )
=82^4(1+ 82)
=82^4 * 83
Answer B #### B
QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture?
options: A)9! B)9×8! C)4x5! D)10!/2! E)10!
SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!*2! ways.
Total - Restriction =
= 6! - 5!*2! =
= 5!(6- 2!) =
= 4*5!.
Answer: C. #### C
QUESTION:If e is an integer, what is the greatest possible value for e that would still make the following statement true: 11*10^e < 1/10 ?
options: A) –4 B) –3 C) –2 D) –1 E) 0
SOLUTION:Just putting values, the LHS becomes
e=0 --> 11
e=-1 --> 11/10
e=-2 --> 11/100
e=-3 --> 11/1000
Anything lower will be smaller than 11/1000. e=-2, equality does not hold but it does for e=-3.
Answer is B. #### B
QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils?
options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44
SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 90 - 90p = 40p --> p = 9/13.
(cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44.
Answer: E. #### E
QUESTION:A car travels uphill at 30 km/hr and downhill at 70 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
options: A)32kmph B)33kmph C)34kmph D)35kmph E)37kmph
SOLUTION:avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/60=5/7;
avg speed=150/(10/3+5/7)=37kmph
ANSWER:E #### E
QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets?
options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes
SOLUTION:(350+250)t=800
600t=800
t=4/3
t=1 hour and 20 minutes
Answer: A #### A
QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean a. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than a+d?
options: A) 16% B) 32% C) 48% D) 84% E) 92%
SOLUTION:16%
________________________________________________ a+d
34%
________________________________________________ a
34%
________________________________________________ a-d
16%
since 68% lies one standard deviation from mean a, => 50% of 68% lies on either side as it is symmetric about a.
thus 16% lie below a-d and 16% lie above a+d
now below a+d = 16+34+34 = 84%
hence D #### D
QUESTION:The C.P of 10 pens is equal to the S.P of 15 pens. Find his gain % or loss%?
options: A)loss 16 2/8% B)loss 16 6/3% C)loss 16 2/3% D)loss 18 2/3% E)loss 33.33%
SOLUTION:10 CP = 15 SP
15 --- 5
100 --- ? => 33.33% (Loss)
Answer:E #### E
QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
options: A)18% B)20% C)25% D)23% E)Cannot be determined
SOLUTION:Answer: C. #### C
QUESTION:Solve below question 2x + 1 = -17
options: A)-8 B)-9 C)9 D)8 E)-7
SOLUTION:1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B #### B
QUESTION:The cost of 3 kg of sugar is $30. What will the cost of 8 kg of sugar be?
options: A)20 B)40 C)80 D)160 E)180
SOLUTION:3 kg costs $30
1 kg costs $10
8 kg costs $80
The answer is C. #### C
QUESTION:16 people can write 52 book in 12 days working 8 hour a day.then in how many day 206 can be written by 64 people?
options: A)309/26 B)309/28 C)309/22 D)319/26 E)339/26
SOLUTION:work per day epr hour per person= 52/(12*8*16) // eq-1
people= 64; let suppose day=p; per day work for 8 hours
acc. to condition
work per day epr hour per person= 206/(p*8*64) // eq-2
eq-1==eq-2;
p= 309/26
ANSWER:A #### A
QUESTION:Consider two statements
Statement 1 => If R is an integer and R=2p+1 where p is not an integer.
Statement 2 => If S is an integer and S=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of R and S respectively
options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined
SOLUTION:answer will be E
R = integer
R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even R would odd
if n odd R would be even
ANSWER IS E #### E
QUESTION:Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
options: A){2, 10} B){16, 16} C){10, 18} D){9, 11} E){7, 13}
SOLUTION:answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is one unit. therefore accepted
answer is D mean is 10 and S.D decreases minimum.
D #### D
QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
options: A)60 B)80 C)100 D)120 E)140
SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 160 books were paperbacks, the dealer would earn a profit of $320.
Since the actual profit was $400, the dealer must have sold 80 hardbacks.
Then the number of paperbacks sold was 160-80 = 80.
The answer is B. #### B
QUESTION:The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π
SOLUTION:=Square - Quarter circle
=12- pi*12/4
=12- pi*3
ANSWER:B #### B
QUESTION:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
options: A)88 B)90 C)96 D)98 E)102
SOLUTION:2 multiples-choice questions can be answered in = 4 x 4 = 16 ways
3 true-false questions can be answered in = 2x2x2 = 8 ways
But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers
Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways
Total ways to answer the quiz = 16 x 6 = 96
Answer C #### C
QUESTION:If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab is even
III. ab > 0
options: A)I only B)II only C)I and II D)I and III E)I, II, and III
SOLUTION:Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
II only.letter B #### B
QUESTION:Sum of the numbers from 1 to 35 is
options: A)630 B)660 C)670 D)450 E)None of these
SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2
Substitute n = 35.
So S20=35×36/2=630
Correct Option: A #### A
QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350
SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C #### C
QUESTION:A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is?
options: A)1250m B)1750m C)950m D)1000m E)1300m
SOLUTION:Speed = 15*5/18 = 15/18 m/sec
Distance covered in 35 minutes = 15/18 *35 *60 = 1750 m
Answer is B #### B
QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
options: A)5% B)8% C)10% D)12% E)6%
SOLUTION:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36)
= Rs. (520 + 1080)
= Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =(80/1600x 100)% = 5%.
Answer is A. #### A
QUESTION:In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ?
options: A)12 B)27 C)26 D)11 E)22
SOLUTION:Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x
= 22 or x
= 11.
Answer: D #### D
QUESTION:In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term?
options: A) 192 B) 154 C) 134 D) 174 E) 120
SOLUTION:1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times)
6 + (3 x 63) = 3 + 189 = 192
Answer A #### A
<<<Examples ends
QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted?
options: A)3 B)6 C)2 D)12 E)27
SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black.
But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2.
Answer: C. #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:How many positive factors do 160 and 96 have in common?
options: A)6 B)12 C)16 D)18 E)24
SOLUTION:The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 160 and 96 is 32
Number of factors of 32 = 6
Answer :A #### A
QUESTION:Rice weighing 3power3/4 pounds was divided equally and placed in 4 containers. how many ounces of rice were in each?
options: A)15 ounces B)25 ounces C)12 ounces D)22 ounces E)35 ounces
SOLUTION:3power3/4 / 4 pounds, = (4x3+3)/4 ponds. = (15/4) /4 ponds. = (15/4) / (1/4) ponds. = 15/16 pounds. 1 pound = 16 ounces. therefore, 15/16 pounds = 15/16*16 ounces = 15 ounces. Correct answer : (A) #### A
QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is
options: A)35 B)37 C)39 D)41 E)46
SOLUTION:Explanation:
Let B's age = x years.
Then, As age = (x+ 9) years.
(x+9+10)=2(x�10)
hence x=39.
Present age of B = 39 years
Answer: Option C #### C
QUESTION:On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 160 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
options: A)600 B)320 C)500 D)520 E)720
SOLUTION:Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 160) = 2 + 2(extra)
=> 2x - 320 = x => x = 320.
ANSWER:B #### B
QUESTION:Bernice's income is 70 percent more than Cathy's income, and Cathy's income is 65 percent less than Camilla's income. What percent of Camilla's income is Bernice's income?
options: A)54.5% B)52.5% C)59.5% D)51.5% E)55.5%
SOLUTION:Camilla's income = 100 (assume);
Cathy's income = 35 (65 percent less than Camilla's income);
Bernice's income = 59.5 (70 percent more than Cathy's income).
Thus, Bernice's income (59.5) is 59.5% of Camilla's income (100).
Answer: C #### C
QUESTION:For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?
options: A)8/5 B)5/2 C)3 D)33/25 E)4
SOLUTION:Let monthly salary for each of the 11 months except December was x, then
11x*1/10 + Nx*1/3 = 1/8(11x + Nx);
11/10 + N/3 = 1/8(11 + N)
33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66
N = 66/50=33/25
Answer: D. #### D
QUESTION:Two dice are thrown together.What is the probability that the sum of the number on the two faces divided by 4?
options: A)3/9 B)4/9 C)1/9 D)2/9 E)5/9
SOLUTION:n(s)=6*6=36
Let e be the event that the sum of the numbers on the two faces is divisible by 4
E={(1,3),(2,2),(3,1),(2,6),(3,5),(4,4),(5,3),(6,2)}
n(e)=8
p(e)=n(e)/n(s)
=8/36
=2/9
Answer is option D #### D
QUESTION:There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
options: A)410 B)490 C)493 D)455 E)445
SOLUTION:Answer: A. #### A
QUESTION:A store reduced the price of all items in the store by 12% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?
options: A)80.0 B)79.2 C)81.0 D)81.1 E)81.9
SOLUTION:consider price of the all items as $100
after a initial reduction of 12% price becomes = 0.88 *100 = $ 88
after the final reduction of 10% price becomes = 0.9* 88 = $ 79.2
price of all items on second day is 79.2% of price on first day
correct answer option B #### B
QUESTION:If the product of the integers j, k, l and m is 770, and if 1 < j< k< l< m, what is the value of j+ m?
options: A)10 B)13 C)16 D)18 E)21
SOLUTION:770 = 2 * 5 * 7 * 11
So j= 2, k= 5, l= 7, m= 11
j+ m= 2 + 11 = 13
Answer - B #### B
QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent?
options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these
SOLUTION:Let CP of an book = 100
MP of an book = 120
Discount 30 % on 120 = 36
SP of the book = 120 - 36 = 84
loss = 16%
Answer : C #### C
QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively?
options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these
SOLUTION:Y:Z = 70000 : 30000 = 7:3.
ANSWER:C #### C
QUESTION:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2?
options: A)7 B)8 C)9 D)10 E)11
SOLUTION:p is a positiveeveninteger with apositive units digit--> the units digit of p can be 2, 4, 6, or 8 -->
In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.
Intersection of values is 6, thus the units digit of p + 2 is 6 + 2 = 8.
Answer: B. #### B
QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?
options: A)9/10 B)6/10 C)2/10 D)3/10 E)5/10
SOLUTION:Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20
Let E = event of getting a multiple of 4 or 15
=multiples od 4 are {4, 8, 12, 16, 20}
And multiples of 15 means multiples of 3 and 5
= {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}.
= the common multiple is only (15).
=> E = n(E)= 6
Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10.
Answer is D #### D
QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:First, reach to the point of getting the equation W: x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D
QUESTION:Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
options: A)4 B)6 C)5 D)7 E)9
SOLUTION:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
Answer: Option A #### A
QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive?
options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000
SOLUTION:There are 5 people inheriting the money.
We have to take the total of the inheritance and divide it by 5 for each person receiving money.
$527,500 / 5 = $105,500.
Therefore the correct answer is D. #### D
QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
options: A)600 B)2877 C)208 D)1882 E)191
SOLUTION:Explanation:
Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A #### A
QUESTION:A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 2 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x?
options: A)x/70 B)2x/63 C)3x/70 D)3x/10 E)3x/7
SOLUTION:cost of boat per day = x
cost per person =x/7
if three more persons afre there, cost =x/9
difference = x/7-x/9
=2x/63
Ans B #### B
QUESTION:Find the distance covered by a man walking for 42 min at a speed of 10km/hr?
options: A)7km B)3km C)4km D)5km E)6km
SOLUTION:Distance = 10*42/60 = 7 km
Answer is A #### A
QUESTION:Before a salary increase, the weekly salary of a worker for 44 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour?
options: A)4 B)6 C)8 D)10 E)12
SOLUTION:Let x be the original salary per hour.
Let y be the salary per hour after the increase.
40y=44x
y=(44/40)x=1.1x
The salary increased 10%.
The answer is D. #### D
QUESTION:Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X?
options: A)25% B)40% C)50% D)60% E)75%
SOLUTION:34% is 9%-points above 25% and 6%-points below 40%.
Thus the ratio of mixture Y to mixture X is 2:3.
The percent of mixture X is 3/5 = 60%.
The answer is D. #### D
QUESTION:If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31
options: A)1 B)3 C)5 D)7 E)9
SOLUTION:P ÷ 44 = 432
=> P = 432 * 44 = 19008
P / 31 = 19008 / 31 = 613, remainder = 5
C #### C
QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer
SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/10 * 480 =48
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 48-68 =20>>> therfore answer is 20 greater
A #### A
QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
options: A)$5 B)$15 C)$50 D)$100 E)$105
SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
1,000(1.10)^2 = 1,000(1.21) = 1,210
and Lana would have
2,000(1.05)^2 = 2,000(1.1025) = 2,205
Thus, Tim earned 210 dollars, while Lana earned 205 dollars
The difference is $5 and the answer is A. #### A
QUESTION:A train is 485 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
options: A)20 seconds B)30 seconds C)40 seconds D)50 seconds E)None of these
SOLUTION:Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 485+140 = 625 meter
Time = Distance/speed
=625∗2/25=50seconds
Option D #### D
QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X
options: A)87501 B)87599 C)87529 D)87520 E)87521
SOLUTION:x+1789+9011-7819=90510
=x+1789+9011=90510+7819
=x+10800=98329
=x=98329-10800
=87529
Answer is C #### C
QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale?
options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these
SOLUTION:Let the original price be x and sale be of y units.
Then, the revenue collected initially = x × y
Now, new price = 0.8x, new sale = 1.8y
Then, new revenue collected = 1.44xy
% increase in revenue = 0.44xy/xy×100
= 44% increase
Answer A #### A
QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
options: A)Rs.12:29 B)Rs.18:90 C)Rs.16.28 D)Rs.16.50 E)Rs.82.09
SOLUTION:Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer:D #### D
QUESTION:(3 x 10^2) + (2 x 10) + 4 =
options: A)302400 B)32400 C)30240 D)3240 E)324
SOLUTION:When you multiply a number by 10 you just add a zero
=> 3 x 10^2 => add 2 zeros => 3 x 10^2 = 300
=>2 x 10 = 20
=> 4 = 4
=>3 x 10^2 + 2 x 10 + 4 = 300 + 20 + 4 = 324
=> answer is E ( 324) #### E
QUESTION:What positive number, when squared, is equal to the cube of the positive square root of 17?
options: A)64 B)32 C)8 D)4 E)2
SOLUTION:Let the positive number be x
x^2 = ((17)^(1/2))^3
=>x^2 = 4^3 = 64
=> x = 8
Answer C #### C
QUESTION:A certain collage has total of 410 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
options: A)60 B)90 C)70 D)80 E)40
SOLUTION:Answer is B.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 410 seniors.
So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f =90.
B #### B
QUESTION:A present value of a machine is $2000. Its value depletiation rate is 20% per annum then find the machine value before 2 years?
options: A)$3125 B)$2945 C)$3012 D)$2545 E)$3150
SOLUTION:P= $2000
R = 20%
T = 2 years
Machine value before 2 years = P/[(1-R/100)^T]
=2000*5/4 * 5/4
=$3125
Answer is A #### A
QUESTION:The difference of two numbers is 8 and one-fourth of their sum is 6. Find the numbers.
options: A)16,8 B)10,2 C)17,6 D)14,10 E)12,4
SOLUTION:Let numbers be x and y.
Equation (i): x - y = 8
Equation (ii): (x + y)/4 = 6
Solve system of equations: x=16, y=8
A is the correct answer. #### A
QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg?
options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these
SOLUTION:Solution
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg
Answer D #### D
QUESTION:If r and s are positive integers and r-s=6, which of the following has the greatest value M?
options: A)2r B)2s C)r +s D)2r-s E)2s-r
SOLUTION:You can answer this question by using Number Properties and logic or by TESTing VALUES.
We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.
IF....
R = 8
S = 2
Answer A: 2R = 2(8) = 16
Answer B: 2S = 2(2) = 4
Answer C: R+S = 8+2 = 10
Answer D: 2R-S = 2(8) - 2 = 14
Answer E: 2S-R = 2(2) - 8 = -4
Final Answer:
A #### A
QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2?
options: A)6 B)7 C)5 D)4 E)18
SOLUTION:So, the numbers should be from 1,000 to 10,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
1,001
1,010
1,100
3 numbers.
2. One 2 and the rest are 0's:
2,000
1 number.
Total = 4 numbers.
Answer:D #### D
QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?
options: A)144 B)150 C)156 D)162 E)168
SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k.
After adding gold coins, the number of coins is 3k and 6k.
Thus k = 16 and the total number of coins is 9k = 144.
The answer is A. #### A
QUESTION:A reduction of 30% in the price of oil enables a house wife to obtain 6kgs more for Rs.940, what is the reduced price for kg?
options: A)72 B)47 C)40 D)28 E)20
SOLUTION:940*(30/100) = 282 ---- 6
? ---- 1 => Rs.47
Answer:B #### B
QUESTION:In a soccer bet,we play 4 teams.first team odd 1.27,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?
options: A)219.5 B)221.26 C)235.01 D)266.74 E)669.0
SOLUTION:in the case we won the bet,we have:
1.27* 5.23* 3.25* 2.0*5.00=219.50
we will win 221.26
so correct answer is B #### B
QUESTION:If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?
options: A)47.6 kg B)52.6 kg C)59.6 kg D)56.6 kg E)57.6 kg
SOLUTION:(3 * 5)/48 = (9 * 2)/ x
x = 57.6 kg
ANSWER:E #### E
QUESTION:In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race?
options: A)2min 10 sec B)2min 30 sec C)2min 40 sec D)2min 50 sec E)2min 20 sec
SOLUTION:100 m = 15 sec
1 m = 15/100 sec
1000 m = 15/100*1000
=150 sec
=2min 30 sec
ANSWER:B #### B
QUESTION:Which of the following is a prime number ?
options: A)27 B)45 C)97 D)98 E)100
SOLUTION:Clearly, 97 is a prime number. #### C
QUESTION:The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
options: A)2:6 B)2:3 C)4:5 D)2:1 E)2:4
SOLUTION:Let the ratio be k : 1. Then,
k * 16.3 + 1 * 15.4 = (k + 1) * 15.8
= (16.3 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.5 = 4/5
Required ratio = 4/5 : 1 = 4:5.
Answer:C #### C
QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec. What is the length of the platform?
options: A)389 m B)350 m C)187.5 m D)299 m E)219.5 m
SOLUTION:Speed = 300/24 = 25/2 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 25/2
=> x = 187.5 m.
Answer:C #### C
QUESTION:What is the units digit of (12^3)(15^4)(31^7)?
options: A)0 B)2 C)4 D)6 E)8
SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8.
The units digit of 15^4 is the units digit of 5^4 which is 5.
The units digit of 31^7 is the units digit of 1^7 which is 1.
The units digit of 8*5*1 is 0.
The answer is A. #### A
QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2400?
options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920
SOLUTION:2400 * 1/3 = 800
Option A #### A
QUESTION:A present value of a machine is $400. Its value depletiation rate is 25% per annum then find the machine value after 2 years?
options: A)$125 B)$100 C)$200 D)$215 E)$225
SOLUTION:P= $400
R = 25%
T = 2 years
Machine value after 2 years = P[(1-R/100)^T]
=400*3/4 * 3/4
=$225 approximately
Answer is E #### E
QUESTION:If w is a positive integer, then 3^w + 3^(w +1) =
options: A)4^a B)3^a − 1 C)3^(2a) + 1 D)3^a*(a − 1) E)4(3^w)
SOLUTION:3^w + 3^(w +1)
= 3^w + (3^w * 3^1)
= 3^w (1 + 3)
= 3^w(4)
Ans. E) 4(3^w) #### E
QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4?
options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1
SOLUTION:Solving for y/x gives, 1/17 (C) #### C
QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these
SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900
Profit(%) = (64900 - 53000)/55000 * 100 = 21.6%
ANSWER:D #### D
QUESTION:The average of first 18 even numbers is?
options: A)19 B)18 C)16 D)11 E)17
SOLUTION:Sum of 18 even numbers = 18 * 19 = 342
Average = 342/18 = 19
Answer:A #### A
QUESTION:There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is
options: A)10 B)15 C)16 D)13 E)18
SOLUTION:Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D #### D
QUESTION:In how many different number of ways 4 boys and 2 girls can sit on a bench?
options: A)700 B)710 C)720 D)800 E)820
SOLUTION:npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
C) #### C
QUESTION:A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
options: A)2400 B)2880 C)2787 D)3087 E)0728
SOLUTION:1200 * 12: x * 9 = 2:3
x = 2400
Answer: A #### A
QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
options: A)3% B)4% C)5% D)6% E)7%
SOLUTION:65*(90/100)*((100-x)/100) = 56.16
x = 4%
ANSWER:B #### B
QUESTION:A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
options: A)3 1/2 sec B)3 5/2 sec C)3 7/2 sec D)8 1/2 sec E)3 1/8 sec
SOLUTION:D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 1/2 sec
Answer: D #### D
QUESTION:A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get:
options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these
SOLUTION:Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3100/25 = 124
So, A’s amount = 124 × 15 = Rs.1860.
Answer: Option C #### C
QUESTION:The ages of two persons differ by 16 years. If 6 years agao, the elder one be 3 times as old as the younger one, find their present ages.
options: A)20 years. B)30 years. C)40 years. D)50 years. E)60 years.
SOLUTION:Sol.
Let the age of the younger person be x years.
Then, age of the elder perosn = (x + 16) years.
∴ 3(x - 6) = (x + 16 - 6) ⇔ 3x - 18 = x + 10
⇔ 2x = 28 ⇔ x = 14
Hence, their present ages are 14 years and 30 years.
Answer B #### B
QUESTION:Ravi and Kavi start a business by investing ₹ 4000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year.
options: A)2 : 28 B)5 : 28 C)7 : 18 D)1 : 18 E)3 : 18
SOLUTION:Ratio of profit = Ratio of investments
= 4000 : 72000 = 1 : 18
Answer : D #### D
QUESTION:The sum of two consecutive integers is 15. Find the numbers.
options: A)17, 18 B)7, 8 C)5, 6 D)1, 2 E)8, 9
SOLUTION:n + (n + 1) = 15
2n + 1 = 15
2n = 14
n = 7
Answer: B #### B
QUESTION:A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is
options: A)83.33 ml B)83.03 ml C)93.33 ml D)63.03 ml E)82.33 ml
SOLUTION:Explanation:
Profit (%) = 9.09 % = \inline \frac{1}{11}
Since the ratio of water and milk is 1 : 11,
Therefore the ratio of water is to mixture = 1:12
Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml]
Answer: A) 83.33 ml #### A
QUESTION:In how many ways can the letters of the word ARRANGED be arranged in a row so that the vowels appear in alphabetic order?
options: A)6720 B)5280 C)6240 D)5202 E)4020
SOLUTION:three letters can be arranged in 3! ways.
only one combination AEI is required.
8 letters can be arranged in 8! ways.
thus 8!/ 3! * 1 = 6720.
A #### A
QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 16.56 years. What was the average age of five new men?
options: A)15.5 B)15.4 C)15.25 D)20.4 E)15.6
SOLUTION:Total age of 20 men = 15.6 x 20 = 312
Now, total age of 25 men = 141.
Total age of five men added later = 414 - 312 = 202.
Hence, the total average of five men = 102/5 = 20.4
ANSWER:D #### D
<<<Examples ends
QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ?
options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these
SOLUTION:Explanation:
Part filled by A in 1 hour = 1/6
Part filled by B in 1 hour = 1/18
Part filled by C in 1 hour = 1/36
Part filled by (A+B+C) in 1 hour =
1/6+1/18+1/36=9/36
So all pipes will fill the tank in 4 hours.
Option C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)?
options: A)37 B)41 C)3.5e-05 D)35 E)3.5e-07
SOLUTION:99*0.35=34.65 approx. 35
Answer : B #### B
QUESTION:Find a a prime number the options below.
options: A)78 B)80 C)81 D)82 E)83
SOLUTION:Clearly, 83 is a prime number.
E #### E
QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
options: A)3999 B)7799 C)2500 D)2772 E)2912
SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500.Answer: C #### C
QUESTION:The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
options: A)65 years B)88 years C)18 years D)55 years E)11 years
SOLUTION:9 * 2 = 18 years
Answer: C #### C
QUESTION:Which is the middle even number between 6 and 14?
options: A)10 B)6 C)8 D)14 E)26
SOLUTION:6+x = 14-x
2 x = 8
X = 4
Now 6+x = 10
ANSWER:A #### A
QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once?
options: A)700 B)720 C)750 D)800 E)820
SOLUTION:The word ‘ORANGE’ contains 6 different letters.
Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time
=6P6
= 6!
= 6*5*4*3*2*1
= 720
ANSWER:B #### B
QUESTION:Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
options: A)Rs 15 B)Rs 12.10 C)Rs 21.70 D)Rs 16.80 E)None of these
SOLUTION:Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 27 - 5 - 0.30
=21.70
Answer : C #### C
QUESTION:If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true?
I. c - a = 2
II. abc is an odd integer.
III. (a + b + c)/3 is an integer.
options: A) I only B) II only C) I and III only D) II and III only E) I, II, and III
SOLUTION:Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is false.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: C. #### C
QUESTION:How much water must be added to 60 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
options: A)10 litres B)12 litres C)15 litres D)18 litres E)None of these
SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 60 litres of milk
= (1⁄4 × 60) litres = 15 litres.
Answer C #### C
QUESTION:A can run 3 Kms in 3 min 18 sec and B can run same distance in 3 min 40 sec, then by how much distance A can beat B?
options: A)300 m B)220 m C)280 m D)195 m E)295 m
SOLUTION:Distance travelled=3000m
Time taken by A=3 m 18 s
Time taken by B=3 m 40 sec=220 sec
speed of B=3000m/220 s=150/11 m/s
Difference between time of A and B=22 sec
when time will be 3 m 18 s A will have travelled 3000m but B need 22 sec more to finish.
Distance travelled by B in 22 sec=(150/11)*22=300 m
Hence, A beat B by 300 m
ANSWER:A #### A
QUESTION:The value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to:
options: A)0.48 B)5.8 C)0.58 D)0.058 E)0.0058
SOLUTION:= 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749
= 489 x 0.05 x 2/0.09 x 93 x 100
= 489/9 x 93 x 10
= 163/279 x 1/10
= 0.58/10
= 0.058 (or) 0.06.
Answer is D. #### D
QUESTION:If each side of a square is increased by 20%, find the percentage change in its area?
options: A)40% B)42% C)46% D)44% E)38%
SOLUTION:let each side of the square be a , then area = a x a
New side = 120a / 100 = 6a / 5
New area =(6a x 6a) / (5 x 5) = (36a²/25)
increased area== (36a²/25) - a²
Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44%
answer :D #### D
QUESTION:Imagine John has 2 blue balls, 3 green balls, 1 black ball and 4 red balls. How many ways can he arrange the balls lining them up?
options: A)10!/(2!)2 1! B)10!/2! 1! 3! 1! C)10!/4! 4! D)9!/4! 3! 2! E)10!/4! 3! 2!
SOLUTION:n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
John has 10 balls which are 4 red balls, 3 green balls, 2 blue balls and 1 black ball.
Number of arrangements = 9!/(2!)2 3!
Answer: E #### E
QUESTION:Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36,
find P (E|F) and P(F|E)
options: A)5 B)8 C)2 D)6 E)12
SOLUTION:Here, E and F are events
P(E|F) = P(EnF)/P(F) = 36/36 = 1
P(F|E) = P(EnF)/P(E) = 36/24 = 2.
C) #### C
QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?
options: A)12 B)23 C)28 D)80 E)84
SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12
Answer is A #### A
QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
options: A)Rs. 3500 B)Rs. 3750 C)Rs. 3840 D)Rs. 3900 E)None
SOLUTION:EXPLANATION
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5b/2 x
15x + 2y = 4000
15x + 2 x 5/2 x= 4000
20x = 4000
x = 200.
So, y = 172 = 500.
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
Answer D #### D
QUESTION:At 12:10 o'clock Bill leaves point A towards point B at a speed of 30 Km/h. At 13:40 o'clock Richi leaves from the same point towards point B also, but at a speed of 60 Km/h. At what time will Richi passes over Bill?
options: A)14:40. B)15:10. C)16:10 D)15:40 E)15:30
SOLUTION:Distance travelled by Bill in 1hr 30min ( 12:10 to 13:40) = 30kmph*(90/60)hr = 45km
Relative speed = Richi's speed ~ Bill's speed = 30kmph
Time taken by Richi to cross Bill = 45/30 = 1.5 hrs
Time at which Richi will cross Bill = 13:40 + 1:30 = 14:70 = 15:10 hrs
Ans. B #### B
QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
options: A)400 B)197 C)278 D)270 E)279
SOLUTION:2000 ---- 50
2000 ---- 40
x ----- 50
x*50 = 2000*40
x=1600
2000
-------
400
Answer: A #### A
QUESTION:A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue?
options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14
SOLUTION:The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer. #### D
QUESTION:If the height of a cone is increased by 100% then its volume is increased by?
options: A)200% B)300% C)100% D)500% E)350%
SOLUTION:Height of=>100%
so increased by 100%
ANSWER C #### C
QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5?
options: A)2 B)3 C)4 D)1 E)5
SOLUTION:For: (4^(2x+5)+3)/5
Let n = 2x + 5
4^n
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256, last digit pattern repeats 4, 6, 4, 6, ....
Rule: x^(m+n) = (x^m)(x^n)
(4^(2x))(4^5)
Rule: x^(mn) = (x^m)^n
(4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4.
Answer: C #### C
QUESTION:There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?
options: A)A)10 B)B)12 C)C)24 D)D)60 E)E)100
SOLUTION:Using anagram method:
4_3_2_1
R_R_B_B
so..
4!/Number of repeated letters (2!)(2!) = 6
ANS:D #### D
QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1
SOLUTION:Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer:A #### A
QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
options: A)897 B)164,850 C)164,749 D)149,700 E)156,720
SOLUTION:Explanatory Answer
Step 1: Identify the series
The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.
The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107.
The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.
It is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2).
So, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3.
Step 2: Compute the sum
Sum of an Arithmetic Progression (AP) = [first term + last term/2]n
We know the first term: 101
We know the last term: 998.
The only unknown is the number of terms, n.
In an A.P., the nth term an = a1 + (n - 1)*d
In this case, therefore, 998 = 101 + (n - 1)* 3
Or 897 = (n - 1) * 3
(n - 1) = 299 or n = 300.
Sum of the AP will therefore, be [101+998/2]∗300 = 164,850
Choice B is the correct answer. #### B
QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is
options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above
SOLUTION:Let distance be D
10 = D/4 + D/6 Answer : D #### D
QUESTION:If a square mirror has a 20-inch diagonal, what is the approximate perimeter E of the mirror, in inches?
options: A) 40 B) 60 C) 80 D) 100 E) 120
SOLUTION:if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter E must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B #### B
QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4?
options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3
SOLUTION:We can have 6 different outcomes on a dice.
Total outcomes on two dices = 6*6
We need only the cases where total sum of the numbers on the dices is 4
They can be {1, 3}, {2, 2}, {3, 1}
A total of 3 outcomes
Probability = favorable outcomes/ total outcomes = 3/36 = 1/12.
Option A #### A
QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face.
options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114
SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C #### C
QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
options: A)39 B)88 C)3 D)7 E)62
SOLUTION:Let the average after 7th inning = x
Then average after 16th inning = x - 3
\inline \fn_jvn \therefore 16(x-3)+87 = 17x
\inline \fn_jvn \therefore x = 87 - 48 = 39
Answer:A #### A
QUESTION:Each factor of 230 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?
options: A)1/16 B)5/42 C)1/8 D)3/16 E)1/4
SOLUTION:210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=3/16.
Answer: D #### D
QUESTION:In a 500 m race, the ratio of speeds of two runners P and Q is 3:5. P has a start of 200 m then the distance between P and Q at the finish of the race is:
options: A)Both reach at the same time B)P wins by 100 m C)Q wins by 50 m D)Q wins by 100 m E)None of these
SOLUTION:Explanation :
When P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5.
According to question P has already covered 200 m when Q is starting at starting point and Q needs to cove 300 m more mean while P covers this 300 m when Q can cover 500 m. So, both P and Q will reach the finishing point at the same time.
Thus, Both reach at the same time.
Answer : A #### A
QUESTION:If n is a natural number, then 6n^2 + 6n is always divisible by?
options: A)6 only B)6 and 12 C)12 only D)18 only E)20 only
SOLUTION:6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Answer is B #### B
QUESTION:Which of the following inequalities is equivalent to −4 < x < 8?
options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above
SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format
-4+y < x+y < 8+y
Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2
Thus, -6< x-2 < 6 => |x-2| < 6.
Hence, answer is D #### D
QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
options: A)11 days B)16 days C)13 days D)15 days E)19 days
SOLUTION:B
16 days
P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days. #### B
QUESTION:The number 0.650 is how much greater than 1/8 ?
options: A)½ B)21/40 C)1/50 D)1/500 E)2/500
SOLUTION:let x be the difference
then
.65-1/8=x
65/100-1/8=x
x=21/40
ans B #### B
QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value
options: A)31 B)32 C)46 D)47 E)48
SOLUTION:- a + b + ((-a)(b)/100)
= -25+75+(-25*75)/100
= -25+75-19
=31
ANSWER:A #### A
QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head?
options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8
SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {HHT,HHH,THH,HTH,TTT}
5/8
E #### E
QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?
options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3%
SOLUTION:Let the price of the article be Rs. 100.
20% of 100 = 20.
New price
= 100 + 20 = Rs. 120
Required percentage
= (120 - 100)/120 * 100
= 20/120 * 100
= 50/3
= 16 2/3%.
Answer:A #### A
QUESTION:Working together, 7 identical pumps can empty a pool in 5 hours. How many hours will it take 4 pumps to empty the same pool?
options: A)4 2/3 B)9 1/4 C)9 1/3 D)8 3/4 E)10 1/2
SOLUTION:The answer is D
7 pumps take 5 hours. 1 Pump will take 5*7 hours . Hence 4 pumps will take (5*7)/4 = 8 75/100 = 8 3/4 hours #### D
QUESTION:4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr?
options: A)50 B)60 C)70 D)80 E)90
SOLUTION:5|5, 10, 15, 20
2|1, 2, 3, 4
|1, 1, 3, 2
L.C.M of 5, 10, 15, 20 is 60
60 times
B #### B
QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1000 per sq.metre.
options: A)Rs. 15,000 B)Rs. 15,500 C)Rs. 15,600 D)Rs. 20,625 E)None
SOLUTION:Solution
Area of the floor = (5.5 x 3.75)m²
= 20.635m ²
Cost of paying = Rs. (1000 x 20.625)
= Rs.20625.
Answer D #### D
QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds
SOLUTION:Let the total number of shots be x. Then,
Shots fired by A =(5/8)x
Shots fired by B =(3/8)x
Killing shots by A =(1/3)of (5/8)x=(5/24)x
Shots missed by B =(1/2) of (3/8)x =(3/16)x
3x/16= 27 or x =(27 x 16)/3= 144.
Birds killed by A =(5x/24) =(5/24*144)= 30.
Answer is C. #### C
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
options: A)200 metres B)180 metres C)324 metres D)228 metres E)150 metres
SOLUTION:Speed= 60 x 5/18 m/sec = 50/3 m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3 x 9 m = 200 m.
Option A #### A
QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-2)(x+1)(2X+5) = 0?
options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2
SOLUTION:x = -1
Prob = 1/12
Answer -A #### A
QUESTION:A watch was sold at a loss of 10%. If it was sold for Rs.196 more, there would have been a gain of 4%. What is the cost price?
options: A)s:1000 B)s:1067 C)s:1278 D)s:1028 E)s:1400
SOLUTION:90%
104%
--------
14% ---- 196
100% ---- ? =>
Rs:1400
Answer: E #### E
QUESTION:16.02 × 0.1 = ?
options: A)0.1602 B)0.001602 C)1.6021 D)0.01602 E)None of these
SOLUTION:16.02 × 0.1 = 1.602
The answer is C. #### C
QUESTION:What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300?
options: A) 100 B) 150 C) 140 D) 200 E) 250
SOLUTION:{100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200.
Answer: D. #### D
QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have?
options: A)50 B)78 C)267 D)20 E)27
SOLUTION:A+B+C = 500
A+C = 200
B+C = 320
--------------
A+B+2C = 520
A+B+C = 500
----------------
C = 20
Answer: D #### D
QUESTION:Let's play a game. I have all the ten digits of numbers available. I use all the digits just once to create a number of ten digits. Can you find out what number I have in mind using the following clues?
One digit is divisible by 1.
Two digits are divisible by 2.
Three digits are divisible by 3.
Four digits are divisible by 4.
Five digits are divisible by 5.
Six digits are divisible by 6.
Seven digits are divisible by 7.
Eight digits are divisible by 8.
Nine digits are divisible by 9.
Ten digits are divisible by 10.
options: A)3816547290 B)3816557290 C)3816547280 D)3813547290 E)3816147290
SOLUTION:A
3816547290 #### A
QUESTION:Solution for 4.75+.303+.432
options: A)2.91 B)5.911 C)5.485 D)5.986 E)2.999
SOLUTION:4.75+.303+.432=0
0=0-4.75-0.303-0.432
0=-5.485
answer :C #### C
QUESTION:A bike covers a certain distance at the speed of 68km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
options: A)85 km/h B)85.34 km/h C)87.67 km/h D)90.66 km/h E)90.64 km/h
SOLUTION:Ans.(D)
Sol. Total distance = 68 × 8 = 544 km
Now speed = 544/6 = 90.66 km/h #### D
QUESTION:{3, 5, 8, y}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y
options: A)16/5, 28/3 B)4, 16/5 C)4, 16/5, 28/3 D)4, 28/3 E)3, 4, 5
SOLUTION:The set can have the following forms:
1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3
2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4
3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4
4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case.
Thus the possible values are 4 and 28/3.
D is the correct answer. #### D
QUESTION:Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
options: A)2a2 – ab + 3b2 B)(a – b)(2a – 3b) + 4ab C)(a – b)2 + (a2 + ab + 2b2) D)(a + b)2 + (a2 + 2b2 – 3ab) E)(a + b)(a – b) + (2a2 – ab + 4b2)
SOLUTION:The other parts are equal to 34.
Answer E #### E
QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 13000, then the share of B is?
options: A)6000 B)12000 C)18000 D)24009 E)24002
SOLUTION:Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 13000
Share of B = 6/13 (13000) = Rs. 6000
Answer: A #### A
QUESTION:Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east?
options: A)3.625 B)3 C)4.5 D)4 E)3.5
SOLUTION:Set up two R x T =D cases.
1. 1/12 km/ min x T = 2.75
from which T= 33 mins.
We know total journey time now is 51 +33 =84.
The rate is the same ie 1/12km/min.
set up second R x T =D case.
1/12 km/min x 84 = 7 km
Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5
E. #### E
QUESTION:If 9x^2-16y^2=3x+4y,then what will give the answer?
options: A)3x-4y=0 B)3x-4y=2 C)3x-4y=1 D)3x+4y=0 E)3x+4y=1
SOLUTION:9x^2-16y^2=3x+4y
(3x+4y)(3x-4y)=3x+4y
3x-4y=(3x+4y)/(3x+4y)
3x-4y=1
Answer is option C #### C
QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
options: A)12 B)15 C)16 D)18 E)14
SOLUTION:Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
10 +8 - 4 = 14
E) #### E
QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 8480, what is the length of the plot in metres?
options: A)20 B)200 C)300 D)90 E)140
SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 8480
[4L - 40] = 8480 / 26.50 = 320
4L = 360
L = 360/4= 90 meters. Answer: D #### D
QUESTION:The value of x + x(xx) when x = 2 is:
options: A)36 B)16 C)18 D)64 E)10
SOLUTION:x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10 #### E
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age 4 years back was:
options: A)12 years. B)14 years. C)17 years. D)20 years. E)19 years.
SOLUTION:Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24
Son's age 4 years back (24- 4) = 20 years.
ANSWER :D #### D
QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least?
options: A)John B)Susan C)Sam D)Mark E)Lynn
SOLUTION:Let J – John’s weight
S – Susan’s weight
M – Mark’s weight
A – Sam’s weight
L – Lynn’s weight
J = 2S
S = 0.6A
M = 0.5L
L = 1.9J
Let us convert these weights to one variable
S = J/2
A = S/0.6 = J/1.2 = 5J/6
L = 1.9J
M = 0.5 * 1.9J = 0.95J
So Susan has the least weight.
Answer - B #### B
QUESTION:If a : b = 5 : 9 and b : c = 4: 7, find a : b : c
options: A)63:36:20 B)36:20:63 C)20:63:36 D)20:36:63 E)None of them
SOLUTION:a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4
a:b:c = 5:9:63/4 =20:36:63.
Answer is D. #### D
QUESTION:A and B are two circles. The radius of A is thrice as large as the diameter of B. What is the ratio between the areas of the circles?
options: A)1:18. B)1:20. C)1:4. D)1:36. E)1:16.
SOLUTION:Given : The radius of A is thrice as large as the diameter of B. => R(a) = 3*D(b) = 3*2*R(b) = 6R(b). The radius are in ratio of 1:6 thus the area will be in the ratio of square of radius. 1:36. Hence D. #### D
QUESTION:Two mechanics were working on your car. One can complete the given job in 5 hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
options: A)7/4 B)4/3 C)14/5 D)10/3 E)17/5
SOLUTION:Rate(1)=1/5
Rate(2)=1/8
Combined = 13/40
Work done in 2 days=13/20
Work left = 7/20
Rate * Time = Work left
1/8 * Time = 7/20
Time=14/5
C #### C
<<<Examples ends
QUESTION:36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ?
options: A)24 B)17 C)18 D)9 E)11
SOLUTION:Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
72 : 36 :: 18 : x
x = 9
Answer: D) 9 days #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
options: A)4 B)16 C)25 D)36 E)100
SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number.
The answer is C. #### C
QUESTION:Naomi was ordering yarn from a discount web site. If she ordered more than $50 worth of
yarn labeled “discountable”, she could take an extra 10% from the price of that yarn. Only
some of the yarn she ordered was eligible for the discount. Here is what Naomi ordered:
2 skeins at $2.50 per skein (not discountable)
8 skeins at $8.40 per skein (discountable)
7 skeins at $5.99 per skein (discountable)
Tax is 5% and shipping is 8%. How much did Naomi pay for her yarn?
options: A)$116.64 B)$216.64 C)$316.64 D)$416.64 E)$516.64
SOLUTION:8 x $8.40 = $67.20 (All money is rounded to hundredths at each step.)
7 x $5.99 = $41.93
$67.20 + $41.93 = $109.13 discountable
$109.13 x .10 = $10.91 (rounded)
$109.13 - $10.91 = $98.22 for discounted yarn
2 x $2.50 = $5.00 for un-discounted
$98.22 + $5.00 = $103.22 cost of yarn
$103.22 x 1.13 = $116.64 with tax and shipping
(5% + 8% = 13%)
correct answer A #### A
QUESTION:Two numbers are in the ratio 5:8 and thier H.C.F is 4. Find the numbers.
options: A)25 and 40 B)20 and 32 C)30 and 48 D)15 and 24 E)16 and 25
SOLUTION:Explanation:
Let two numbers 5x, 8x their H.C.F = 4
Therefore H.C.F is 4
i.e, x in this case.
Therefore The numbers are 5 x 4 = 20
8 x 4 = 32
Answer: Option B #### B
QUESTION:Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries?
options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140
SOLUTION:Probability of basket = 3/5
Probability of no basket = 2/5
Required probability=3* 3/5*2/5*2/5
=36/125
A is the answer . #### A
QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
options: A)11 B)408 C)2881 D)287 E)221
SOLUTION:1h ----- 5
? ------ 60
12 h
RS = 13 + 21 = 34
T = 12
D = 34 * 12 = 408
Answer:B #### B
QUESTION:At a meeting of 8 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
options: A)2400 B)2800 C)3200 D)3600 E)4000
SOLUTION:8 people can be arranged around a table in 7! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 7 units around a table is 6!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 7! - 2*6! = 5*6! = 3600
The answer is D. #### D
QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest?
options: A)3% B)2% C)1% D)6% E)7%
SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\
Rate = (100 * 3000) / (12500 * 4) = 6%
Answer: D #### D
QUESTION:If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 6 children have two children of the same sex and one of the opposite sex?
options: A)1/3 B)2/3 C)1/4 D)3/16 E)3/5
SOLUTION:No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 6 = 6C2
Total possible outcomes - 2^6 (each child can be either a girl or a boy)
Probability=2C1*6C2/2^6= 2*6/2*2*2*2*2*2=12/64=3/16
Ans=D #### D
QUESTION:During a trip, joe traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
options: A)(180-x)/2 B)(x+60)/4 C)(300-x)/5 D)600/(115-x) E)12000/x+300
SOLUTION:total distance =100 ;total time = T
t1 = x/30 t2 = 100-x /40
T =t1+t2 = x/30 + 100-x/40 = (40x + 3000- 30x)/1200
= (10x+3000)/1200
= x+300/120
av speed = 100*120/x+300 = 12000/x+300
E #### E
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?
options: A)75% B)67% C)29% D)55% E)45%
SOLUTION:600 --- 400
100 --- ? => 67%
Answer: B #### B
QUESTION:In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
options: A)5/6 B)3/9 C)5/0 D)5/3 E)5/9
SOLUTION:Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer: Option A #### A
QUESTION:A tap can fill a tank in 12 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
options: A)5 hr 30 mins B)7 hr 30 mins C)4hr 30 mins D)2 hr 30 mins E)3 hr 30 mins
SOLUTION:Explanation:
A tap can fill a tank in 12 hours.
Therefore the tap can fill half the tank in 6 hours.
One tap take time to fill half of the tank = 6 hrs
4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins
Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins
Answer : B #### B
QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items?
options: A)15% B)12.16% C)13.4% D)20.2% E)None of these
SOLUTION:Explanation :
Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively.
And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively.
Overall loss percentage of the 1st two items = 14.33%
=>(0.21p+0.11q)/(p+q)=0.1433
=>p/q=1/2.
Overall loss percentage of the 2nd and 3rd item =10.4%
=>(0.11q+0.1r)/(q+r)=0.104.
=>q/r=2/3.
Therefore, the overall loss percentage is :
=>(0.21p+0.11q+0.1r)x100/(p+q+r).
=>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3).
=>0.1216×100.
=>12.16%.
Answer : B #### B
QUESTION:A set consists of 12 numbers, all are even or multiple of 5. If 4 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10?
options: A) 0 B) 1 C) 2 D) 3 E) 5
SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since{Neither}=0(allare even or multiple of 5) then:
12 = 4 + 10 - {Both} + 0;
{Both}=2(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: C. #### C
QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies
options: A)231 B)150 C)200 D)450 E)451
SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
Ans: C #### C
QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount?
options: A)1240 B)1120 C)1190 D)1634 E)None of these
SOLUTION:Explanation :
TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950
BG = BD – TD
=> 684= BD - 950
=> BD = 684 + 950 = 1634 Answer : Option D #### D
QUESTION:Sharmila works 10 hours per day on Monday, Wednesday and Friday, and 8 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $460 per week. How much does she earn in dollars per hour?
options: A)8 B)9 C)9.5 D)10 E)11
SOLUTION:So, she works 30 hours in 3 days
So, she works 16 hours in 2 days
So in a week she works 46 hours ( 30 + 16 ) and earns $460
So, Hourly wage is 460/46 => 10
Hence answer will be (D) 10 #### D
QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?
options: A)11 B)12 C)13 D)14 E)15
SOLUTION:Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q × (130/100) = 1/23
=> q = 100/(23×130) = 10/(23×13)
Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13
=> P and Q together can do the work in 13 days
Answer is C. #### C
QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender?
options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2
SOLUTION:There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128
case 2 .all girls.
1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128
We will add the cases to get 1/64 #### A
QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.5
II. 15.3
III. 9.5
options: A)I only B)I and II only C)II only D)III only E)I and III only
SOLUTION:Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
14.5 and 9.5 lies in the range of 2SD from mean
Answer: Option C #### C
QUESTION:Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?
options: A)1/2 B)1/4 C)1/6 D)1/8 E)1/16
SOLUTION:Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible).
Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8.
Answer: D. #### D
QUESTION:A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
options: A)2 kmph B)8 kmph C)16 kmph D)4 kmph E)6 kmph
SOLUTION:30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
ANSWER:B #### B
QUESTION:Little Praveen had $50.50. He spent $12.25 on sweets and gave same money to his two friends and the amount left with him is $31.25. Find how much he spent to two of his friends?
options: A)$ 16.65 B)$ 18.65 C)$ 19.25 D)$ 16.55 E)$ 17.65
SOLUTION:Praveen spent and gave to his two friends a total of
12.25 + 2x= $4.65, x is the amount spent to one friend.
Money left
50.50 -2x = $31.85. Then 2x=$18.65.
correct answer is B) $ 18.65 #### B
QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160
SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 8*12=96 five-minute intervals, thus total of 96*30 tickets were sold.
Say x student and 3x regular tickets were sold, then x+3x=96*30 --> x=24*30 and 3x=3*(24*30)=24*90.
Therefore, the total revenue from ticket sales that day was 24*30*6+24*90*10=$25,920.
Answer: B. #### B
QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
options: A)6 days B)4 days C)8 days D)5 days E)1 days
SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4
=> 4 days
Answer: B #### B
QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there?
options: A)20 coin B)30 coins C)28 coins D)25 coins E)None of these
SOLUTION:Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 35
⇒ 1.75x = 35 ⇒ x = 20 coin
Answer A #### A
QUESTION:Set D consists of 19 elements. The average of set D is L. If a new element is added to the set and the average grows by K, what is the value of the new element?
options: A)a) L(1 + K / 5) B)b) L * (K/100) - 20L C)c) 20L(1+K/100) D)d) 20(1+K/100)-19L E)e) L*(K/5)-19
SOLUTION:Let's assume the value of new element to bea. So converting the word problem into equation,
(19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K
But according to the answer options, problem writer wanted to conveyk% percent rise in average value.
If we consider this case than resulting equation will be,
(19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]
==> a= 20L + KL/5 -19L
==> a= L + KL/5 , which is equivalent to option [A] #### A
QUESTION:What is the greatest positive integer T such that 3^T is a factor of 9^10?
options: A)5 B)T=9 C)T=10 D)T=20 E)30
SOLUTION:What is the greatest positive integer T such that 3^T is a factor of 9^10?
9^10 = (3^2)^10 = 3^20
D. 20 #### D
QUESTION:Two coins are tossed, find the probability that two Tails are obtained
options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3
SOLUTION:The sample space S is given by.
S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two heads are obtained".
E = {(T,T)}
P(E) = n(E) / n(S) = 1/4
B #### B
QUESTION:The average of 10 numbers is calculated as 5. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:10 * 5 + 36 – 26 = 60/10 = 6
ANSWER:E #### E
QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c?
options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12
SOLUTION:6a/100 = 12
a = 200
12b/100 = 6
b = 50
c = b/a = 50 / 200 = 1/4
The answer is C. #### C
QUESTION:A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.2 hours, then the distance covered at 40 kmph is
options: A)130 km B)120km C)100km D)124km E)none of these
SOLUTION:Let the partial distance covered at 40 kmph be X
Let the another partial distance covered at 60 kmph be (250 - x)
Thus, x/40 - (250 - x)/60 = 5.2
or, x/40 + (250 - x)/60 = 5.2
or, (3x + 500 - 2x)//120 = 5.2
or 500 + x = 624
x=124
ANSWER:D #### D
QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.?
options: A)4.5 B)5 C)5.5 D)5.8 E)6
SOLUTION:if $x$ is the number, x/6 * 12 = 11
=> 2x = 11
=> x = 5.5
C #### C
QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
options: A)30% B)70% C)100% D)250% E)300%
SOLUTION:cp = 100
profit = 320 ans SP = 420
new CP = 125% of RS 100 = Rs 125
New SP = 420
profit = (420-125) = 295
req % (295/420*100)% = 1475/21% = 70%
ANSWER B #### B
QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But
whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11
mornings and 12 afternoons. How many days did they stay there totally?
options: A)16 B)18 C)20 D)13 E)14
SOLUTION:Explanation :
Clearly 11 mornings and 12 afternoons = 23 half days
=> Since 13 days raining means 13 half days.
=> So 23-13 =10 halfdays ( not effecetd by rain )
=> So 10 halfdays =5 fulldays
Hence ,
Total no. of days = 13+5 =18 days
Answer : B #### B
QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?
options: A)1/26 B)1/20 C)1/25 D)1/29 E)1/23
SOLUTION:Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26.Answer: A #### A
QUESTION:Find the odd man out
864, 420, 200, 96, 40, 16, 6
options: A)420 B)200 C)96 D)40 E)6
SOLUTION:6x2+4=16
16x2+8=40
40x2+12=92
92x2+16=200.. and so on.
ANSWER:C #### C
QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 3 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
options: A)1/20 B)1/6 C)1/5 D)4/21 E)3/23
SOLUTION:series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 3*x
Hence, a1+a2+..+a20+n = 23x
So, the fraction asked = 3x/23x =3/23
Answer E #### E
QUESTION:If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there?
options: A)62 B)66 C)70 D)74 E)78
SOLUTION:There are 12 integers from -5 to 6 inclusive.
12C2 = 66.
The answer is B. #### B
QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is:
options: A)153601 B)153600 C)86400 D)153603 E)153604
SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1200 or x = 120.
Length = 360 m and Breadth = 240 m.
Area = (360 x 240) m2 = 86400 m2.
Answer: C #### C
QUESTION:Virat buys an old car for Rs. 50000 and spends Rs. 6000 on its repairs. If he sells the scooter for Rs. 70000, his gain percent is:
options: A)25% B)11 (1/9) % C)12 (2/3) % D)12% E)None of these
SOLUTION:Explanation:
C.P. = Rs. (50000 + 6000) = Rs. 56000
S.P. = Rs. 70000.
Gain% = ( (14000 / 56000) * 100 ) % = 25%
ANSWER A #### A
QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is?
options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400
SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4
Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C
QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
options: A)$5 B)$15 C)$50 D)$100 E)$105
SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
1,000(1.10)^2 = 1,000(1.21) = 1,210
and Lana would have
2,000(1.05)^2 = 2,000(1.1025) = 2,205
Thus, Tim earned 210 dollars, while Lana earned 205 dollars
The difference is $5 and the answer is A. #### A
QUESTION:If the number 481*673 is completely divisible by 9, what is the the smallest whole number in place of *?
options: A)4 B)5 C)6 D)7 E)8
SOLUTION:Let x be the smallest whole number in place of *
481x673 is completely divisible by 9
=> (4+8+1+x+6+7+3) is divisible by 9
=> (29+x) is divisible by 9
x should be the smallest whole number.
Hence, (29+x)=36
=>x=36−29=7
Answer is D. #### D
QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is?
options: A)7 B)9 C)8 D)5 E)4
SOLUTION:x + y = 25
xy = 144
(x- y)2 = (x + y)2 – 4xy
(x- y)2 = 625 – 576 => (x – y) = 7
ANSWER: A #### A
QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students?
options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9
SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760
Sum of the marks for the class of 45 students = 45 * 70 = 3150
Sum of the marks for the class of 85 students =
2760 + 3150 = 5910
Average marks of all the students = 5910/85 = 69.5.Answer: D #### D
QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10 is?
Can someone please explain intuitively what the question is asking?
options: A)5 B)9 C)12 D)15 E)30
SOLUTION:In order x! to be divisible by 1,0, it should have at least 1 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 1.
5! = 120 has 1 trailing zeros.
Answer: A #### A
QUESTION:A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
options: A)388 B)277 C)266 D)280 E)191
SOLUTION:80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D #### D
QUESTION:A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 1.25 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 40 worth of diesel fuel?
options: A)20 seconds B)1 minute C)1 minute 20 seconds D)20 minutes E)1 hour 20 minutes
SOLUTION:No. of gallons = 40 / 1.25 = 32
for 2 gallons it takes 5 secs
for 32 gallons it will take 80 secs = 1 min and 20 secs
Answer: C #### C
QUESTION:A and B finish the job in 15 days.while A,B and C can finish it in 12 days . C alone will finish the job in
options: A)40 days B)30 days C)60 days D)70 days E)50 days
SOLUTION:Explanation:
12 = (15 * x)/(15 + x)
180+12x=15x
3x=180
X=60
Answer: Option C #### C
QUESTION:P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days?
options: A)12 days B)12.5 days C)13 days D)13.5 days E)15.5 days
SOLUTION:Both together worked for 3 days.
In 3 days , P can do = 3 x
1
18
=
1
6
th work
In 3 days, Q can do = 3 x
1
15
=
1
5
th work
In 3 days , work finished =
1
6
+
1
5
=
11
30
Balance work =
19
30
Balance work finished by Q => Time taken by Q to finish the balance work =
19
30
x 15 = 9.5 days
The whole work was completed in 9.5 + 3 = 12.5 days
B #### B
QUESTION:The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of R is?
options: A)A)Rs.4078 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.6400
SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10100 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv)
Subtracting (i) from (iv), we get, P = 6400.
P's monthly income = Rs.6400.
Answer: E #### E
QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals?
options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6
SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15
ANSWER:D #### D
QUESTION:A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred.
options: A)Rs. 5750 B)Rs. 6000 C)Rs. 5500 D)Rs. 5000 E)Rs. 7000
SOLUTION:The price varies as the square of the weight,
P = K x W2
12250 = K x 352
K = 10
Thus, P = 10W2
When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively.
Their values should be :
10g piece: 10 x 102 = Rs. 1000;
25g piece: 10 x 252 = Rs. 6250.
Total value of stone now, = 1000 + 6250 = Rs. 7250
Loss incurred = 12250 - 7250 = Rs. 5000
ANSWER:D #### D
QUESTION:The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
options: A)17 litres B)21.3 litres C)11 litres D)07 litres E)38 litres
SOLUTION:262.85(32)+3,104.35x = 1,399.45(32 + x)
Solve the equation.
262.85(32)+3,104.35x = 1,399.45(32 + x)
8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x
8,411.2 + 1,704.9x = 44,782.4
1,704.9x = 36,371.2
x ≈ 21.3
Answer is B. #### B
QUESTION:A car takes 6 hours to cover a distance of 504 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
options: A)48 Kmph B)50 Kmph C)52 Kmph D)56 Kmph E)60 Kmph
SOLUTION:Time = 6
Distence = 504
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 504/9 = 56 Kmph
D #### D
QUESTION:Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 250 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
options: A)0.6 B)0.06 C)0.006 D)0.0006 E)6.0e-05
SOLUTION:Suppose machine A produce 1000 units
total defective = 9
Machine B then produces=1500 units
total defective=6
probability=15/2500
=0.006
C . correct #### C
QUESTION:If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is
options: A)1/2 B)1 C)2 D)4 E)8
SOLUTION:Given: 5/w + 5/x = 5/ywx=y
Find: (w+x)/2 = ?
5(1/w + 1/x) = 5(1/y) - divide both sides by 5
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A #### A
QUESTION:The three competitors in a race have to be randomly chosen from a group of three men and three women. How many different such trios contain at least one woman?
options: A)13 B)15 C)17 D)19 E)21
SOLUTION:The total number of ways to choose three runners 6C3 = 20
The number of trios with only males is 3C3 = 1
The number of trios which include at least one woman is 19.
The answer is D. #### D
QUESTION:What is the difference between the local value of 1 and 2 in the number 2124?
options: A)70 B)75 C)20 D)80 E)60
SOLUTION:Explanation:
100 – 20 = 80
Answer: D #### D
QUESTION:Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
options: A)4! B)8! C)9! D)10! E)12!
SOLUTION:Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways #### B
QUESTION:A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 95, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
options: A)74 B)75 C)76 D)77 E)81
SOLUTION:ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 95 + 77*5x) = 260x+570x+385x = 1215x
total number of students = 15x
average = 1215x/15x = 81
E is the answer #### E
QUESTION:By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph
SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km
He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x
=30 kmph.
Answer: A #### A
QUESTION:In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat?
options: A)4! B)5! C)7! D)8! E)9!
SOLUTION:There are seven positions to be filled.
The first position can be filled using any of the 7 letters contained in PROBLEM.
The second position can be filled by the remaining 6 letters as the letters should not repeat.
The third position can be filled by the remaining 5 letters only and so on.
758
Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways.
C #### C
<<<Examples ends
QUESTION:What is the are of an equilateral triangle of side 4 cm?
options: A)2√3 B)3√3 C)5√3 D)4√3 E)8√3
SOLUTION:Area of an equilateral triangle = √3/4 S2
If S = 4, Area of triangle = √3/4 * 4 * 4
= 4√3 cm2;
Answer:D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 14?
options: A)7 B)21 C)34 D)8 E)55
SOLUTION:So the number given is N = 143Q + 45
If this number is divided by 13, the remainder would be R[(143Q + 45)/13]
Since 143 is divisible by 13 , the product 143Q gives no remainder
This means the remainder of 45/13 should be the remainder of the entire number N
which is 6
To make it divisible by 13 , the smallest number that can be added = 14 - 6 = 8
Correct Option : D #### D
QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water?
options: A)29 B)30 C)20 D)50 E)55
SOLUTION:Explanation :
Here, Large, Medium and Small ships are denoted by the symbol L, M and S.
Now, according to the question,
4L = 7S. ------(i)
3M = 2L + S. ------(ii)
Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :-
7: 6 : 4.
Let, the number of journeys required be x. Since, quantity of water remains the same, so :-
=((15×7+7×6+14×4)36) = x (12×7+14×6+21×4).
=>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x
=>x=7308/252
=>x=29.
Answer : A #### A
QUESTION:For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3).
If 3y = –30, then y =
options: A) –15 B) –6 C) -3 D) 6 E) 15
SOLUTION:(3+2)(y-3)=-30..
x-3=-6..
x=-3
C #### C
QUESTION:Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes. Each inlet pipe can fill the tank in 9 hours and each outlet pipe can empty the tank in 6 hours. On opening all the pipes, an empty tank is filled in 9 hours. How many inlet pipes are there?
options: A)2 B)4 C)3 D)5 E)6
SOLUTION:x / 9 – y / 6 = 1/9; 2x – 3y + 2
We can compute that x = 4 and y = 2.
Thus, Inlet pipe = x = 4.
Answer: B #### B
QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
options: A)60 B)80 C)100 D)120 E)140
SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 160 books were paperbacks, the dealer would earn a profit of $320.
Since the actual profit was $400, the dealer must have sold 80 hardbacks.
Then the number of paperbacks sold was 160-80 = 80.
The answer is B. #### B
QUESTION:Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?
options: A)a) 90 B)b) 100 C)c) 110 D)d) 130 E)e) 140
SOLUTION:C. 110
sum of all lengths of all 5 pieces of wood = 128 * 5 = 640
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 640 - 420 = 220
each of these 2 will have length 220/2 = 110
Answer C #### C
QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture?
options: A)9! B)9×8! C)4x5! D)10!/2! E)10!
SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!*2! ways.
Total - Restriction =
= 6! - 5!*2! =
= 5!(6- 2!) =
= 4*5!.
Answer: C. #### C
QUESTION:The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits M of the larger integer?
options: A)M=2 B)M=5 C)M=8 D)10 E)11
SOLUTION:Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A). #### A
QUESTION:A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
options: A)$200 B)$333.33 C)$100.25 D)$277.78 E)$377.00
SOLUTION:Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 )
$25000 is 60% of total amount.
So total amount = 25000 * 100/60
Remaining amount is 40% of total amount.
40% of total amount = 25000 * (100/60) * (40/100) = 50000/3
This amount has to be divided by 50( remaining people are 50 )
So per head amount is 50000/3 / 50 = 32000/180 = 333.33;
ANSWER:B #### B
QUESTION:A military garrison in a wild frontier has 600 men who have provisions to last 25 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?
options: A)13 1/3 B)12 1/3 C)38 D)36 E)12 3/4
SOLUTION:Total provisions=600*25*7=105000
Provisions used for in 6 weeks=6*7*600=25200
remaining provisions=79800
remaining provisions need to be split between 900(600+300) people.
Number of provisions per person= 79800/900
we need to find the answer in terms of weeks=(79800/900)/7=38
Answer:C #### C
QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
options: A)8% B)7% C)10% D)6% E)9%
SOLUTION:Explanation:
Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol,
such that Benson buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Benson spends additional 15% on petrol,
amount spent by Benson = 100× (100+15)/100 = Rs.115
Hence Quantity of petrol that he can purchase = 115/125 Litre
Quantity of petrol reduced = (1−115/125) Litre
Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8%
Answer: Option A #### A
QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
options: A)5 B)6 C)7 D)1 E)2
SOLUTION:160 = (180*4*R)/100
R = 5%
Answer: A #### A
QUESTION:Indu gave Bindu Rs.3750 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
options: A)5 B)6 C)9 D)3 E)1
SOLUTION:3750
= D(100/4)2
D = 6
Answer: B #### B
QUESTION:By how much is 50% of 250 greater than 25% of 400.
options: A)25 B)26 C)29 D)39 E)26
SOLUTION:(50/100) * 250 – (25/100) * 400
125 - 100 = 25
Answer:B #### B
QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is?
options: A)12 B)72 C)48 D)99 E)11
SOLUTION:Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.75 + 1.25 = 3 km = 3000 m.
Required time = 3000 * 3/125 = 72 sec.
Answer: B #### B
QUESTION:A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?
options: A)22 days B)4 days C)13 days D)6 days E)9 days
SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Answer is D. #### D
QUESTION:A walks at 10 kmph and 5 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?
options: A)100km B)150km C)50km D)120km E)200km
SOLUTION:Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 5 hours.
x/10 - x/20 = 5
x = 100 km
Answer is A #### A
QUESTION:A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
options: A)A B)B C)C D)all alike E)None of these
SOLUTION:Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
ANSWER:C #### C
QUESTION:The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.90 per metre.
options: A)2399 B)3888 C)2999 D)5808 E)6468
SOLUTION:Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.90) = Rs. 6468.
Answer: E) 6468 #### E
QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?
options: A)4.5 B)5 C)5.5 D)5.8 E)6
SOLUTION:if $x$ is the number, x/6 * 12 = 9
=> 2x = 9
=> x = 4.5
A #### A
QUESTION:For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.25 – 6.25*?
options: A)1.5 B)0.5 C)6.25 D)0.25 E)6.0
SOLUTION:Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.25* =6 (the greatest positive even integer less than or equal to 6.25 is 6).
Hence, 6.25 – 6.25* = 6.25 - 6 = 0.25
Answer: D. #### D
QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
options: A)1244 B)1532 C)1349 D)1423 E)1543
SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C #### C
QUESTION:If x and y are perfect squares, then which five of the following is not necessarily a perfect square?
options: A)x^2 B)xy C)4x D)x+y E)x^5
SOLUTION:If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square.
Answer: A. #### A
QUESTION:D is the set of all the multiples of 5 between 20 and 100. E is the set of all the factors of 999. Set D and Set E have how many numbers in common?
options: A)2 B)1 C)3 D)0 E)12
SOLUTION:D is a set of multiples of 5.
999 is NOT a multiple of 5, hence none of its factors is a multiple of 5.
Therefore, those two sets won't have any overlap.
Answer: D #### D
QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers?
options: A)28 B)56 C)76 D)84 E)85
SOLUTION:Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 48
=> 12x = 48
=> x = 48/12 = 4
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 4 = 28
Answer: Option A #### A
QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
options: A)289 B)132 C)279 D)277 E)278
SOLUTION:2 * 22/7 * 14 = 88
88 * 1 1/2
= Rs.132
Answer: B #### B
QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit?
options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62
SOLUTION:Explanation:
We are given selling price = Rs. 580 and expected profit of 15 %
Therefore, we can easily solve this numerical, considering basic formulae of profit and loss.
Let cost price = x
Selling price = C.P. + Profit
S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price)
580 = x + (0.15 x)
580 = 1.15 x
Therefore,
x = 504.347
Cost Price = Rs. 504.35
Now, we have the cost price and hence,
Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65
The trader gets a profit of Rs. 75.65
ANSWER IS A #### A
QUESTION:150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration C of the acid in the mixture?
options: A)1/2 B)1/3 C)1/4 D)1/6 E)1/5
SOLUTION:Do not need any computation
30%-----------21%---------12%
if volume of both sol. were equal the concentration C would be 21%=1/5, but 12% is more than 3 times
only possibility is 1/6
D #### D
QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively?
options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these
SOLUTION:Y:Z = 70000 : 30000 = 7:3.
ANSWER:C #### C
QUESTION:One student to pass the subject as probability 1/4. another man to get driving licence and student passed subject probability 1/6. find the probability man get driving licence.
options: A)1/3 B)2/3 C)4/3 D)5/3 E)1/4
SOLUTION:Let the probability of the man get driving licence is x.
so, 1/4 * x = 1/6
x = 2/3.
ANSWER:B #### B
QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
options: A)1 B)2 C)34 D)12 E)13
SOLUTION:46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A #### A
QUESTION:Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die.
options: A)1/2 B)1/6 C)0 D)5/6 E)1
SOLUTION:Determine if E and F are independent.
P(E|F) = the probability of event E occurring given that event F has already occurred
P(E|F) ≠ P(E) as P(E) is changed if it is given that F occurs.
Consequently, P(E∩F) ≠ P(E)P(F) since the events are not independent. As a result, P(E∩F) ≠ 1/4 = P(E)P(F)
We must use the more complex formula for finding the intersection of E and F:
P(E∩F) = P(F)P(E|F)
P(F) = the probability of event F occurring
The probability of rolling a 1, 2, or 3 is 3/6 = 1/2
P(E|F) = the probability of event E occurring given that event F has already occurred
If event F already occurred, we are limited to the numbers 1, 2, or 3. Within this range of 3 possible numbers, only one number--namely, 2--is an even number. Therefore, P(E|F) = 1/3
P(E∩F) = P(F)P(E|F) = (1/2) * (1/3) = 1/6
Answer B #### B
QUESTION:Bradley owns x video game cartridges. If Bradley’s total is one-third the total owned by James and four times the total owned by Charles, how many video game cartridges do the three of them own altogether, in terms of x?
options: A)(16/3)x B)(17/14)x C)(13/4)x D)(19/12)x E)(17/4)x
SOLUTION:x = Bradley’s total
3x = James’s total
(1/4)x = Charles’s total
Add each total
x + 3x+ (1/4)x = 4x + (1/4)x = = (17/4)x
Answer : E #### E
QUESTION:In an exam, Dibi scored 25 percent, Balan scored 38 percent and Cristen 23 percent. The maximum score awarded in the exam is 1200. Find the average mark scored by all the three boys?
options: A)322 B)342 C)344 D)328 E)320
SOLUTION:Average mark scored by all the three boys =
[25/100 (1200) +38 /100 (1200) + 23/100 (1200)] / 3
300+456+276= 344
Answer: C #### C
QUESTION:Which of the following has the most number of divisors?
options: A)99 B)101 C)176 D)182 E)179
SOLUTION:Explanation:
99 = 1 x 3 x 3 x 11
101 = 1 x 101
176 = 1 x 2 x 2 x 2 x 2 x 11
182 = 1 x 2 x 7 x 13
So, divisors of 99 are 1, 3, 9, 11, 33, .99
Divisors of 101 are 1 and 101
Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176
Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
Hence, 176 has the most number of divisors. Answer: C #### C
QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5
SOLUTION:Rate of flow of water in second hour = 18 gallons per hour
Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour
Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons
Answer B #### B
QUESTION:Which number is the odd one out?
159
248
963
357
951
852
options: A)154 B)248 C)536 D)645 E)135
SOLUTION:B
248
In the rest there is the same difference between each digit, eg: 8 (–3) 5 (–3) 2. #### B
QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train?
options: A)7:00 B)8:00 C)9:00 D)10:00 E)11:00
SOLUTION:In one hour and thirty minutes the first train travels 105 km.
The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h.
The second train will catch the first train in 105/10 = 10.5 hours, so at 9:00 pm.
The answer is C. #### C
QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B?
options: A)2160 B)3000 C)3018 D)3019 E)3012
SOLUTION:60*5:36*6:75*3
100: 72: 75
72/247 * 7410 = 2160
Answer: A #### A
QUESTION:Sum of 53 odd numbers is?
options: A)2709 B)2809 C)2909 D)3009 E)3109
SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 53 odd numbers = 53^2 = 2809
ANSWER:B #### B
QUESTION:If Mason is now twice as old as Gunther was 5 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now?
options: A)3G+14 B)3G+8 C)3G+15 D)3G+10 E)3G+9
SOLUTION:G is Gunther's current age.
Let Mason's current age be M.
given M = 2(G-5).
four years from now Mason's age will be = 2(G-5) + 10 = 2G
four years from now Gunther's age will be = G+10
Sum of ages of Mason and Gunther's after 4 years = 2G+G+10 = 3G+10
Ans : D #### D
QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
options: A)28% B)25% C)23% D)45% E)15%
SOLUTION:SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B #### B
QUESTION:Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ???
options: A)a,b B)a,c C)b,c D)a,d E)b,d
SOLUTION:a. 3i+2j
and
c. 2i-3j
are orthogonal pair.
as the dot product of two vectors is zero;so they are orthogonal.
ANSWER:B #### B
QUESTION:A project scheduled to be carried out over a single fiscal year has a budget of $12,000, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,540. By how much was the project over its budget?
options: A) $380 B) $540 C) $1,050 D) $1,380 E) $1,430
SOLUTION:Difficulty level: 600
Each month's budget = 12000/12 = 1000
Budget for 4 months = 4*1000 = 4000
Actual amount spent = 4540
Amount spent over the budget = 4540 - 4000 = 540
Answer (B),
Regards, #### B
QUESTION:Each term of a certain sequence is 4 less than the previous term. The first term of this sequence is 19. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?
options: A)1 B)13 C)15 D)19 E)47
SOLUTION:We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.
What does this imply?If the sum of the first n terms of the sequence is n
Since number of terms will definitely be positive, we are looking for a positive sum.
19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on
Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...
Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.
Answer (C) #### C
QUESTION:A sum was put at simple interest at a certain rate for 6 years Had it been put at 4% higher rate, it would have fetched 144 more. Find the sum.
options: A)500 B)600 C)700 D)800 E)900
SOLUTION:Difference in S.I. = P×T/100(R1−R2)
⇒ 144 = P×6x4/100(∵ R1 - R2 = 2)
⇒ P = 144×100/6×4=600
Answer B #### B
QUESTION:The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:Perimeter = 2(W+L) = 5W
3W = 2L
W = 2L/3
WL = 54
2L^2/3 = 54
L^2 = 81
L = 9 cm
The answer is D. #### D
QUESTION:If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is?
options: A)20 B)98 C)66 D)54 E)12
SOLUTION:Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%
Answer: A #### A
QUESTION:A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?
options: A)1/4 B)2/4 C)1/2 D)1/3 E)2/3
SOLUTION:Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by
(number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3
correct answer D #### D
QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142
options: A)23 B)25 C)46 D)49 E)50
SOLUTION:(C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 . #### C
QUESTION:A rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown. AB = 8 cm and BC = 4 cm. The perimeter of the figure ABCPQRA (in cm) is :
options: A)24 B)28 C)36 D)48 E)None of these
SOLUTION:Solution
Required perimeter = (AB + BC +CP + PQ + QR + RA)
= AB + BC + (CP + QR) + (PQ + RA)
= AB + BC + AB + BC = 2(AB + BC)
= [2(8 + 4 )] cm = 24 cm. Answer A #### A
QUESTION:A 25% stock yielding 20% is quoted at:
options: A)s. 83.33 B)s. 110 C)s. 112 D)s. 125 E)s. 140
SOLUTION:Income of Rs 20 on investment of Rs 100
Income of Rs 25 on investment of ?
= (25*100)/20=125
ANSWER:D #### D
QUESTION:The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg. What is the correct weight?
options: A)58kgs B)58.85kgs C)58.9kgs D)59kgs E)59.85kgs
SOLUTION:Actual total weight is (20X 58.4 - 56 + 66) = 1178 Kgs
Actual average weight is 1178/20 = 58.9kgs
C #### C
QUESTION:Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket
to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
options: A)$8 B)$14 C)$5 D)$15 E)$0
SOLUTION:1/5 x $60 = $12 for sandwich
1/6 x $60 = $10 for museum
1/2 x $60 = $30 for book
$12 + $10 + $30 = $52 spent
$60 - $52 = $8 left over
correct answer A #### A
QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
options: A)508 B)500 C)800 D)570 E)503
SOLUTION:We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.
Answer:B #### B
QUESTION:A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue?
options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14
SOLUTION:The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer. #### D
QUESTION:6x − 12 = 6y
5y + 5x = 10
Which of the following is the number of solutions to the system of equations shown above?
options: A)More than three B)Exactly three C)Exactly two D)Exactly one E)None
SOLUTION:6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
5y + 5x = 10
=>x + y = 2 -- 2
From equation 1 and 2 , we get
2x = 4
=> x=2
y=0
Therefore , the given system will have Exactly one solution
D #### D
QUESTION:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?
options: A)3x+32 B)5x-1 C)(7x+15)/2 D)(9x-4)/2 E)6x+2
SOLUTION:We can take
X+1 = 9
X= 8
So 4c envelopes will be 6
and 5c envelopes will be 3
So total cost will be 39
Then that is our target
Plug x =8 in answer choices
Only B works
Correct Answer : B #### B
QUESTION:The area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is?
options: A)7 B)7.67 C)8.75 D)8.98 E)8.28
SOLUTION:(4 * 3.5)/2
= 7
Answer:A #### A
QUESTION:Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics?
options: A)7/12 B)4/9 C)5/9 D)1/4 E)2/3
SOLUTION:Lets pick smart numbers. Total number of students: 12
Biology (1/2): 6
Chemistry (1/3): 4
Physics (1/6): 2
After leaving school
Biology: 4
Chemistry: 4
Physics: 1
New Total number of students: 9
Biology and Physics: 5
Answer 5/9 or C #### C
QUESTION:The surface of a cube is 24sq cm. Find its volume?
options: A)8 B)6 C)4 D)3 E)1
SOLUTION:6a2 = 24
a = 2 => a3 = 8cc
Answer: A #### A
QUESTION:If 5^10 x 2^10 = 10^n what is the value of n?
options: A)16 B)14 C)12 D)10 E)18
SOLUTION:5^10*2^10 = 10^n
or 10^10 =10^n
n=10
D #### D
QUESTION:The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?
options: A)55 B)44 C)66 D)60 E)12
SOLUTION:H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60.
Answer:D #### D
QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples?
options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24
SOLUTION:The cost of one apple=20/12=1.67
The cost of twenty apples= 1.67x20= $ 33.33
Answer: B #### B
<<<Examples ends
QUESTION:In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people?
options: A)11C6 * 9! *4! B)11C3 * 6! *3! C)15C4 * 9! *3! D)15C2 * 10! *3! E)16C5 * 10! *4!
SOLUTION:7 people can be selected from 11 people in 11C7 ways.
Remaining 4 people can be selected from 4 people in 4C4 ways.
Now, arranging 7 people on a round table = (7-1) ! = 6!
Arranging 4 people on a round table = (4-1) ! = 3!
Hence, total number of ways = 11C7 * 6! * 4C4 * 3!
= 11C3 * 6! * 3!
B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
options: A)37 sec B)89 sec C)36 sec D)87 sec E)45 sec
SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 250 + 120 = 370 m.
Time taken = 370/10
=37 sec.
Answer: A #### A
QUESTION:If the cost price is 96% of the selling price, then what is the profit percent?
options: A)4.17% B)5% C)6.12% D)3.25% E)5.75%
SOLUTION:Let S.P. = $100
C.P. = $96
Profit = $4
Profit% = 4/96 * 100 = 25/6 = 4.17%
Answer is A #### A
QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is
options: A)0.092 B)0.92 C)9.2 D)92 E)920
SOLUTION:F(69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33
Now,
7 × 2 = 14
7 × 1 = 7
or better:
6.9 × 1 = 6.9
6.9 × 2 = 13.8
hence,
6.9 <6.928 × 1.33 < 13.8
9.2 is the only answer that satisfies this condition.C #### C
QUESTION:A car covers a distance of 424 km in 6 ½ hours. Find its speed?
options: A)65.9 kmph B)75.2 kmph C)65.2 kmph D)66.2 kmph E)55.2 kmph
SOLUTION:424/(13/2) = 424*2/13
=65.2 kmph
ANSWER:C #### C
QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent?
options: A)10% B)20% C)30% D)40% E)50%
SOLUTION:5*SP = 7*CP
SP = 1.4*CP
The profit percent is 40%.
The answer is D. #### D
QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
options: A)8 B)12 C)18 D)24 E)48
SOLUTION:In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6
Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E
QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.
options: A)I only B)I and II C)II and III D)I, II, and III E)IV only
SOLUTION:This is a very good 'trap question'.
Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3
If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'.
Ans: E #### E
QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch?
options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these
SOLUTION:Explanation:
CP of Meenal is 75% of the Original SP.
:. Original SP = 1545x100/75 = Rs.2060.
Answer: Option D #### D
QUESTION:Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?
options: A)2 B)3 C)4 D)5 E)7
SOLUTION:2 + 3 + 5 + 7 + 11= 28 ( sum is even)
Least number = 2
A #### A
QUESTION:If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
options: A)None B)I only C)II only D)III only E)I and II
SOLUTION:given 2x/y is prime and greater than 2.
=> 2x/y could be any of the following
3,5,7....
=> 2x/y is odd and prime (as 2 is the only even prime number and its not in this set)
1. x = y , can't be true
if x=y , 2x/y = 2 which is not odd and prime.
2. y=1. can't be true.
if y=1,2x/y = 2x = even which is not odd & prime.
3. x and y are prime integers, need not be true.
lets say 2x/y = 3 and say y=2 prime
=>x = 6/2 = 3 prime
satisfies the given condition here.
but when 2x/y = 3 and y=5 prime
=> x = 15/2 not prime
My Answer is A #### A
QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins
SOLUTION:The pool was 1/5 full initially.
In 6/5 hrs, it was filled to 8/9 of its capacity.
Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled.
So, 6/5 hrs = 8/9 - 1/5 = 31/45
Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins.
Hence D #### D
QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12
SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A #### A
QUESTION:What is the smallest positive integer that can be multiplied by 605 to make it a perfect square?
options: A)2 B)3 C)5 D)7 E)11
SOLUTION:605 is multiplied by 5 gives 3025
Its a square root of 55
Answer is 5 -Option C #### C
QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day?
options: A)10 B)41 C)31 D)21 E)22
SOLUTION:Explanation:
1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12
1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16
1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48
Let ‘x’ be the No. of boys required.
Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1
= (4 + 3 + x)/48 = 1
i.e. 7 + x= 48 and x = 41.
Answer: Option B #### B
QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women?
options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35
SOLUTION:METHOD- 1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A #### A
QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have?
options: A)9 B)12 C)18 D)28 E)36
SOLUTION:Lets take an example: find the number of factors of 100
try to represent 100 in least possible prime numbers
100= 2^2 * 5^2=p^a*q^b
no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9
similarly find the number of factors of p^3 * q^6--->a=3,b=6
(3+1)(6+1)=28 Ans D. #### D
QUESTION:Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is:
options: A)0.20887 B)0.3887 C)0.33487 D)0.20833 E)0.38222
SOLUTION:Explanation:
Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
Answer: D #### D
QUESTION:If 8 men or 12 women can do a piece of work in 40 days, in how many days can the same work be done by 6 men and 11 women?
options: A)10 days B)11 days C)13 days D)15 days E)24 days
SOLUTION:8men = 12women (i.e 2men = 3women)
12women 1 day work= 1/40
soln:
6men(9women)+ 11women=20women=?
1 women 1 day work =12*40= 1/480
so, 20 women work= 20/480=1/24
ans: 24 days
ANSWER:E #### E
QUESTION:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
options: A)2 B)2 1/2 C)3 D)3 1/2 E)4
SOLUTION:Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable.
So correct ans is 2.5 gallons. B #### B
QUESTION:A vendor bought Headphones at 5 for Rs 100.How many for Rs 100 must he sell to gain 50%?
options: A)8 B)3 C)5 D)6 E)None
SOLUTION:C.P. of 9 Headphones= Rs100
S.P. of 9 Headphones = 150% of Rs 100 = Rs150
For Rs.150 , Headphones sold = 9.
For Rs. 100,Pens sold=(9/150)*100=6
Answer: Option D #### D
QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is:
options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg
SOLUTION:EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (30 x 3) = 90 …. (i)
A + B = (25 x 2) = 50 …. (ii)
B + C = (28 x 2) = 56 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 106 …. (iv)
Subtracting (i) from (iv), we get : B = 16.
B’s weight = 16 kg.
Answer E #### E
QUESTION:The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability.
options: A)1/120 B)1/235 C)1/24 D)1/76 E)1/53
SOLUTION:Explanation :
There are total 4 letters. The probability that P gets the first position is 1/4.
The probability that O is in the second position is 1/3.
Likewise, probability for C and Y are 1/2 and 1/1.
Hence, the required probability is:-
=> (1/4) x (1/3) x (1/2) x 1.
=> 1/24.
Answer : C #### C
QUESTION:City A to city B, Andrew drove for 1hr at 46 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
options: A)56.5 B)57.5 C)61 D)61.5 E)62.5
SOLUTION:The total distance is 1×46+3×60=226
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=226/4=56.5
A #### A
QUESTION:If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:
options: A)53.33 B)54.68 C)55 D)56 E)None of these
SOLUTION:Explanation:
Required average = (55 × 50 + 60 × 55 + 45 × 60/55 + 60 + 45)
= (2750 + 3300 + 2700/160)
= 8750/160
= 54.68
Answer: B #### B
QUESTION:Line W has the equation 3x + y = 7. Which of the following lines is perpendicular to Line W?
options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5
SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line W as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line W? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C
QUESTION:A work can be finished in 15 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is
options: A)4:3 B)3:4 C)2:3 D)3:2 E)5:4
SOLUTION:Work done by 20 women in 1 day = 1/15
Work done by 1 woman in 1 day = 1/(15×20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×16)
Ratio of the capacity of a man and woman =1/(15×16) : 1/(15×20) = 1/16 : 1/20
= 1/4 :1/5 = 5:4
Answer is E. #### E
QUESTION:Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase?
options: A)3 B)4 C)6 D)9 E)10
SOLUTION:We have 5, 10, 10 and 20 to work with
From least to greatest, we have...
5 (the least)
10
15
20
25
30
35
40
45 (the greatest)
Total options = 9
Final Answer:D #### D
QUESTION:The population of a town is 8100. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
options: A)9000 B)8000 C)8500 D)9500 E)10000
SOLUTION:Formula :
( After =100 denominator
Ago = 100 numerator)
8100 × 100/90 × 100/90 = 10000
E) #### E
QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder. The dividend is
options: A)74 B)78 C)86 D)92 E)106
SOLUTION:Divisor = (6 * 3) + 7 = 25
5 * Quotient = 25
Quotient = 5.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 5) + 6 = 106.
E) #### E
QUESTION:A train passes a platform in 34 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
options: A)280 meter B)240 meter C)210 meter D)200 meter E)None of these
SOLUTION:Explanation:
Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 34
=> 300+L = 15×34 = 510
=> L = 510-300 = 210 meter
Answer: Option C #### C
QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600
SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.
Let p be the population of the least populated district.
Then 160,080 = p + 7(1.1)p
8.7p=160,080
p = 18,400
The answer is C. #### C
QUESTION:A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent?
options: A)70% B)45% C)48% D)30% E)40%
SOLUTION:Explanation:
840 ---- 380
100 ---- ? => 45%
Answer: B #### B
QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
options: A)160 B)175 C)180 D)195 E)205
SOLUTION:Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 * 8 * 4) = 160.
Therefore, 160 * 2.40 + x * 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER:B #### B
QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
options: A)90. B)45. C)50. D)40. E)25.
SOLUTION:STREET-CAT DOMESTIC-Cat
70 130
(25gray+45other) 85gray+45other
Answer:B #### B
QUESTION:The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?
options: A)40% B)8% C)25% D)16.66% E)9%
SOLUTION:Original cost before weight adjustment: X
Cost after 90% weight adjustment: 9/10 X
20% profit on 9/10X: (120/100)(9/10)(X) or 108X/100
Mark up on original cost of X: (108X/100)/X-1 = 8/100
ANSWER:B #### B
QUESTION:If a and b are positive integers and x = 4^a and y = 9^b, which of the following is a possible units digit of xy?
options: A)1 B)4 C)5 D)7 E)8
SOLUTION:unit digit of x=4^a will either be 4 or 6 (4 if a is odd and 6 if a is even)
and unit digit of y=9^b will either be 1 or 9 (9 if b is odd and 1 if b is even)
now we have total 4 possible combinations
1) a=odd, b=odd
unit digit=9*4=6
2)a=odd, b=even
unit digit=4*1=4
3) a=even,b=odd
unit digit=6*9=4
4)a=even, b=even
unit digit=6*1=6
thus, only two values are possible for the unit digits (4 or 6). out of these values only 4 is mentioned in the given choices. hence answer must be B. #### B
QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y?
options: A)3/2 B)2 C)4/3 D)4 E)9/2
SOLUTION:Its simple
equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.
Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4.
Thus, correct ans is E #### E
QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd?
options: A)15% B)25% C)35% D)50% E)80%
SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even.
The percentage of odd numbers is about (1/2)(300) / 1000 = 15%
The answer is A. #### A
QUESTION:In a certain neighborhood, there are half as many beige houses as white houses, and 3 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?
options: A)4:1 B)3:5 C)2:3 D)1:3 E)1:4
SOLUTION:The ratio of beige:white:brown = 3:6:2
The answer is C. #### C
QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years?
options: A)2500 B)2800 C)3500 D)3600 E)2050
SOLUTION:P = 4032
R = 20%
Required population of town = P/(1 + R/100)^T
= 4032/(1 + 20/100)^2
= 4032/(6/5)^2
= 2800(approximately)
Answer is B #### B
QUESTION:How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
options: A)20 B)40 C)80 D)140 E)60
SOLUTION:Explanation:
The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
Answer:E #### E
QUESTION:A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 50km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
options: A)8.95km/hr B)26.7km/hr C)27.8km/hr D)28.5km/hr E)8.45km/hr
SOLUTION:average speed = (2*50*20)/50+20 km/hr
=28.5 km/hr
Answer (D) #### D
QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 20 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
options: A)90. B)80. C)50. D)40. E)25.
SOLUTION:STREET-CAT DOMESTIC-Cat
70 130
(20gray+50other) 90gray+40other
Answer:D #### D
QUESTION:which of the following could be the greatest common factor of positive integers 10 and 15 ? I) 5 II) 4 III) 2
options: A)II only B)I only C)III only D)I,II only E)I,III only
SOLUTION:10=2*5
15=3*5
GCF =5
Answer : B #### B
QUESTION:A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
options: A)1.4 B)1.5 C)1.6 D)1.8 E)1.0
SOLUTION:Let the speed be 's' and let the distance between rose and poppy be 'x'
The problem boils down to:
Rose to Poppy: s+3=x/6 ------- 1
Daisy to Rose: s=(x+18)/10------ 2
so from 1 we can re write x as x=6s+18
substitute the value of x in 2 gives us s=1.8 m/s
D #### D
QUESTION:Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
options: A)66 B)74 C)78 D)80 E)None of these
SOLUTION:Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 74
Therefore total marks in 6 subjects = 74 * 6 = 444
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 444 – 370 = 74
ANSWER B #### B
QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?
options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 %
SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6
S.P. of 1 kg = Rs. 6.50
Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C
QUESTION:How many numbers from 29 to 79 are exactly divisible by 11?
options: A)4 B)6 C)8 D)5 E)7
SOLUTION:Numbers=(79/11)-(29/11)
=7-2
=5 numbers
Option D is answer #### D
QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
options: A)1500 B)2999 C)2772 D)2987 E)2661
SOLUTION:P = 15(100/10)2 => P = 1500.Answer:A #### A
QUESTION:The digit in unit's place of the product 81 ×82×.....×89 is
options: A)0 B)2 C)6 D)8 E)4
SOLUTION:Solution
Required digit = Unit digit
=(1×2×3×4×5×6×7×8×9) =0.
Answer A #### A
QUESTION:If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true?
I. ab is even
II. ab > 0
III. c is even
options: A)I only B)II only C)I and II D)I and III E)I, II, and III
SOLUTION:ab2/c is positive which means a and C >0 or a and c<0 since b2 is positive
Case 1 - a=3 b=2 c=3 or c=6 where ab2 /2 would be even when c= 3 or c=6
lets see III option where C is even as per our assumption C can be even and odd, hence it is out.
lets see option II ab>0 a and b can positive or negative hence sign of ab cannot be determined hence it is out
So options B,C,D,E are gone and ans is A #### A
QUESTION:If −y ≥ x, and −x < −4, then which of the following must be true?
options: A)y = −4 B)y > −4 C)−y > 4 D)y ≤ −4 E)y ≥ −4
SOLUTION:−y ≥ x, and −x < −4
y <= -x < -4
As '-x' is less than '-4' and Y is less than or equal to '-x'
we have y < -4 which is similar to -y > 4.
C) -y >4 #### C
QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
options: A)36 B)76 C)98 D)27 E)24
SOLUTION:(3x-9):(5x-9)
= 9:17
x = 12 => 3x
= 36
Answer:A #### A
QUESTION:A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr.
What is the speed of the boat?
options: A)2.5 kmph B)3.5 kmph C)4.5 kmph D)1.5 kmph E)9.5 kmph
SOLUTION:speed upstream = 10/3
speed of boat down stream = 10/6
speed of boat = 1/2(10/3 + 10 /6 ) = 2.5 kmph
ANSWER:A #### A
QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph
SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (26 - 18)/2 = 4 kmph
Answer:B #### B
QUESTION:Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -7 then by what factors will the Mean,Variance and Standard Deviation respectively change ?
options: A)-7,-7,-7 B)-7,7,7 C)1,1,1 D)-7,49,7 E)7,7,49
SOLUTION:Mean: If all values are multiplied by -7 then their sum will also be multiplied by -7 so Mean will also get -7
Variance:
Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values
When we multiply all the values by -7 then the difference between the mean and the individual values also gets multiplied by -7 and the square of that difference becomes 49. So, the variance gets multiplied by a factor of 49
SD:
Standard Deviation is the square root of variance so sqrt(49)=7. So SD gets multiplied by a factor of 7.
So, answer will be D. #### D
QUESTION:A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze?
options: A)154 cm2 B)113 m2 C)123 m2 D)115 m2 E)None of these
SOLUTION:Area of the shaded portion
= 1⁄4 × π × (12)2 = 113 m2
Answer B #### B
QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold?
options: A)6 B)4 C)8 D)10 E)12
SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies;
14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22
# of paperback copies sold is 30-22=8
Answer: C #### C
QUESTION:How much is 90% of 40 is greater than 4/5 of 25?
options: A)29 B)776 C)66 D)16 E)99
SOLUTION:(90/100) * 40 – (4/5) * 25
36 - 20 = 16
Answer: D #### D
QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
options: A)15% B)25% C)15.125% D)27.78% E)none
SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options.
The correct answer is (D). #### D
QUESTION:A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
options: A)175/256 B)451/365 C)312/456 D)156/754 E)164/784
SOLUTION:The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans:A #### A
QUESTION:A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
options: A)48 km/hr B)56 km/hr C)60 km/hr D)52 km/hr E)None of these
SOLUTION:Explanation:
Method : 1
If a car covers a certain distance atxkmph and an equal distance at y kmph,
the average speed of the whole journey = 2xy/x+y kmph.
By using the same formula, we can find out the average speed quickly
Speed with which he travels from A to B = x = 40 km/hr
Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr
average speed = (2×40×60)/(40+60) = 48 km/hr
Assume that distance from A to B = x km
Speed with which he travels from A to B = x = 40 km/hr
Time to travel from A to B = distance/speed = x/40 hr
Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr
Time to travel from B to A = distance/speed = x/60
Total distance traveled = x+x = 2x
Total time taken = x/40 + x/60
Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60)
= 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr
Answer: Option A #### A
QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 8?
options: A)2/13 B)3/45 C)5/36 D)6/73 E)4/15
SOLUTION:n(S) = 6*6 = 36
E = {(2,6),(3,5),(4,4),(5,3),(6,2)}
Probability = 5/36
Answer is C #### C
QUESTION:A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C
together need 3 hours to finish the same work. In how many hours B can complete the work ?
options: A)10 hours B)12 hours C)16 hours D)18 hours E)None of these
SOLUTION:ExplanaƟon:
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12
Work done by B in 1 hour = (7/12)�(1/2) = 1/12
=> B alone can complete the work in 12 hour
Answer: B #### B
<<<Examples ends
QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water?
options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3
SOLUTION:G = 10W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
10W+5Wx = x+1 * 6W
10+5x = 6(x+1)
x = 4
Ratio of gold with copper = 1:4 = 1:4
Answer is B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
options: A)4 B)8 C)6 D)2 E)1
SOLUTION:Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer:A #### A
QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work?
options: A)2days B)4days C)6days D)7days E)10days
SOLUTION:The required answer = (15-5)*9 / 15 = 40/10 = 6days
Answer is C #### C
QUESTION:The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
options: A)76 kg B)76.5 kg C)85 kg D)Data inadequate E)None of these
SOLUTION:EXPLANATION
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer C #### C
QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M?
options: A)278 B)2890 C)270 D)2702 E)1050
SOLUTION:504/M = 384/800
(504 * 800) / 384 = M
M = 1050
Answer:E #### E
QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?
options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 %
SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6
S.P. of 1 kg = Rs. 6.50
Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C
QUESTION:A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 6% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
options: A) 0.25 B) .05^10 C) 1-0.94^10 D) 1-0.05^10 E) 0.95^10
SOLUTION:Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.94^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.94^10.
Answer: C. #### C
QUESTION:A computer wholesaler sells 11 different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?
options: A)15/56 B)3/28 C)1/28 D)1/56 E)3/55
SOLUTION:Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 9 avilable. so 9C1 is the numerator.
Total no of ways we can choose 3 from 11 is 11c3, which is the denominator.
So, the probability: 9c1/11c3= 3/28 ans is E. #### E
QUESTION:Find the unit's digit in the product 2467 153 * 34172?
options: A)1 B)3 C)2 D)5 E)7
SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172
Now 7 4 gives unit digit 1
7 152 gives unit digit 1
7 153 gives 1*7=7.Also 172 gives 1
Hence unit's digit in the product =7*1=7.
Option A #### A
QUESTION:A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ?
options: A)9 B)10 C)11 D)12 E)13
SOLUTION:A
5 cartons for large boxes = 5 * 6 = 30 boxes
4 cartons for small boxes = 4 * 9 = 36 boxes
He will need 9 cartons to place 66 boxes. #### A
QUESTION:If the selling price of 8 articles is same as the cost price of 10 articles. Find the gain or loss percentage?
options: A)25% B)45% C)35% D)65% E)55%
SOLUTION:Let the C.P of each article be Re 1. Then,
S.P of 8 articles = C.P of 10 articles = Rs. 10
Now, C.P of 8 articles = Rs. 8, S.p of 8 articles = Rs 10
Gain = Rs ( 10 - 8 ) = Rs 2.
Gain% = ( 2/8 × 100 ) % = 25%
Answer : A #### A
QUESTION:Find the next term in series - 25, 37, 49, 61, ?
options: A)71 B)72 C)73 D)74 E)75
SOLUTION:Series is Increased by 12.
25 +12 =37
37 +12 =49
49 +12 =61
61 +12 =73
ANSWER:C #### C
QUESTION:30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there?
options: A)800 B)1000 C)1200 D)1500 E)1800
SOLUTION:800score Official Solution:
People who do both hunting and fishing make 30% of fishermen and 20% of hunters. There are 1500 hunters so 1500 × 20% = 300 pers. do both hunting and fishing. Same people make 30% of all fishermen.30% of fishermen = 300 pers.
Fishermen = (300 / 30) × 100 pers. = 1000 pers.
The correct answer is choice (B). #### B
QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {1,2,3}, what`s the probability that xy will be even?
options: A)1/6 B)1/3 C)2/3 D)1/2 E)5/6
SOLUTION:The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: C. #### C
QUESTION:A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?
options: A)80 B)288 C)4^4 D)576 E)288^2
SOLUTION:The condition that TWO boys or TWO girls cannot be together means they should be alternate..
Total five means 3 of one and 2 of other..
1) choose 3 girls and arrange them... 4C3*3! = 4!= 24
2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C2*2!= 12
Total ways = 24*12 = 288..
2) same as above.. 2 girls and 3 boys.. 288
Total 288*2=576
ANS:D #### D
QUESTION:If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,711 minutes earlier? (Assume standard time in one location.)
options: A)6:22 B)6:24 C)6:27 D)6:36 E)6:32
SOLUTION:6:27minus 2,880,711in any way must end with 6, the only answer choice which ends with 6 is D.
Answer: D. #### D
QUESTION:Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
options: A)306.05 B)306.00 C)306.04 D)306.05 E)306.01
SOLUTION:A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer: A #### A
QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages.
options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these
SOLUTION:Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 136
20x = 160 => x = 8
Their present ages are 32, 56 and 72 years respectively.
ANSWER:D #### D
QUESTION:If a trader sold two cars each at Rs. 404415 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is ?
options: A)1.44 % B)2.02 % C)1.04 % D)2.25 % E)3.40 %
SOLUTION:Explanation:
SP of each car is Rs. 404415, he gains 15% on first car and losses 15% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100
= (15)(15)/100 % = 2.25%
ANSWER IS D #### D
QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was
options: A)960 B)980 C)900 D)970 E)1000
SOLUTION:Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 1000
Answer: E) Rs 1000 #### E
QUESTION:If the average (arithmetic mean) of a and b is 110, and the average of b and c is 150, what is the value of a − c?
options: A)−220 B)−100 C)100 D)−80 E)It cannot be determined from the information given
SOLUTION:Question: a - c = ?
(a + b)/ 2 =110 ===> a + b = 220
(b + c)/2 = 150 ===> b + c = 300
(a + b) - (b + c) = 220 - 300 ===> a + b - b - c = - 80 ===> a - c = - 80
Answer: D #### D
QUESTION:A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
options: A)5520 B)2789 C)5550 D)2889 E)2788
SOLUTION:Total production of salt by the company in that year = 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year = 66600/12 = 5550.
Answer: C #### C
QUESTION:Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 7 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
options: A)$10,350 B)$10,395 C)$10,593 D)$11,500 E)$12,705
SOLUTION:the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10593. So the answer is (C). #### C
QUESTION:For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6?
options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4.
SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6
= 6*0 + 2*7.2 + 8 - 6.6
= 0 +14.4 +1.4
15.8
Answer B #### B
QUESTION:When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 3. If 1 < m < 300, what is the greatest possible value of m?
options: A)173 B)203 C)233 D)263 E)293
SOLUTION:13*9 = 117
Let's start with 3, and keep adding 13 until we find a number with the form 9k+2.
3, 16, 29 = 9*3+2
The next possible number is 29 + 117 = 146
The next possible number is 146 + 117 = 263
The next possible number would be greater than 300.
The answer is D. #### D
QUESTION:In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 80 and a standard deviation of 14, which of the following is exactly 2.60 standard deviations more than the mean?
options: A)a) 43.6 B)b) 60 C)c) 72 D)d) 77.5 E)e) 81
SOLUTION:Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 80
2) The standard deviation of the group is 14
If you go 1 SDupfrom the average, you hit.....80+14 = 94
If you go 1 SDdownfrom the average, you hit.....80-14 = 66
If you go 2 SDsupfrom the average, you hit.....80+2(14) = 108
If you go 2 SDsdownfrom the average, you hit.....80-2(14) = 52
Etc.
Here, we're asked for the number that is EXACTLY 2.60 SDs above the mean....
2.60 SDsupwould be.....80 + 2.60(14) = 43.6
A #### A
QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $27. What is the cost of the carpet, in dollars per square yard? (1 square yard = 6 square feet)
options: A)xy/297 B)11xy/3 C)3xy/11 D)297/(xy) E)162/(xy)
SOLUTION:The area of the carpet in feet is xy.
The area in square yards is xy / 6.
The price per square yard is 27 / (xy/6) = 162/(xy).
The answer is E. #### E
QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price
options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/-
SOLUTION:100 % ------> 200 (100 * 2 = 200)
120 % ------> 240 (120 * 2 = 240)
Selling price = Rs.240/-
Answer : D #### D
QUESTION:B @ K I 9 D © 5 2 T $ M 4 E J # U R 1 A δ K 5 W 6 % F Q 7 H P 8 Z
Which of the following should come in place of the question mark(?) in the following series based on the elements in the above arrangement?
K9D 2$M JUR ?
options: A)δKW B)δK5 C)δ56 D)δW6 E)None of these
SOLUTION:Explanation:
K +6 2 +6 J +6 δ
9 +6 S +6 U +6 5
D +6 M +6 R +6 W
ANSWER IS E #### E
QUESTION:In a recent head-to-head run-off election, 10,000 absentee ballets were cast. 2/3 of the absentee ballets were thrown out and 2/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?
options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000
SOLUTION:1/3 * 3/5 (total absentee votes) = 1/5 (total votes)=1/5*10000=2000
Answer is A #### A
QUESTION:The perimeter of one face of a cube is 24 cm. Its volume will be:
options: A)216cm3 B)400cm3 C)250cm3 D)625cm3 E)None of these
SOLUTION:Explanation:
Edge of cude = 24/4 = 6 cm
Volume = a*a*a = 6*6*6 = 216 cm cube
Option A #### A
QUESTION:If a dozen of oranges cost $5, what would be the cost of 10 oranges?
options: A)3.56 B)4.16 C)4.86 D)5.1 E)5.2
SOLUTION:The cost of one orange=5/12=0.416
The cost of ten oranges= 0.416x10= $ 4.16
Answer: B #### B
QUESTION:If S = {50, 72, 108, 120, 205}, how much less is the mean of the numbers in S than the median of the numbers in S?
options: A)2 B)3 C)5 D)8 E)9
SOLUTION:Mean = (50 + 72 + 108 + 120 + 205)/5 = 111
Median = 108
Difference = 111-108 = 3
Option B #### B
QUESTION:One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?
options: A)120 sq. m B)140 sq. m C)125 sq. m D)130 sq. m E)110 sq. m
SOLUTION:Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m
Area = 15 x 8 =120 sq. m
ANSWER:A #### A
QUESTION:Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 40 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
options: A)4:5 B)9:25 C)5:4 D)25:9 E)Cannot be determined from the information provided
SOLUTION:Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B
Time A = 2*pi*25/Speed A
Time B = 2*pi*20/Speed B
Since the times are same,
50pi/Speed A = 40pi/Speed B
SpeedA/Speed B = 50pi/30pi = 5/4
Correct Option: C #### C
QUESTION:A mixture contains alcohol and water in the ratio 2:5. If 10liters of water is added to the mixture, the ratio becomes 2:7. Find the quality of alcohol in the given mixture.
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:Let the quantity of alcohol and water be 2x and 5x
2x/(5x+10) = 2/7
20x = 4(3x+5)
x=5
Quantity of alcohol = 2*5 = 10liters.
Answer is B #### B
QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2
SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer: B #### B
QUESTION:Insert the missing number
..., 4, 8, 16, 32, 64, 128, 256
options: A)6 B)5 C)2 D)3 E)8
SOLUTION:series is 2* Previous Number.
ANSWER:C #### C
QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full?
options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes
SOLUTION:1/20 - 1/40 = 1/40
40 minutes
Answer:C #### C
QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ?
options: A)7/17 B)7/22 C)7/18 D)7/19 E)7/15
SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 7C2/¹15C2 + 8C2/15C2
= 7/15
Answer: E #### E
QUESTION:5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3294, how much was it in the beginning?
options: A)2988 B)2776 C)4079 D)2871 E)881
SOLUTION:X * (95/100) * (85/100) = 3294
X = 4079
Answer:C #### C
QUESTION:A man wants to sell his scooter .There are two offers one at Rs12000 cash and other at a credit of Rs12880 to be paid after 8 months ,money being at 18% per annum which is better offer?
options: A)Rs.12880 B)Rs.12000 C)Both are equally good D)None of the above E)Cannot be determined
SOLUTION:Explanation:
PW of Rs.12,880 due 8 months hence
=Rs.[12880×100/100+(18×812)]=Rs.11500=
Clearly 12000 in cash is a better offer.
Answer: B #### B
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)123 B)166 C)240 D)157 E)198
SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C #### C
QUESTION:How many quarters are equal to 7 dollars?
options: A)1 B)28 C)12 D)9 E)7
SOLUTION:7 * 4 = 28 quarters
Answer : B #### B
QUESTION:There are 6 red shoes, 2 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
options: A)1/9 B)2/9 C)5/9 D)3/4 E)2/3
SOLUTION:total 8 from take one.
8c1=8
red 6 from one
6c1=6
6/8=3/4
ANSWER:D #### D
QUESTION:In the xy-coordinate system, line k passes through points (-8m, 0) and (0, 2m). Which of the following is a possible equation of line k?
options: A)y = -4x + 2m B)y = 1/4*x - 8m C)y = 4x + 2m D)y = 1/4*x + 2m E)y = -1/4*x - 8m
SOLUTION:The slope of the line is 2m/8m=1/4.
The y-intercept is 2m.
the equation of the line is: y = 1/4*x +2m
The answer is D. #### D
QUESTION:In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13. If the shop carries 352 dogs and bunnies total in stock, how many dogs are there?
options: A)42 B)66 C)98 D)112 E)154
SOLUTION:Let us assume the number of dogs, cats and bunnies to be 3x, 7x and 13x
Total dogs and bunnies = 16x.
And we are given that 16x = 352.
Hence x = 22.
Dogs = 3x = 3*22 = 66 (Option B) #### B
QUESTION:30 liters of a mixture contains milk and water in the ratio 2:1. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be?
options: A)3:2 B)3:1 C)4:1 D)5:2 E)2:1
SOLUTION:Quantity of milk in 30 liters if mix = 30*2/3 =20 liters
Quantity of milk in 35 liters of new mix = 20+5 = 25 liters
Quantity of water in it = 35-25 = 10 liters
Ratio of milk and water in new mix = 25:10 = 5:2
Answer is D #### D
QUESTION:A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get:
options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these
SOLUTION:Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3100/25 = 124
So, A’s amount = 124 × 15 = Rs.1860.
Answer: Option C #### C
QUESTION:In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/4.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
options: A)5. B)7. C)9. D)10. E)17.
SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10
Lets take LCM of three balls 4,5 and 10 =20.
The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls.
The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls.
The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS.
Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls.
IMO option C is correct. #### C
QUESTION:The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what is the speed of the car?
options: A)30km/h B)40km/h C)50km/h D)60km/h E)80km/h
SOLUTION:The main idea used in this kind of problems is that the distance equals speed multiplied by time S=V⋅t
Car x + 5 (V (km/hr)) 4 t (hr) 4(x +5) S (km)
Truck X V (km/hr) 4 t (hr) 4x S (km)
4(x+5)+4x=380
4x+4x=380−20
8x=360
x=3608
x=45
Therefore the truck's speed is 45 km/hr, and the car's speed is 45+5=50 km/hr
correct answer is C)50km/hr #### C
QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference W between the greatest and least of the five integers?
options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4
SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference W= 10k - 3 - (10k - 7)
= 4
Answer - D #### D
QUESTION:117 x 217 + 83 x 83=?
options: A)79698 B)20578 C)80698 D)81268 E)None of them
SOLUTION:=(117)^2 + (83)^2
=(100+17)^2 + (100-17)^2
=2[(100)^2+(17)^2]
=2[10000+289]
=2 x 10289 = 20578
Answer is B #### B
QUESTION:There is a certain relation between two given words on one side of : : and one word is given on another side of : : while another word is to be found from the given alternatives, having the same relation with this word as the given pair has.
options: A)Landslides B)Strains C)Resistances D)Volcanoes E)Volcanoe1
SOLUTION:Explanation:
Seismography is an instrument to measure the intensity of an earthquake.
Similarly, taseometer is an instrument to measure strains.
Answer: B) Strains #### B
QUESTION:A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A?
options: A)Rs.240 B)Rs.340 C)Rs.260 D)Rs.280 E)Rs.440
SOLUTION:LCM = 180
Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c
= (180/15)/(180/15 +180/20 + 180/45)
= (12/25) * 500
= Rs.240
ANSWER:A #### A
QUESTION:Ifaequals the sum of the even integers from 2 to 60, inclusive, andbequals the sum of the odd integers from 1 to 59, inclusive, what is the value of a - b ?
options: A)1 B)10 C)30 D)20 E)21
SOLUTION:This is a solution from Beatthegmat:
even numbers:
(60-2)/2 + 1 = 30 even integers.
(60+2)/2 = 31 is the average of the even set.
sum = avg*(#of elements) = 31*30 = 930 = a
odd numbers:
(59-1)/2 + 1 = 30 odd integers.
(59+1)/2 = 30 is the average of the odd set.
sum = avg*(#of elements) = 30*30 = 900 = b
a-b = 930 - 900 = 30. Answer : C #### C
QUESTION:Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone?
options: A)6 B)12 C)14 D)15 E)17
SOLUTION:Renu’s one day’s work = 1/6
Suma’s one day’s work = 1/3 - 1/6 = 1/6
Suma can do it alone in 6 days.
ANSWER:A #### A
QUESTION:There are 50 students in a class. If 10 % are absent on a particular day, find the number of students present in the class.
options: A)43 B)36 C)28 D)45 E)11
SOLUTION:Number of students absent on a particular day = 10 % of 50
i.e., 10/100 × 50 = 5
Therefore, the number of students present = 50 - 5 = 45 students.
Answer:D #### D
QUESTION:How many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number?
options: A)4 B)10 C)11 D)12 E)15
SOLUTION:The Question basically asks how many positive odd integers less than 100 are odd multiples of 5
So we have 5,15,25,35,45,55,65,75,85,95
=10
Ans B #### B
QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer?
options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5
SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9
Probability to become a secretary = (9/10 * 1/9) = 1/10
Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8
probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10
Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E
QUESTION:A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
options: A)13 B)25 C)17 D)12 E)11
SOLUTION:11 cartons total
7 large boxes (7 * 8 = 56 boxes)
4 small boxes (4 *10 = 40 boxes
11 total cartons and 96 boxes #### E
QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X
options: A)35 B)56 C)142 D)87 E)98
SOLUTION:(C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 142 #### C
QUESTION:How many numbers between 100 and 600 are divisible by 2, 3, and 7 together?
options: A)112 B)77 C)267 D)12 E)99
SOLUTION:Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 600
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 600:
600/42 = 14.28
Hence, 42*14 = 588 is the last number divisible by 42 within 600
Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12
ANSWER: D #### D
QUESTION:What number has a 3:4 ratio to the number 400?
options: A)130 B)100 C)200 D)300 E)120
SOLUTION:3:4 = x: 200
4x = 3*400
x=300
ANSWER:D #### D
QUESTION:subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 15 pages.
options: A)8 B)10 C)12 D)14 E)6
SOLUTION:subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(15/2.5)=6 hrs
ANSWER:E #### E
<<<Examples ends
QUESTION:Two numbers have a H.C.F of 9 and a product of two numbers is 1800. Find the L.C.M of the two numbers?
options: A)200 B)150 C)160 D)170 E)180
SOLUTION:L.C.M of two numbers is given by
(Product of the two numbers) / (H.C.F of the two numbers) = 1800/9 = 200.
ANSWER:A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:If C.P. of 28 books is equal to S.P of 30 books , then your gain or loss is ?
options: A)23 1/3 gain % B)30 10/23 loss % C)6.67 loss % D)30 1/3 loss % E)40 1/3 loss %
SOLUTION:Say the cost price of 28 books is $28 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 28$, hence the loss = ($30 - $28)/$30 = ~6.67%.
Answer: C. #### C
QUESTION:69 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
options: A)20 B)23 C)24 D)25 E)26
SOLUTION:According to the chain rule,
M1 x T1 = M2 x T2
Therefore, 69 x 12 x 5 = 30 x 6 x X
X = 23
Hence, the number of days = 23.
ANSWER:B #### B
QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
options: A)10 B)12 C)16 D)18 E)21
SOLUTION:Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B #### B
QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball?
options: A)(y+4)/(y+r+7)*(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)*(r+4)/(y+r+6) D)(y+3)/(y+r+7)*(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6)
SOLUTION:Currently we have r red and y yellow balls.
After adding new balls, we have
red = r + 3
Yellow = y + 4.
Total = r + y + 7
Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1
So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1]
Answer : option A. #### A
QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs?
options: A)15 B)16 C)17 D)18 E)19
SOLUTION:16
ANSWER:B #### B
QUESTION:The product Z of two prime numbers is between 10 and 30 . If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24, then what is Z?
options: A)21 B)15 C)14 D)10 E)6
SOLUTION:The smallest possible product is 21 which is 3*7.
All other products are too big.
The answer is A. #### A
QUESTION:Calculate the ratio between x and y if 30% of x equal to 50% of y?
options: A)4 : 5 B)3 : 5 C)3 : 7 D)3 : 2 E)4 : 5
SOLUTION:Explanation:
30 x = 50 y
x: y = 30: 50 = 3 : 5
Answer:B #### B
QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased?
options: A) 100% B) 500% C) 300% D) 600% E) 800%
SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times.
The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%.
Answer: B. #### B
QUESTION:What number is 60 more than two-fourth of itself?
options: A)180 B)225 C)288 D)324 E)336
SOLUTION:2/4x+60= x
That means 60=2/4x
x= 60*3= 180
A is the answer #### A
QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer?
options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5
SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9
Probability to become a secretary = (9/10 * 1/9) = 1/10
Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8
probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10
Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E
QUESTION:What least value must be assigned to * so that th number 197*5462 is divisible by 9?
options: A)2 B)4 C)6 D)1 E)3
SOLUTION:Let the missing digit be x
Sum of digits = (1+9+7+x+5+4+6+2)=34+x
For 34+x to be divisible by 9 , x must be replaced by 2
The digit in place of x must be 2.
ANSWER A 2 #### A
QUESTION:There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
options: A)1/9 B)2/9 C)5/9 D)4/9 E)2/3
SOLUTION:total 9 from take one.
9c1=9
red 5 from one
5c1=5
5/9
ANSWER:C #### C
QUESTION:An enterprising businessman earns an income of Re 5 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 10th day of business, he earns an income of:
options: A)21 B)22 C)20 D)45 E)30
SOLUTION:2nd day he earns = 3(2 – 5)
3rd day he earns = 3(3 – 5)
On 20th day he earns 3(20 -5) = 45 rupees
ANSWER:D #### D
QUESTION:The average (arithmetic mean) of four numbers is 7x + 6. If one of the numbers is x, what is the average of the other three numbers?
options: A)9x + 8 B)3x + 3 C)5x + 1 D)5x + 4 E)15x + 12
SOLUTION:If the average of four numbers is 7x + 3, then the sum of all four numbers if 4 * (7x + 6) = 28x + 24. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 24 - x)/3 = (27x + 24)/3 = 9x + 8.
Answer is A. #### A
QUESTION:R campers fished for 2 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour?
options: A)2m + n(R-m) B)(2m + n(R-m))/3 C)(2m + n(m-R))/3 D)(2m + n)/2 E)(2m + n)/R
SOLUTION:m of the campers caught 2 fish apiece in 2 hours --> total fish caught by m campers = 2m;
The rest caught a combined total of n fish.
Total fish caught in 2 hours = 2m+n --> per hour (2m+n)/2.
Answer: D. #### D
QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ?
options: A)20 B)45 C)55 D)90 E)85
SOLUTION:Explanation:
Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45.
Answer: B #### B
QUESTION:If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ?
options: A)Equal to 3 B)Less than 3 C)More than 3 D)Less than 1/3 E)none of these
SOLUTION:Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3
ANSWER:C #### C
QUESTION:If x is negative and y is positive, which of the following cannot be positive?
options: A)x/y B)-x*y C)-x/y D)x^2+y E)x^6+y
SOLUTION:- /+ = -
x/y is negative.
Answer : A #### A
QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
options: A)27% B)25% C)21% D)85% E)24%
SOLUTION:SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer:B #### B
QUESTION:The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
options: A)A)8:9 B)B)3:5 C)C)4:3 D)inadequate E)of these
SOLUTION:Let P's age and Q's age be 6x and 8x years respectively.
Then, 8x - 6x = 4 => x =2
Required ratio = (6x + 4) : (7x + 4)
16 : 18 = 8:9
ANSWER:A #### A
QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
options: A)10years B)12 years C)5 years D)3 years E)24 years
SOLUTION:Explanation:
9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3 years
Answer:D #### D
QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2430 votes. How many votes were cast?
options: A)7500 B)3388 C)8100 D)2888 E)2661
SOLUTION:35%-----------L
65%-----------W
------------------
30%----------2430
100%---------? => 8100
Answer: C #### C
QUESTION:There are 8 magazines lying on a table; 4 are movie magazines and the other 4 are education magzines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the movie magazine will be selected?
options: A)9/14 B)11/14 C)13/14 D)1/14 E)3/14
SOLUTION:1- (4c3/8c3) = 13/14
Answer : C #### C
QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P?
options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36
SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house.
J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs
Answer:B #### B
QUESTION:Three walls have wallpaper covering a combined area of 280 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 36 square meters. What is the area that is covered with three layers of wallpaper?
options: A)5 Square Meters B)32 Square Meters C)42 Square Meters D)83.3 Square Meters E)120 Square Meters
SOLUTION:280 - 180 = 100 sq m of the wallpaper overlaps (in either two layers or three layers)
If 36 sq m has two layers, 100 - 36 = 64 sq m of the wallpaper overlaps in three layers. 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m.
Answer (B). #### B
QUESTION:There are 680 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
options: A)425 B)345 C)375 D)380 E)400
SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 680. Hence
3x + 5x = 680
Solve for x
8x = 680
x = 85
Number of boys
3x = 3 × 85 = 255
Number of girls
5x = 5 × 85 = 425
A #### A
QUESTION:In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows.
options: A)12 B)14 C)16 D)18 E)20
SOLUTION:Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 28 + 2(c + d)
=> d + 2c = 14 + c + d
=> 2c = 14 + c
=> c = 14
i.e., total number of cows = 14
Answer is B. #### B
QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him?
options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7
SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E
QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 4
II. 12
III. 24
options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only
SOLUTION:Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three #### A
QUESTION:Based on this year's costs, a builder budgets P dollars for planing N new buildings next year. If the average cost of building each building were to increase 10% from this year's cost, then the greatest number of buildings that the builder could build next year using P dollars would be:
options: A)9% less than N B)11% less than N C)Equal to N D)9% greater than N E)11% greater than N
SOLUTION:Correct answer is (A).
This year, the price of a building is price1=P/N.
If this price increases by 50% it becomes Price2=P/N*1.1
Then with P dollars, you can build P/Price2 buildings i.e. P/(P/N*1.1) i.e. N/1.1 i.e. 0.91*N
Which is 9% less than N. #### A
QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these
SOLUTION:Reqd ratio 4 × 140â„100 : 7 × 150â„100 : 8 × 175â„100
= 4 × 140 : 7 × 150 : 8 × 175 = 8 : 15 : 20
Answer C #### C
QUESTION:If a - b =4 and
a2+b2=52
, find the value of ab.
options: A)8 B)26 C)18 D)42 E)36
SOLUTION:Explanation:
We know
2ab=(a2+b2)−(a−b)2
2ab=52−16=36
=>ab=18
Option C #### C
QUESTION:A train is 288 meter long is running at a speed of 29 km/hour. In what time will it pass a bridge of 101 meter length?
options: A)48.29 B)50 C)26.8 D)45.29 E)30
SOLUTION:Speed = 29 Km/hr = 29*(5/18) m/sec = 145/18 m/sec
Total distance = 288+101 = 389 meter
Time = Distance/speed
= 389 * (18/145) = 48.29 seconds.
Answer: A #### A
QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed?
options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5!
SOLUTION:Explanation:
Total number of letters = 5
Using these letters the number of 5 letters words formed is 5!.
Answer: Option E #### E
QUESTION:The sum of 55 consecutive integers is 5555. What is the greatest integer in the set?
options: A)126 B)128 C)130 D)132 E)134
SOLUTION:Let x be the first integer in the set, then x+54 is the largest integer.
The sum is: x+(x+1)+(x+2)+...+(x+54)
= 55x + 54*55/2
= 55(x+27)
Then x+27=101
x=74
The largest integer in the set is 74+54=128
The answer is B. #### B
QUESTION:It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
options: A)142 B)144 C)3680 D)3280 E)3680
SOLUTION:Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th .
Now, number of even places = 3.
Number of girls to occupy the even places = 3.
Even places can be filled = P (3, 3) ways.
Number of boys = 4.
The remaining 4 places can be filled by 4 boys = P (4, 4) ways
By the fundamental principle of counting:
The required number of seating arrangements
P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144
ANSWER:B #### B
QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor?
options: A)14 B)16 C)18 D)20 E)22
SOLUTION:d = (D-R)/Q
= (122 - 2)/6
= 122/6 = 20
D) #### D
QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
options: A)877m B)180m C)786m D)165m E)456m
SOLUTION:Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B #### B
QUESTION:A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent?
options: A)33 1/8 % B)33 7/3 % C)50 % D)33 5/8 % E)34 1/3 %
SOLUTION:The total number of mangoes bought by the shopkeeper be 24.
If he buys 6 a rupee, his CP = 4
He selling at 4 a rupee, his SP = 6
Profit = SP - CP = 6 - 4 = 2
Profit Percent = 2/4 * 100 = 50 %
Answer: C #### C
QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Tuesday, what was the expected day when both the brothers were to return home and when did Rohit Return?
options: A)Wednesday, Sunday B)Thursday, Monday C)Friday, Tuesday D)Monday, Friday E)none
SOLUTION:Rajat returned on Tuesday -i.e. 3 days earlier
so actual day to return home is Friday.
Rohit returned after days so Tuesday.
ANSWER:C #### C
QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item
options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these
SOLUTION:Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 1300
= 80/100 * 1300
= 1040
Option D #### D
QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is
options: A)16 B)24 C)48 D)96 E)78
SOLUTION:Solution
Required number = (2×4×6)
= 48.
Answer C #### C
QUESTION:What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
options: A)$788 B)$812 C)$864 D)$878 E)$912
SOLUTION:After one year: 1.2 * $500
After two years: (1.2)^2 * $500
After three years: (1.2)^3 * $500 = $864
The answer is C. #### C
QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
options: A)14700 B)14500 C)14900 D)14300 E)14000
SOLUTION:Total amount invested = 50000
Assume that investment of C =x.
Then investment of B =5000+x,
Investment of A =4000+5000+x=9000+x
x+5000+x+9000+x=50000
⇒3x+14000=50000
⇒3x=50000–14000=36000
⇒x=36000/3=12000
Investment of C =x=12000
Investment of B =5000+x=17000
Investment of A =9000+x=21000
Ratio of the investment of A, B and C
=21000:17000:12000
=21:17:12
Share of A = Total profit ×21/50
=35000×21/50=700×21=14700
Answer is A. #### A
QUESTION:What is the area of a square field whose diagonal of length 24 m?
options: A)256 B)289 C)200 D)288 E)178
SOLUTION:d2/2 = (24 * 24)/2
= 288
Answer: D #### D
QUESTION:Jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?
options: A)5 B)10 C)22 D)25 E)30
SOLUTION:Let's TEST Answer C: 22 seashells...
With 22 seashells, Jamie would have 22(20) =440 cents. This would allow him to buy 8 books for 440 cents total, so this is the correct answer.
C #### C
QUESTION:What approximate value should come in place of the question mark (?) in the following equation?
1.542 × 2408.69 + 5134.632 = ?
options: A)4600 B)4800 C)5200 D)6400 E)8800
SOLUTION:Explanation 3700 + 5100 = 8800
Answer E #### E
QUESTION:A cycle is bought for Rs.450 and sold for Rs.520, find the gain percent?
options: A)18 B)14 C)20 D)15 E)15.55
SOLUTION:450 ---- 70
100 ---- ? => 15.55%
Answer: E #### E
QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
options: A)8 B)12 C)18 D)24 E)48
SOLUTION:In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6
Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E
QUESTION:A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
options: A)18 years B)20 years C)24 years D)32 years E)34 years
SOLUTION:Explanation:
Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
ANSWER IS A #### A
QUESTION:If (-12x)^(4x) = 12x^(15 - x) and x is an integer, what is the value of x ?
options: A)5 B)4 C)3 D)2 E)-2
SOLUTION:Since x is an integer, (-12x)^(4x) is always positive.
So, 12x^4x = 12x^(15 - x)
4x = 15 - x
5x = 15
x = 3
Answer: C #### C
QUESTION:Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent?
options: A)705 B)655 C)656 D)657 E)658
SOLUTION:total cost 940
940*25/100=235
so the cut in amount is 235
the less amount to be spend is 940-235=705
ANSWER:A #### A
QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm.
options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm²
SOLUTION:AB² = AC² - BC²
= 15² - 12²
= 225 - 144
= 81
Therefore, AB = 9
Therefore, area of the triangle = ¹/₂ × base × height
= ¹/₂ × 12 × 9
= 54 cm²
ANSWER : C #### C
QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
options: A)8 B)2 C)9 D)4 E)6
SOLUTION:Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96
15000[(1 + R/100)2 - 1 - 2R/100] = 96
15000[(100 + R)2 - 10000 - 200R]/10000 = 96
R2 = (96 * 2)/3 = 64 => R = 8
Rate = 8%
Answer: Option A #### A
QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:One. You cannot have more mice if you start with one!
Answer A #### A
QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle?
options: A)16 B)25 C)33 D)46 E)58
SOLUTION:The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*9 + 2*9 which is about 46.
The answer is D. #### D
QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
options: A)1100 B)1200 C)1349 D)1430 E)1340
SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C #### C
QUESTION:12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
options: A)990 B)495 C)1980 D)none E)Cannot be determined
SOLUTION:Explanation :
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals.
Answer : B #### B
QUESTION:If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
options: A)141 B)200 C)618 D)391 E)412
SOLUTION:The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...
A + (A+2) + (A+4) = 3A + 6
We know that 3A + 6 COULD equal one of those five answers; we just have to find it...
Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer
Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer
Could 3A + 6 = 618
3A = 612
A = 204
This IS an EVEN INTEGER! The numbers would be 204, 206 and 208. This IS the answer
Final Answer:
C #### C
QUESTION:How much interest will $8,000 earn in 9 months at an annual rate of 6%?
options: A)$250 B)$350 C)$360 D)$550 E)$650
SOLUTION:Soln:-
9 months = 3/4 of year;
6% = 6/100=3/50;
$8,000(principal)*3/50(interest rate)*3/4(time)=$360.
ANSWER:C #### C
QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins
SOLUTION:The pool was 1/5 full initially.
In 6/5 hrs, it was filled to 8/9 of its capacity.
Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled.
So, 6/5 hrs = 8/9 - 1/5 = 31/45
Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins.
Hence D #### D
QUESTION:If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b?
options: A)35 B)42 C)45 D)49 E)54
SOLUTION:First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
35 = 7 * 5
45 = 3 * 3 * 5
so, (105)^3 = 3 * 7 * 7 * 5 * 3 *3 *5 *b
Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2
b = 5*7 = 35
Correct answer A. #### A
QUESTION:Bob bikes to school every day at a steady rate of e miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
options: A)(x + y) / t B)2(e + t) / ey C)2eyt / (e + y) D)2(e + y + t) / ey E)x(y + t) + y(x + t)
SOLUTION:If we choose for d (distance): 10 miles, for e 10 and for y 5.
t would be 90 minutes or 1,5 hours.
If I try this for answer choice C it fits. #### C
QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
options: A)32:21 B)22:21 C)21:32 D)31:21 E)32:28
SOLUTION:Here capital is not the same.
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.
Hence his term of ratio
=( 20000*6 + 15000*6)
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.
Hence his term of ration
= (30000*4 : 50000*4)
Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4)
= (20*6 + 15*6) : (30*4 + 50*4)
= (20*3 + 15*3) : (30*2 : 50*2)
= 105:160
= 21:32
Answer is C #### C
<<<Examples ends
QUESTION:Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32
SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A,B,C can complete a piece of work in 24,6 and 12 days respectively. Working together, they will complete the same work in how many days?
options: A)13/8 B)26/11 C)24/7 D)12/13 E)1/2
SOLUTION:(A+B+C)'s 1day work = (1/24)+(1/6)+(1/12) = 7/24
A,B,C together will complete the work in 24/7 days
Answer is C #### C
QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
options: A)5 B)10 C)15 D)20 E)25
SOLUTION:Solution
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
Tens place can be filled by any of the remaining 5 numbers.
So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it.
So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D
QUESTION:A division of a company consists of seven men and five women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
options: A)1/6 B)2/5 C)2/9 D)5/12 E)5/33
SOLUTION:First, the denominator. We have twelve different people, and we want a combination of two selected from these twelve. We will use the formula:
nC2 = n(n-1)/2
which, for profound mathematical reasons we need not address here, is also the formula for the sum of the first (n – 1) positive integers. Here
12C2=12(11)/2=6*11=66
That’s the total number of pairs we could pick from the twelve employees. That’s our denominator.
For the numerator, we want every combination of two from the five female employees. That’s
5C2=5(4)/2=5*2=10
That’s the number of pairs of female employees we could pick from the five. That’s our numerator.
probability= 10/66 =5/55
Answer = E #### E
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
options: A)120 metres B)180 metres C)324 metres D)150 metres E)100 meters
SOLUTION:Speed=60 x5/18m/sec=50/3 m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3 x 9m = 150 m.
ANSWER:D #### D
QUESTION:Find the compound interest on $1000 in 2years at 4% per annum, the interest being compounded half-yearly?
options: A)$645.56 B)$82.43 C)$954.26 D)$745.69 E)$1020.45
SOLUTION:Principle = $10000
Rate = 2% half yearly = 4 half years
Amount = 1000*(1 + 2/100)^4 = 1000 * 51/50 * 51/50 * 51/50 * 51/50
= $1082.43
C.I. = 1082.43-1000 = $82.43
Answer is B #### B
QUESTION:A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
options: A)48 km/hr B)56 km/hr C)60 km/hr D)52 km/hr E)None of these
SOLUTION:Explanation:
Method : 1
If a car covers a certain distance atxkmph and an equal distance at y kmph,
the average speed of the whole journey = 2xy/x+y kmph.
By using the same formula, we can find out the average speed quickly
Speed with which he travels from A to B = x = 40 km/hr
Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr
average speed = (2×40×60)/(40+60) = 48 km/hr
Assume that distance from A to B = x km
Speed with which he travels from A to B = x = 40 km/hr
Time to travel from A to B = distance/speed = x/40 hr
Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr
Time to travel from B to A = distance/speed = x/60
Total distance traveled = x+x = 2x
Total time taken = x/40 + x/60
Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60)
= 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr
Answer: Option A #### A
QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides?
options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4
SOLUTION:XY=3
YZ=1+XY = 4
XZ=1+YZ=5
B is the correct option. #### B
QUESTION:Which of the following numbers is a perfect square?
options: A)1266 B)1444 C)2022 D)4034 E)8122
SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022.
38*38 = 1444
ANSWER:B #### B
QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place.
options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours
SOLUTION:1/5+2/8 + 3/x = 1
x =20 hours. ANSWER =D #### D
QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true?
i. s=u
ii. u is not equal to v
iii. s > v
options: A)None B)I only C)II only D)III only E)II and III
SOLUTION:Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.
Answer: D. #### D
QUESTION:The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number
options: A)400 B)256 C)120 D)490 E)None of these
SOLUTION:Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 14 * 5040
x = (14*5040)/144 = 490
Option D #### D
QUESTION:Find the one which does not belong to that group ?
options: A)237 B)232 C)223 D)426 E)111
SOLUTION:Explanation:
525 => 5 52,
39 => 3 32,
24 => 2 22,
636 => 6 62. The above pattern is not followed in 426.
Answer: D #### D
QUESTION:Let B represent a set of four distinct prime numbers. If the sum of the numbers in B is even and x is a member of B, then what is the least possible value that x can be?
options: A)1 B)2 C)3 D)5 E)7
SOLUTION:We are told that B is a set of four distinct prime numbers, and the sum of the numbers in B is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of B must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number. #### C
QUESTION:8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work?
options: A)5 days B)15 days C)28 days D)4 days E)7 days
SOLUTION:Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
20 women’s 1 day’s work = 1/192 × 20 = 5/48
1 child’s 1 day’s work = 1/240
10 children’s 1 day’s work = 1/24
Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24
=1/4
The required No. of days = 4 days
Answer: Option D #### D
QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.
options: A)I only B)I and II C)II and III D)I, II, and III E)IV only
SOLUTION:This is a very good 'trap question'.
Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3
If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'.
Ans: E #### E
QUESTION:Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
options: A)66 B)70 C)72 D)75 E)78
SOLUTION:Let the distance one way be x
Time from home to work = x/60
Time from work to home = x/100
Total time = 2 hrs
(x/60) + (x/100)= 2
Solving for x, we get x = 75
Time from home to work in minutes= (75)*60/60 = 75 minutes
Ans= D #### D
QUESTION:Submarine M and Submarine N are equipped with sonar devices that can operate within a 4,000 yard range. Submarine M remains in place while Submarine N moves 3,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West
options: A)I,II only B)II,III only C)II only D)I and III only E)III only
SOLUTION:It's evident if we make a diagram for the Movement of N respect to M.
From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.
Thus it can only move north or west or anything in that curve.
Answer : D #### D
QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z?
options: A)50% B)40% C)37.5% D)331⁄3% E)25%
SOLUTION:Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) Q= 3/8 = 37.5%
Answer (C) #### C
QUESTION:There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is
options: A)0.9 B)0.8 C)0.5 D)0.7 E)0.2
SOLUTION:Ans: Very interesting question.
As we are allowed to move the balls, we keep only one red ball in first box and move all the remaining balls to the second box
So fist box contains 1 redball, second box contains 38 red + 26 green = 64 balls
Probability of choosing any box is 1/ 2.
So probability of taking one red ball = 12×(1)+12(3864)≃0.8
Answer:B #### B
QUESTION:Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
options: A)2 : 3 : 4 B)6 : 7 : 8 C)6 : 8 : 9 D)4 : 6 : 8 E)None of these
SOLUTION:Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
(140/100 * 5x), (150/100 * 7x) and (175/100* 8x)
7x, 21x/2 and 14x
The required ratio = 7x : 21x/2 : 14x
14x : 21x : 28x
2 : 3 : 4
Answer = A #### A
QUESTION:Calculate the cost of j bottles of wine given that the cost of k bottles of said wine is c rupees?
options: A)Rs.(c*k) B)Rs.(j*k) C)Rs.(j-k) D)Rs.(c/k) E)Rs.(jc/k)
SOLUTION:Cost of k bottles = Rs. c.
Cost of 1 bottle = Rs. c/k
Cost of j bottles = Rs.(c/k)* j= Rs.(jc/k)
Answer is E. #### E
QUESTION:Two brothers took the GMAT exam, the higher score is M and the lower one is N. If the difference between the two scores is equal to their average, what is the value of N/M ?
options: A)3 B)2 C)1/2 D)1/3 E)There isn't enough data to answer the question.
SOLUTION:M - N = (M + N)/2
Solving for N/M = 1/3
D #### D
QUESTION:One-sixth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
options: A)4% B)5% C)6% D)11% E)16%
SOLUTION:1/6 of the switches are defective.
The defective switches that are not rejected are 1/5*1/6 = 1/30 = 4/120 of all switches.
The non defective switches that are sold are 5/6*19/20 = 95/120 of all switches.
The percent of switches sold that are defective is 4/99 which is about 4%.
The answer is A. #### A
QUESTION:A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
options: A)59 7/12 min. past 3 B)4 p.m. C)58 7/12 min. past 3 D)58 7/11 min. past 4 E)2 3/11 min. past 4
SOLUTION:Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = 37/4 hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock.
37/720 hrs of this clock =1/20 hrs of the correct clock.
37/4 hrs of this clock =1/20 x 720/37 x 37/4 hrs of the correct clock.
= 9 hrs of the correct clock.
The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.
Answer: B #### B
QUESTION:A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
options: A)120 B)335 C)784 D)217 E)210
SOLUTION:Let x be the number he chose, then
2*x*138=102
2x=240
x=120
correct answer A #### A
QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
options: A)15 B)19 C)20 D)21 E)22
SOLUTION:A's 1day work=1/10;
B's 1day work=1/30;
(A+B) 1day work=(1/10+1/30)=2/15;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 2/15 work in 1 day...
They did 2/3 w in 5 days.
Total days=(5+10) = 15
ANSWER:A #### A
QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer
SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/10 * 480 =48
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 48-68 =20>>> therfore answer is 20 greater
A #### A
QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ?
options: A)10 B)20 C)21 D)22 E)23
SOLUTION:Time taken by A to finish the work = XY/(Y-X)
= 10 x 20 / (20-10)
= 200/10
= 20 days
ANSWER : OPTION B #### B
QUESTION:Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
options: A)30 B)35 C)37 D)41 E)42
SOLUTION:Explanation:
Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ lO) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years
Option B #### B
QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres?
options: A)20 B)200 C)300 D)400 E)100
SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 9540
[4L - 40] = 9540 / 26.50 = 360
4L = 400
L = 400/4= 100 meters. Answer: E #### E
QUESTION:In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 10 is
options: A)8 B)625 C)16 D)20 E)24
SOLUTION:I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 10
A. x+y+x-y = 10 --> x=5
B. x+y-x+y = 10 --> y=5
C. -x-y +x-y= 10 --> y=-5
D. -x-y-x+y=10 --> x=-5
The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be25*25=625
Answer: B #### B
QUESTION:Positive Integer A gives the remainder of 18 when divided by another positive Integer B. If A/B = 147.24, what is the value of B?
options: A)96 B)75 C)48 D)25 E)12
SOLUTION:.24 of B = Remainder
.24 of B = 18
B = (18*100) / 24 = 75.
B #### B
QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
options: A)23% B)56% C)70% D)35% E)20%
SOLUTION:C
C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70% #### C
QUESTION:3,9,27,81,....
options: A)583 B)604 C)616 D)243 E)636
SOLUTION:1*3=3
3*3=9
9*3=27
27*3=81
81*3=243
ANSWER:D #### D
QUESTION:Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
options: A)2288 B)2677 C)6000 D)2700 E)2881
SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x
10 * 20 * 90 = 15 * 2 * x => x = 6000
Answer: C #### C
QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 215 m long?
options: A)40 B)46 C)88 D)77 E)21
SOLUTION::
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 215 = 575 m
Required time = 575 * 2/25 = 46 sec
Answer:B #### B
QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets?
options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes
SOLUTION:(350+250)t=800
600t=800
t=4/3
t=1 hour and 20 minutes
Answer: A #### A
QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.)
Can somebody explain?
options: A)6720 B)7720 C)7820 D)7950 E)8120
SOLUTION:First ring can be worn in 4 ways (on any of the four fingers);
Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1);
Third ring can be worn in 6 ways (the same logic as for the second ring);
Fourth ring can be worn in 7 ways;
Fifth ring can be worn in 8 ways;
Total: 4*5*6*7*8=6720. ANS:A #### A
QUESTION:Mohit sold an article for Rs. 18000. Had he offered a discount of 25% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
options: A)12500 B)27767 C)16688 D)26678 E)19987
SOLUTION:Let the CP be Rs. x.
Had he offered 25% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 25/100(18000) = Rs. 13500
=> 1.08x = 13500
=> x = 12500
\Answer: A #### A
QUESTION:A tank is filled in 10 hours by three pipes A, B and C. Pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
options: A)70 hours B)30 hours C)35 hours D)50 hours E)40 hours
SOLUTION:Efficiency of pipes A,B,C =1:2:4
Therefore, in 10 hours, part of the tank filled by A =17
Therefore, pipe A alone requires 10×7=70 hours to fill the tank.
Answer: Option A #### A
QUESTION:A 2member committee comprising of one male & one female member is to be constitute out of 5 males and 3females. Among st the females. Ms.A refuses to be a member of the committee in which Mr.B is taken as the member. In how many different ways can the committee be constituted ?
options: A)10 B)14 C)16 D)18 E)21
SOLUTION:5C1 * 3C1 -1
= 15-1
= 14
B #### B
QUESTION:Find the smallest number which should be multiplied with 520 to make it a perfect square
options: A)337 B)297 C)266 D)116 E)130
SOLUTION:Explanation:
520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5
Required smallest number = 2 * 13 * 5 = 130
130 is the smallest number which should be multiplied with 520 to make it a perfect square.
Answer: E #### E
QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water?
options: A)29 B)30 C)20 D)50 E)55
SOLUTION:Explanation :
Here, Large, Medium and Small ships are denoted by the symbol L, M and S.
Now, according to the question,
4L = 7S. ------(i)
3M = 2L + S. ------(ii)
Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :-
7: 6 : 4.
Let, the number of journeys required be x. Since, quantity of water remains the same, so :-
=((15×7+7×6+14×4)36) = x (12×7+14×6+21×4).
=>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x
=>x=7308/252
=>x=29.
Answer : A #### A
QUESTION:A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item
options: A)Rs. 480 B)Rs. 760 C)Rs. 860 D)Rs. 960 E)None of these
SOLUTION:Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 600
= 80/100 * 600
= 480
Option A #### A
QUESTION:Pandiyan buys an old scooter for Rs. 6000 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is :
options: A)20% B)12% C)9.09% D)5% E)None of these
SOLUTION:Explanation :
Solution: C.P. =Rs. (6000+600) =Rs. 6600; S.P. = Rs. 7200.
Gain% = 7200-6600/6600*100 = 9.09%
Answer : C #### C
QUESTION:How many of the positive factors of 17 are not factors of 34?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:Factors of 17 - 1, 17
factors of 34- 1, 2, 17, 34,
Comparing both, we have three factors of 17which are not factors of 34- no factors
The answer is A #### A
QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A - B is also a Even number.
(3) A^B is also a prime number.
options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3.
SOLUTION:Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A - B is also a Even number. : True
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans : C #### C
QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers?
options: A)4 B)2 C)3 D)5 E)1
SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42
factors of 104 - 1,2,4,8,13,26,52,104
Comparing both, we have two common factors of 40 and 104- 1,2,
Answer(B) #### B
QUESTION:Which of the following is a prime number ?
options: A)27 B)45 C)97 D)98 E)100
SOLUTION:Clearly, 97 is a prime number. #### C
QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches?
options: A)24 B)26 C)28 D)30 E)32
SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x
x=30
answer is D #### D
QUESTION:Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 7 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
options: A)22 km B)40 km C)65 km D)18 km E)16 km
SOLUTION:Distance = Relative Speed * Time
= (7 + 3) * 4 = 40 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: B #### B
QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ?
options: A)1000 B)1100 C)1200 D)1300 E)1400
SOLUTION:let profit rate of b = x
acc to question profit rate of a becomes 5/3 x
and that of c= 1/3 x which is given as 10%
1/3 x= 10
therefore x=30
now b=30% , a=50%
now we will find out c's price-
11/10 * price = 2145
price = 1950
in similar way we will find out b's price as we know that profit is 30%
therefore 130/100 * price = 1950
so b 's price =1500
similarly for a ('profit is 50%)
150/100 * price = 1500
on solving it we get
a's price = 1000
ANSWER:A #### A
QUESTION:A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested?
options: A)$360 B)$380 C)$400 D)$420 E)$440
SOLUTION:S.I for 5 years = $680 - $480 = $200
The S.I. is $40/year
S.I. for 2 years = $80
Principal = $480 - $80 = $400
The answer is C. #### C
QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is :
options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None
SOLUTION:Explanation:
Ratio of rents
=(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3)
=72:50:140:63
Let total rent = Rs.x
Then, A's share = Rs.(x×72/325)= Rs.(72x/325)
72x/325=360 or x = 325×360/72=1625
Correct Option: C #### C
QUESTION:Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 42 minutes. The waste pipe can empty the full cistern in?
options: A)8 min B)7 min C)5 min D)9 min E)4 min
SOLUTION:1/10 + 1/15 - 1/x
= 1/42
x = 7
Answer: B #### B
QUESTION:A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The
rate on interest per annum is.
options: A)4% B)5% C)6% D)7% E)10%
SOLUTION:Explanation:
S.I. on Rs 800 for 1 year = 80
Rate = (100*80)/(800*1) = 10%
Answer: E #### E
QUESTION:By selling an article at Rs.500, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
options: A)s.600 B)s.480 C)s.300 D)s.450 E)s.550
SOLUTION:SP = 500
Profit = 25%
CP = (SP)*[100/(100+P)]
= 500 * [100/125]
= 400
Loss = 25% = 25% of 400 = Rs.100
SP = CP - Loss = 400 - 100 = Rs.300
ANSWER:C #### C
QUESTION:What least value must be assigned to * so that th number 197*5462 is divisible by 9?
options: A)2 B)4 C)6 D)1 E)3
SOLUTION:Let the missing digit be x
Sum of digits = (1+9+7+x+5+4+6+2)=34+x
For 34+x to be divisible by 9 , x must be replaced by 2
The digit in place of x must be 2.
ANSWER A 2 #### A
QUESTION:24 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
options: A)10 B)6 C)4 D)7 E)5
SOLUTION:Required number of machines = 24*10/40 = 6
Answer is B #### B
QUESTION:The ratio of the prices of three articles X, Y and Z is 8 : 5 : 3. If the prices of X , Y and Z are increased by 25%, 20% and 33 1/3% respectively, then what would be the ratio of the new prices of X, Y and Z?
options: A)5 : 3 : 1 B)5 : 3 : 2 C)10 : 7 : 4 D)10 : 8 : 5 E)None of these
SOLUTION:Let the prices of X, Y and Z be 8k, 5k and 3k respectively.
After increase
Price of X = 8k * 125/100 = 10k
Price of Y = 5k * 120/100 = 6k
Price of Z = 3k * (133 1/3)/100 = 4k
Required ratio = 10k : 6k : 4k = 5 : 3 : 2.
ANSWER:B #### B
QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform?
options: A)338 B)240 C)287 D)400 E)191
SOLUTION:Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m.
Answer: D #### D
QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players?
options: A)45 B)56 C)64 D)78 E)90
SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players.
=> Required number of ways = 13C11
= 78
D #### D
QUESTION:8 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
options: A)66 B)52 C)58 D)55 E)56
SOLUTION:Though 2*(8C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 7, so he'll play 14 matches.
Similarly, second guy has to play with the rest of 6 as his 2 games with the first guy are already played. So he plays 12 matches.
This continues like this and the total matches are 14+12+10...+2
14+12+...+2 = 2(7+6+...+1) = 2((7*8)/2) = 7*8 =56.
ANSWER:E #### E
QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?
options: A)22 B)40 C)28 D)21 E)27
SOLUTION:A.M. of 75 numbers = 35
Sum of 75 numbers = 75 * 35 = 2625
Total increase = 75 * 5 = 375
Increased sum = 2625 + 375 = 3000
Increased average = 3000/75
= 40.
Answer: B #### B
<<<Examples ends
QUESTION:For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2?
options: A)5 B)3 C)2 D)1 E)0
SOLUTION:4”2= 4 - 4=0
Answer: E #### E
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the difference of the numerator and denominator of the original fraction?
options: A) 49 B) 9 C) 28 D) 26 E) 21
SOLUTION:x/y = 2/5 -> 1
(x+4)/2y = 1/3 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 6/5
=> 5x = 3x + 12
=> x = 6
=> y = 5/2 * 6 = 15
so x - y = 9
The answer is B #### B
QUESTION:How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.
options: A)17280 B)4320 C)720 D)80 E)None of thsee
SOLUTION:Explanation:
word SIGNATURE contains total 9 letters.
There are four vowels in this word, I, A, U and E
Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now
So total letter are 6.
6 letters can be arranged in 6! ways = 720 ways
Vowels can be arranged in themselves in 4! ways = 24 ways
Required number of ways = 720*24 = 17280
Option A #### A
QUESTION:Given that 268x74= 19632, find the value of 2.68x.74.
options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None
SOLUTION:Solution
Sum of decimals places =(2+2)
= 4.
Therefore, = 2.68×.74
= 1.9632
Answer A #### A
QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25%
SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D
QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2
SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2
= 62 m2.
answer :D #### D
QUESTION:In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together?
options: A)120 B)360 C)1440 D)13440 E)4320
SOLUTION:The word 'SOFTWARE' contains 8 different letters.
when the vowels OAE are always together, they can be supposed to form one letter.
Thus, we have to arrange the letters SFTWR (OAE)
Now, 5 letters can be arranged in 6!=720 ways.
The vowels (OAE) can be arranged among themselves in 3!=6 ways.
Required number of ways =(720*6)=4320.
Answer is E #### E
QUESTION:In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
options: A)200 B)210 C)216 D)224 E)235
SOLUTION:The number must be a multiple of both 8 and 7 so the answer is 224.
The answer is D. #### D
QUESTION:Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ?
options: A)0.5% B)1% C)5% D)50% E)500%
SOLUTION:x percent can be written as x/100
So, we get: (30/100)(40/100)(50) = (60/100)(x/100)(200)
Simplify all fractions to get: (3/10)(2/5)(50) = (3/5)(x/100)(200)
Expand: 300/50 = 600x/500
Simplify: 6 = 6x/5
Multiply both sides by 5 to get: 30 = 6x
Solve: x = 5
Answer: C #### C
QUESTION:Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $35.42. How much did the meal cost without the tip?
options: A)$28.98 B)$29.91 C)$30.15 D)$30.60 E)$30.80
SOLUTION:The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.
Thus, 115% of this price equals $35.42:
1.15x = 35.42
Divide both sides by 1.15:=>x=35.42/1.15=30.80
correct answer E)$30.80 #### E
QUESTION:Find the odd number
options: A)21 B)17 C)3 D)14 E)12
SOLUTION:Each of the numbers except 14 is an odd number.
The number '14' is the only EVEN number.
answer :D #### D
QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers?
options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr
SOLUTION:speed of man = 20km/hr
number of rests = (120/30)-1 = 3
time taken for the man = (120/20)+3*(20/60) = 7 hr
Answer is D #### D
QUESTION:The length of a rectangular plot is 10 meters more than its width. If the cost of fencing the plot at $15.50 per meter is $744, what is the length of the plot in meters?
options: A)11 B)13 C)15 D)17 E)19
SOLUTION:perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20
cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 744
62L = 1054
L = 17 meters
The answer is D. #### D
QUESTION:You are filling up your car with gas. Your tank can hold 19 gallons. Your car started with x gallons in it. You paid $20 in gas. What was the cost of gas per gallon?
options: A)19/20 B)x/20 C)(19-x)/20 D)x-19)/20 E)19+20/x
SOLUTION:Amount of gas you added to your car: 19-x
Price per gallon: (19-x)/20
Answer: C #### C
QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the
second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take
both the punctures together to make it flat ?
options: A)315min B)325min C)335min D)345min E)None of these
SOLUTION:Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st
puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(19+16)=(518)
So both punctures will make the type flat in
(185)mins=335mins
Answer: C #### C
QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 4. What is the ratio of their heights?
options: A)A)2:5 B)B)2:7 C)C)2:2 D)D)2:1 E)E)4:3
SOLUTION:The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(4)2h2
=> h1/h2 = 4/3
i.e. h1 : h2 = 4 : 3
Answer: E #### E
QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.6400?
options: A)8100 B)3388 C)7767 D)2009 E)22888
SOLUTION:6400* 9/8 * 9/8
= 8100
Answer: A #### A
QUESTION:On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 160 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
options: A)600 B)320 C)500 D)520 E)720
SOLUTION:Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 160) = 2 + 2(extra)
=> 2x - 320 = x => x = 320.
ANSWER:B #### B
QUESTION:Simplify: 256 x 256 - 144 x 144
options: A)761200 B)44800 C)761800 D)761500 E)None of them
SOLUTION:(256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800
Answer is B #### B
QUESTION:I. a^2 - 9a + 20 = 0,
II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?
options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b
SOLUTION:I. (a - 5)(a - 4) = 0
=> a = 5, 4
II. (2b + 3)(b - 4) = 0
=> b = 4, -3/2 => a ≥ b
Option E #### E
QUESTION:If 280 people, constituting 5 percent of the population of a town, ride bicycles, and the others do not, then how many people in the town do not ride bicycles?
options: A)5930 B)5600 C)5320 D)5110 E)4980
SOLUTION:5 % of X is 280
5/100 * X = 280
X = 280*100/5 = 5600
So C. 5320 is the correct Answer
No. of people Not Riding Bike = 5600 - 280 = 5320
answer is C #### C
QUESTION:Set S is the prime integers between 0 and 40. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?
options: A)15/56 B)3/8 C)15/28 D)5/8 E)3/4
SOLUTION:Total number of combinations=12C3=220................(1)
Total number of combinations including 2 and two other numbers=11C2=55......................(2)
Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(220-55)=165
So, probability=165/220=3/4
E #### E
QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip?
options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph
SOLUTION:So The Answer is Plainly A....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles
in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours
so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles
Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A
QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day.
options: A)20 B)10 C)25 D)15 E)24
SOLUTION:work completed in a day by one men = 1/25 = (1/5)*(1/5)
So it takes 25 men to complete this job = 25 * (1/25) = 1
Answer: C #### C
QUESTION:The difference between a number and its three-fifths is 50.What is the number?
options: A)75 B)100 C)125 D)Cannot be determined E)None of these
SOLUTION:Suppose the number is N.
Then N - 3⁄5N = 50
⇒ 2N⁄5 = 50
∴ N=50×52=125
Answer.C #### C
QUESTION:If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $81, how much does one shirt cost?
options: A)$10 B)$12 C)$13.20 D)$21 E)$16.80
SOLUTION:3J + 2S = 69
2J + 3S = 81
----------------
5J + 5S = 150 ----(divide by 5)---> J + S = 30
3J + 2S = J + 2(J + S) = J + 60 = 69 ---> J = 9
3*9 + 2S = 69
27 + 2S = 69
2S = 42
S = 21
Answer: D #### D
QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={13,13,13...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
options: A)a) k(n+m+mn)+ k B)b) (1+n+m+mn)(k+1) C)c) k^2(mn+n/m) D)d) kmn(k+m+n) E)e) None of the above.
SOLUTION:a) how many 2's are included?
b) how many 3's are included?
and
c) how many 11's are included?
For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.
NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.
The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
Mike
B #### B
QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/5 meter and also 1/8 meter, and then if the cable were cut at each mark, how many different size length of cable would result?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:In this particular example length (10 meter) is just extraneous information.
The location of the marks for 1/3 meter would be 8/40, 16/40, 24/40, 32/40, 40/40, etc...
The location of the marks for 1/8 meter would be 5/40, 10/40, 15/40, 20/40, 25/40, 30/40, 35/40, 40/40, etc...
The distances between marks are 5/40, 3/40, 2/40, 1/40, and 4/40.
The answer is E. #### E
QUESTION:Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C?
options: A)127 B)150 C)177 D)167 E)122
SOLUTION:A+B+C = 590
5A = 6B = 8C = x
A:B:C = 1/5:1/6:1/8
= 24:20:15
15/59 * 590 = Rs.150
Answer:B #### B
QUESTION:A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
options: A)525 B)665 C)412 D)235 E)856
SOLUTION:Answer: Option B
8 * 84 = 672 – 7 = 665 #### B
QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit
SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1
[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1
[(5.4 + 2.4 + 1.8)/8] - [8/8]
+1.6/8
+20%
answer is D #### D
QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
options: A)388 B)299 C)266 D)400 E)2871
SOLUTION:2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400.Answer: D #### D
QUESTION:What percent is 400 gm of 1 kg?
options: A)25% B)40% C)10% D)8% E)12%
SOLUTION:1 kg = 1000 gm
400/1000 × 100 = 40000/1000
=40 %
Answer is B #### B
QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
options: A)60 B)80 C)100 D)120 E)140
SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 160 books were paperbacks, the dealer would earn a profit of $320.
Since the actual profit was $400, the dealer must have sold 80 hardbacks.
Then the number of paperbacks sold was 160-80 = 80.
The answer is B. #### B
QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit?
options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62
SOLUTION:Explanation:
We are given selling price = Rs. 580 and expected profit of 15 %
Therefore, we can easily solve this numerical, considering basic formulae of profit and loss.
Let cost price = x
Selling price = C.P. + Profit
S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price)
580 = x + (0.15 x)
580 = 1.15 x
Therefore,
x = 504.347
Cost Price = Rs. 504.35
Now, we have the cost price and hence,
Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65
The trader gets a profit of Rs. 75.65
ANSWER IS A #### A
QUESTION:In May Mrs Lee's earnings were 50 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
options: A)55 B)56 C)34 D)78 E)23
SOLUTION:Lets say the Family Income is 100
In May, lee earned 50Family income is 50
In june, Lee earned 20% more than May, so it is (50+20*50/100 = 60)
Family Income is same 50
In June Lee's Income percent is 60*100/110 ~ 55
Ans is A #### A
QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?
options: A)36 B)66 C)132 D)264 E)152
SOLUTION:12 * 396 = 36 * x
x = 132
ANSWER:C #### C
QUESTION:If k^2 = h^2, which of the following must be true?
options: A)k = m B)|k| = |h| C)k = |m| D)k = -|m| E)k = -m
SOLUTION:Solution:
We are given that k^2 = h^2, and we can start by simplifying the equation by taking the square root of both sides.
√k^2 = √h^2
When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:
√k^2 = √h^2 is |k| = |h|
Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.
Answer: E #### E
QUESTION:In a certain game, a player begins with a bag containing tiles numbered 3 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?
options: A)5/18 B)13/36 C)3/8 D)5/8 E)23/36
SOLUTION:player begins with containing tiles 1 to 10 and have equal probability of selecting means
Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.
Next , player draws one title , if number is even player stops or otherwise title is odd without replacement
player draws second title.
If second title is even , player stops or title is odd without replacement player draws third title.
in third title , without replacement of first and second title, player draws and stops it.
the sum of tilte probability is odd. here two conditions are possible.
1st condition is
1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.
Here are we are not selecting 1st condition as even stops because sum of tile is odd.
Here 5 odd numbers are there we can select 1out of 5 odd numbers.
without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.
here we are selecting one number out of remaining 9 numbers. so probability is 5/18.
we are selecting 1 even number out of 5.
2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.
Then probability is 5/10*4/9*3/8=1/12.
Finally sum of probability of two conditions is 5/18+1/12
=5/18.
so option A is correct. #### A
QUESTION:Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her nine kids?
options: A)8 B)9 C)3 D)7 E)10
SOLUTION:cost of each apple = 4 dollars
Apples that Benny can buy with the amount she has=360/4 = 90.
Apples that each kid gets evenly = 90/9 =10 Apples.
So the answer is E=10 #### E
QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 7?
options: A)56 B)112 C)224 D)448 E)425
SOLUTION:Solution: sequence of 7 lets say sequence is 7n, 7(n+1), 7(n+2), 7(n+3), 7(n+4)
so range is 7n+28-7n = 28
if we put the different values of n we will get different but the range will be multiple of 28
and only 425 is not multiple of 28
Answer : E #### E
QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least?
options: A)John B)Susan C)Sam D)Mark E)Lynn
SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 160% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.6*J)=0.8*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John.
Answer: B. #### B
QUESTION:In how many ways can the letters of the word STATE be arranged?
options: A)60 B)1348 C)2520 D)3000 E)3478
SOLUTION:STATE has 5 words, but T is repeated two times. Thus ways = 5! / 2! = 60 ways
A #### A
QUESTION:Three coins are tossed. Find the probability of at least 1 head and 1 tail ?
options: A)1/2 B)1/4 C)3/4 D)7/8 E)1/8
SOLUTION:n(s) = 2^3 = 8 ....(3 coins tossed)
let E is the event of getting at least 1 head and 1 tail
n(E) = TTH , HTT, THT, HHT, HTH, THH = 6
P(E) = n(E) / n(s)
= 6/8
= 3/4
Ans- C #### C
QUESTION:A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 1/2 days. How many more days are required to complete the remaining work if they work together?
options: A)3 (5/18) B)3 (5/16) C)3 (5/11) D)4 (21/22) E)3 (5/21)
SOLUTION:A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 1/2 days.
The number of days required to complete remaining work => 60/11 - 1/2 = 109/22 = 4 (21/22) days.
Answer:D #### D
QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house?
options: A)25 B)49 C)3 D)87 E)36
SOLUTION:Aravind can select one or more than one of his 8 gang.
=> Required number of ways = 2^2 – 1= 3.
C #### C
QUESTION:A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts?
options: A)2 B)3 C)4 D)5 E)7
SOLUTION:if average of 3 is 9 so sum of 3 should be 27
3 recording can be from 0-10 inclusive
to find one smallest other two should be highest
so, lets assume three var are a,b,c
say a is smallest and give b and c greatest readings say 10 and 10
so a has to be 7
E #### E
QUESTION:The mean of 1^3,2^3,3^3,4^3,5^3 is?
options: A)30 B)45 C)50 D)60 E)75
SOLUTION:1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2
1^3+2^3+3^3+-----+5^3 = (5*6/2)^2 = 225
Required average is = 225/5 = 45
Answer is B #### B
QUESTION:How many numbers from 29 to 79 are exactly divisible by 11
options: A)5 B)7 C)8 D)9 E)11
SOLUTION:29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers
Option 'A' #### A
QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these
SOLUTION:Solution
Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr.
Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B
QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
options: A)80% B)20% C)40% D)50% E)None of these
SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84
Number of students failed = 140 - 84 = 56.
Required percentage = 28/56 * 100 = 50%.
ANSWER:D #### D
QUESTION:The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
options: A)42cm B)44cm C)46cm D)48cm E)49cm
SOLUTION:Explanation:
Side of first square = (80/4) = 20 cm;
Side of second square = (64/4)cm = 16 cm.
Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2.
Side of third square = (144)(1/2) cm = 12 cm.
Required perimeter = (12 x 4) cm = 48 cm.
Answer: Option D #### D
QUESTION:Determine the value of 62/54 divided by 62/54
options: A)0 B)1 C)2 D)3 E)none
SOLUTION:Solution:
Each number divided by itself equals 1.
Answer B #### B
QUESTION:Calculate the HCF of 64, 318, 250
options: A)6 B)5 C)4 D)3 E)2
SOLUTION:Explanation:
Lets solve this question by factorization method.
64=2 x 2 x 2 x 2 x 2 x 2,
318=2 × 3 × 53,
250=2 × 5 × 5 × 5
So HCF will be minimum term present in all three, i.e.
2×32=18
Answer: Option E #### E
QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2490 ?
options: A)Rs. 832 B)Rs. 830 C)Rs. 822 D)Rs. 812 E)Rs. 810
SOLUTION:Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830.
Answer: B #### B
QUESTION:What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it?
options: A)600 B)602 C)604 D)606 E)608
SOLUTION:The nth term is 2+3*(n-1).
The 201st term is 2 + 3(200) = 602
The answer is B. #### B
QUESTION:A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %?
options: A)62 2/3% B)64 2/3% C)66 2/3% D)66 5/3% E)68 2/3%
SOLUTION:Gain=40 lemons
Total 100 lemons
CP 100-40=60
(40/60)*100
=66 2/3%
Ans C #### C
QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision?
options: A)2003 B)2009 C)2005 D)2006 E)2007
SOLUTION:She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009.
Answer: B. #### B
QUESTION:The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000?
options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796.
SOLUTION:30,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option B fulfills the condition and hence is the answer #### B
QUESTION:To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. The time in minutes that the three pipes together will take to fill the cistern is
options: A)5 B)6 C)8 D)3 E)9
SOLUTION:A
5 #### A
QUESTION:There are 6 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
options: A)1/9 B)2/9 C)3/5 D)4/9 E)2/3
SOLUTION:total 10 from take one.
10c1=10
red 6 from one
6c1=6
6/10= 3/5
ANSWER:C #### C
QUESTION:The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
options: A)227 B)299 C)276 D)600 E)211
SOLUTION:Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 20 è x = 20 * 60 / 2 = 600
Answer: D #### D
QUESTION:What is the decimal equivalent of (1/2)^2?
options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5
SOLUTION:(1/2)² = (1/2)(1/2)= 1/4
APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25
D #### D
QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss?
options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents
SOLUTION:50 % profit on $ 1
= $ 50/100 × 1
= $ 0.50× 1
= $ 0.50
Similarly, 40 % loss on $ 1
= $ 40/100 × 1
= $ 0.40× 1
= $ 0.40
Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40
So profit by amount $0.40.
Answer is E. #### E
QUESTION:Two hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 400 selected numbers are odd?
options: A)20% B)25% C)40% D)50% E)80%
SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even.
The percentage of odd numbers is about (1/2)(200) / 400 = 25%
The answer is B. #### B
<<<Examples ends
QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?
options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these
SOLUTION:Explanation :
Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30
Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15.
For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number.
So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6
Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24
So total probability = 24/90 = 4/15
Answer : C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is?
options: A)1250m B)1750m C)950m D)1000m E)1300m
SOLUTION:Speed = 15*5/18 = 15/18 m/sec
Distance covered in 35 minutes = 15/18 *35 *60 = 1750 m
Answer is B #### B
QUESTION:If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is:
options: A)80% B)90% C)33% D)40% E)10%
SOLUTION:Explanation:
Let C.P. of each pen be Re. 1.
Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12.
Gain % = 3/9 * 100 = 33%
Answer:C #### C
QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils?
options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44
SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 90 - 90p = 40p --> p = 9/13.
(cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44.
Answer: E. #### E
QUESTION:A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability Q that both will be juniors?
options: A)1/10 B)1/5 C)2/9 D)2/5 E)1/2
SOLUTION:I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.
2 seniors = P(Senior) * P(Senior) = 2/9
1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9
Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability Q that it is two juniors is 1- (7/9) = 2/9.C #### C
QUESTION:If watches bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425. What is the greatest possible profit that might be made in selling eight watches?
options: A)Rs 900 B)Rs 800 C)Rs 1,800 D)Rs 2,800 E)None of these
SOLUTION:Profit would be maximum if watches are brought for Rs 200 and sold for Rs 425
Profit = Rs (425 - 200) = Rs 225
Profit of 8 watches = Rs 225 x 8 = Rs 1,800
ANSWER:B #### B
QUESTION:The overall age of X and Y is 19 year greater than the overall age of Y and Z. Z is how many decades younger that X?
options: A)11 B)15 C)12 D)19 E)20
SOLUTION:D
19
(X + Y) – (Y + Z) = 19
X – Z = 19 #### D
QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed?
options: A)104 B)130 C)298 D)269 E)213
SOLUTION:520/4 = 130 kmph
Answer:B #### B
QUESTION:What is the sum of all even numbers from 1 to 401?
options: A)122821 B)281228 C)281199 D)122850 E)40200
SOLUTION:Explanation:
400/2 = 200
200 * 201 = 40200
Answer: E #### E
QUESTION:What comes next in the series?
16 72 38 94 50 __
options: A)11 B)25 C)17 D)19 E)16
SOLUTION:E
16
Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit. #### E
QUESTION:Which of the following numbers is not prime?
options: A)50+70 B)150 -23 C)100+67 D)156-7 E)103+36
SOLUTION:10 can be factored out of both 50 and 70. -->50+70= 10*(5+7). The correct answer is A. #### A
QUESTION:Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes?
options: A) 911 B) 100 C) 101 D) 160 E) 785
SOLUTION:Let's take the approach that uses the answer choices to eliminate wasted time.
32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt.
Looking at the answers it is clear...we can only choose (D)
THE CORRECT ANSWER IS D. #### D
QUESTION:A circular well with a diameter of 6 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out?
options: A)678.6 m3 B)36 m3 C)40 m3 D)44 m3 E)None
SOLUTION:Solution
Volume = πr2h
‹=› (22 /7 ×3×3×24)m3
‹=›678.6 m3.
Answer A #### A
QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is:
options: A)153601 B)153600 C)86400 D)153603 E)153604
SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1200 or x = 120.
Length = 360 m and Breadth = 240 m.
Area = (360 x 240) m2 = 86400 m2.
Answer: C #### C
QUESTION:The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
options: A)15% B)32% C)40% D)62% E)80%
SOLUTION:We need multipliers.
multiplier for a 10% increases = 1 + 0.10 = 1.1
multiplier for a 20% decreases = 1 – 0.20 = 0.8
multiplier for a 50% increases = 1 + 0.50 = 1.5
Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3
(0.8)*(1.5) = (0.4)*(3) = 1.2
Now, multiply this by 1.1
1.2*1.1 = 1.32
Thus, the three percent changes combined produce a 32% increase. Answer = (B). #### B
QUESTION:A person walking at 4 Kmph reaches his office 6 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
options: A)4 1/5 Km B)4 1/7 Km C)3 1/5 Km D)3 1/7 Km E)2 4/5 Km
SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 14/6
= 24/2 * 14/60
= 7 * 2/5
= 14/5 = 2 4/5 Km
E) #### E
QUESTION:In a school 10% of the boys are same in number as 1/3th of the girls. what is the ratio of boys to the girls in the school?
options: A)5:2 B)2:3 C)10:3 D)3:7 E)2:5
SOLUTION:10% of B = 1/3 G
10B/100 = G/3
B = 10G/3
B/G = 10/3
B:G = 10:3
Answer is C #### C
QUESTION:On a ferry, there are 32 cars and 8 trucks. The cars have an average mass of 900 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry?
options: A)1200 B)1240 C)1280 D)1320 E)1360
SOLUTION:The total mass of the vehicles is 32*900+8*3000=52800
The average mass is 52800/40=1320
The answer is D. #### D
QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ?
options: A)87 B)95 C)99 D)100 E)103
SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.
Answer: C. #### C
QUESTION:Half of 5 percent written as decimal is
options: A)5 B)0.5 C)0.05 D)0.025 E)None of these
SOLUTION:Explanation:
It will be 1/2(5%) = 1/2(5/100) = 5/200 = 0.025
Answer: Option D #### D
QUESTION:A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
options: A)3.6 sec B)18 sec C)36 sec D)72 sec E)None of these
SOLUTION:Speed of train relative to jogger
= (45 – 9) km/h = 36 km/h
= (36 × 5⁄18) m/sec = 10 m/sec
Distance to be covered = (240 + 120) m = 360 m.
∴ Time taken = (360⁄10) sec = 36 sec.
Answer C #### C
QUESTION:The average age of three boys is 40 years and their ages are in proportion 6:10:8. What is the age in years of the youngest boy?
options: A)8 B)10 C)7 D)6 E)5
SOLUTION:6x + 10x + 8x = 40
x =1.6
6x = 10
Answer:B #### B
QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum E of even integers from 102 to 200 inclusive?
options: A)5100 B)7550 C)10100 D)15500 E)20100
SOLUTION:My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
E=2550+(100*50)=7550.B #### B
QUESTION:In a class, the average age of 42 boys is 12 years and the average of 28 girls is 10 years. what is the average age of the whole class?
options: A)11.2 Years B)12.6 Years C)13 Years D)13.5 Years E)14 Years
SOLUTION:Total age of 70 students
(42X 12+28 X 10) = 784
Average = 784/70 = 11.2 Years
A) #### A
QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 54 km/hr?
options: A)2.5 B)2.9 C)6.67 D)2.8 E)2.1
SOLUTION:Speed = 54 * 5/18 = 15 m/sec
Time taken = 100/15
= 6.67 sec.
Answer:C #### C
QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers?
options: A)56% B)57% C)58% D)45% E)35%
SOLUTION:let assume he sells 1 buffet daily,
now
then 300*1 = revenue (eq -1)
if he reduced his price by 20% then ,
240*(customer) = 125/100*revenue
customer = 1.25*300/240 = 1.56
means 56 % increase in customer.
ANSWER:A #### A
QUESTION:In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 240 vote’s majority. What is the total number of votes polled?
options: A)600 B)700 C)800 D)850 E)None of these
SOLUTION:Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 280 (40*6 = 240)
100% -----> 600 (100*6 = 600)
Answer: Option A #### A
QUESTION:If the product of two numbers is 17820 and their H.C.F. is 12, find their L.C.M.
options: A)2574 B)2500 C)1485 D)1574 E)None of these
SOLUTION:Explanation:
HCF * LCM = 17820, because we know
Product of two numbers = Product of HCF and LCM
LCM = 17820/12 = 1485
Option C #### C
QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ?
options: A)10 B)20 C)21 D)22 E)23
SOLUTION:Time taken by A to finish the work = XY/(Y-X)
= 10 x 20 / (20-10)
= 200/10
= 20 days
ANSWER : OPTION B #### B
QUESTION:A train covers a distance of 12 km in 10 min. If it takes 8 sec to pass a telegraph post, then the length of the train is?
options: A)100 B)110 C)160 D)130 E)140
SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 8 = 160 m.
Answer: Option C #### C
QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
options: A)1.99 km B)2.88 km C)4.49 km D)2.99 km E)7.88 km
SOLUTION:M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B #### B
QUESTION:Martins made a part payment of $650 toward buying a brand new washing machine, which represents 15% of the total cost of the washing machine, how much remains to be paid?
options: A)$1116.3 B)$3583.3 C)$3283.3 D)$3683.3 E)$2683.3
SOLUTION:Explanation:
Let's start with what the total price of the washing machine would be. If 15% is equal to $650 then 100% equals $x. We just have to multiply $650 by 6.67 to get total amount=$4333.3. Out of this amount we then need to deduct the amount already paid which was $650 so we have $4333.3-$650=$3683.3
Answer: Option D #### D
QUESTION:If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ?
options: A)Equal to 3 B)Less than 3 C)More than 3 D)Less than 1/3 E)none of these
SOLUTION:Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3
ANSWER:C #### C
QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have?
options: A)9 B)12 C)18 D)28 E)36
SOLUTION:Lets take an example: find the number of factors of 100
try to represent 100 in least possible prime numbers
100= 2^2 * 5^2=p^a*q^b
no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9
similarly find the number of factors of p^3 * q^6--->a=3,b=6
(3+1)(6+1)=28 Ans D. #### D
QUESTION:A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp?
options: A)248 B)312.5 C)346.5 D)392.5 E)424
SOLUTION:Area covered by lamp = Pi*r^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot)
where r= 21 m = length of part lit
So area = (22/7)*21*21/4 = 346.5 sq m
answer :C #### C
QUESTION:In how many ways the word "KIT" can be arranged?
options: A)6 B)8 C)18 D)21 E)24
SOLUTION:Explanation :
The required number of ways = 3!
= 6
Answer : A #### A
QUESTION:If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be
options: A)2 B)5 C)6 D)7 E)14
SOLUTION:i just tried plugging in the numbers and found out that
5*8820 = 44, 100, which is a square of 210
B #### B
QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
options: A)22 B)21 C)88 D)37 E)29
SOLUTION:Explanation:
Lot the total number of workers be v Then,
8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21
Answer: B) 21 #### B
QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs?
options: A)15 B)16 C)17 D)18 E)19
SOLUTION:16
ANSWER:B #### B
QUESTION:The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is
options: A)25 years B)30 years C)35 years D)40 years E)None
SOLUTION:Sol.
Let their ages of x years and (x + 10) years respectively.
Then, (x + 10) - 15 = 2(x - 15)
⇔ x - 5 = 2x - 30
⇔ x = 25.
∴ Present age of the elder person = (x + 10)
= 35 years.
Answer C #### C
QUESTION:A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width?
options: A)12 by 2 B)11 by 3 C)20 by 5 D)10 by 4 E)9 by 3
SOLUTION:2x+2y=50
x+y=25
x+4x=25
5x=25
x=5
Answer C #### C
QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit?
options: A)28000 B)30000 C)32000 D)34000 E)None of these
SOLUTION:Explanation :
Suppose B's investment = x. Then A's investment= 3x
Suppose Bs period of investment = y, then A's period of investment = 2y
A : B = 3x * 2y : xy
= 6 : 1
Total profit * 1/7 = 4000
=> Total profit = 4000*7 = 28000. Answer : Option A #### A
QUESTION:The radius of a semicircular plot is 25. What is the approximate perimeter of the plot?
options: A)114 B)150 C)129 D)25 E)57
SOLUTION:perimeter of a circle =2pi*r
perimeter of a semicircle = pi*r + 2r
aprox perimiter = 3.14*25 + 2*25 = 128.50 approximately 129
answer C #### C
QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is:
options: A)14 B)7 C)20 D)70 E)35
SOLUTION:Explanation :
Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2.
Number of Apples = 10x = 20.
Answer : C #### C
QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
options: A)6 hours B)10 hours C)15 hours D)30 hours E)35 hours
SOLUTION:suppose first pipe filled the tank in x hour
so second in x-5 and third in x-9
1/x+1/(x-5)=1/(x-9)
by solving it we get x=15
ANSWER:C #### C
QUESTION:4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
options: A)4 days B)6 days C)7 days D)9 days E)1 days
SOLUTION:1 women's 1 day work = 1/28
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/28 + 10/140) = 1/4
5 women and 10 children will complete the work in 4 days.
Answer: A #### A
QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A.
options: A)256 B)388 C)379 D)277 E)122
SOLUTION:Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 672 = 256
Answer: A #### A
QUESTION:A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
options: A)15 1/3 days B)13 1/3 days C)19 1/3 days D)11 1/3 days E)12 1/3 days
SOLUTION:B
13 1/3 days
5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days #### B
QUESTION:The area of a triangle is with base 4m and height 5m?
options: A)20 m2 B)10 m2 C)82 m2 D)54 m2 E)28 m2
SOLUTION:1/2 * 4 * 5
= 10 m2
Answer:B #### B
QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?
options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1
SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40 => x = 20.
Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3
Answer:B #### B
QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is?
options: A)1994 B)1494 C)1349 D)1496 E)1500
SOLUTION:LCM = 1400
1400 - 6 = 1394
ANSWER:C #### C
QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%?
options: A)41 B)48 C)49 D)44 E)43
SOLUTION:96% ---- 72
144% ---- ?
96/144 * 72 = 48
Answer: B #### B
QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days?
options: A)25 B)19 C)39 D)61 E)64
SOLUTION:Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers 4 : 16 :: 4 : x
Days 4:16
4 * 4 * x = 16 * 16 * 4
x = (16 * 16 * 4)/(4 x 4)
x = 64.
Answer is E. #### E
QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week?
options: A)40 B)30 C)35 D)25 E)45
SOLUTION:For 30 hrs = 30*16=480
Excess = 760-480=280
For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28
Number of extra hrs =280/28=10
Total hrs =30+10=40
Answer A 40 #### A
QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
options: A)18% B)12% C)22% D)24% E)21
SOLUTION:1500 ---- 270
100 ---- ? => 18%
Answer:A #### A
QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets?
options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes
SOLUTION:(350+250)t=800
600t=800
t=4/3
t=1 hour and 20 minutes
Answer: A #### A
QUESTION:The positive integer x has a factor of 16. If the square root of x is > 16, which of the following could equal x/16?
options: A)13 B)14 C)15 D)16 E)17
SOLUTION:Given: x=16k (where k is a positive integer) and √x=√16k >16 --> x=16k>16^2 --> divide by 16. So as x/16=k=integer>16, then x/16 can be 17, 18, ...
Answer: E. #### E
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age 4 years back was:
options: A)12 years. B)14 years. C)17 years. D)20 years. E)19 years.
SOLUTION:Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24
Son's age 4 years back (24- 4) = 20 years.
ANSWER :D #### D
QUESTION:The area of a triangle will be when a = 3m, b = 5m, c = 10m, a, b, c being lengths of respective sides?
options: A)3 B)6 C)4 D)9 E)1
SOLUTION:S = (3 + 5 + 10)/2
= 9 Answer:D #### D
QUESTION:At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.)
options: A)96 B)240 C)E=256 D)E=384 E)E=480
SOLUTION:Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E #### E
QUESTION:The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees.
options: A)$2291.7 B)$1546.8 C)$2546.5 D)$1879.3 E)$3125.3
SOLUTION:mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7
Answer is A #### A
QUESTION:A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%?
options: A)7 B)6 C)5 D)9 E)8
SOLUTION:C
5
C.P. of 6 toffees = $ 1
S.P. of 6 toffees = 120% of $ 1 = $ 6/5
For $ 6/5, toffees sold = 6. For $ 1.
Toffees sold = 6 * 5/6 = 5 #### C
QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is?
options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5
SOLUTION:3:1
Answer:B #### B
QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94
SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 96, there are 47 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (47 + 12)/94
= 59/94
= 5/8
Ans is E #### E
QUESTION:Can you deduce the pattern and find the next number in the series?
7, 15, 27, 99, __?
options: A)276 B)277 C)278 D)279 E)None of these
SOLUTION:Solution:
277
Explanation:
7 = (1^1 + 2^1 + 3^1) +1
15 = (1^2 + 2^2 + 3^2) +1
37 = (1^3 + 2^3 + 3^3) +1
99 = (1^4 + 2^4 + 3^4) +1
Thus the next number will be
(1^5 + 2^5 + 3^5) +1 = 277
Answer B #### B
<<<Examples ends
QUESTION:The arithmetic mean of the set S = {8, K, 7, 13, M, 8} is 9. If K and M are integers, and K ≠ M, what is the median of the numbers in the set?
options: A)7 B)7.5 C)8 D)8.5 E)9
SOLUTION:The sum of the numbers is 6*9 = 54
K+M = 54 - 13 - 8 - 8 - 7 = 18
Since K ≠ M, K and M do not equal 9.
Thus one of the two numbers is 8 or less and one is 10 or more.
Then middle two numbers in the set are 8 and 8.
The median is 8.
The answer is C. #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Every student at Parcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Parcy School?
options: A)63 B)69 C)74 D)82 E)86
SOLUTION:the total number of students at Parcy School The answer is 86 or any multiple of 43.E #### E
QUESTION:On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:
options: A)48759 B)51236 C)47619 D)6974 E)1235
SOLUTION:Explanation:
By hit and trial, we find that
47619 x 7 = 333333.
ANSWER:C #### C
QUESTION:If |z|/w = 5,which of the following must be true?
options: A)z = -5w B)z = 5w C)z^2 = 25w^2 D)z^2 = 25w^3 E)z^3 = 125w^3
SOLUTION:|z|/w = 5.
|z| = 5w.
Then z = 5w or -5w and so z^2 = 25w^2.
The answer is C. #### C
QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n?
options: A)-200 B)-130 C)-104 D)51 E)305
SOLUTION:2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:
-51 < c < 151
-51 < n < 151
-102 < c+n < 302.
Only option D is in this range.
Answer: D. #### D
QUESTION:In my core I have 5 But 500 stand in the beginning and the end of mine. I also include the first letter and the first number to make me complete. I am the name of a King.
Who am I?
options: A)Johny B)Jacky C)Ricky D)David E)Alex
SOLUTION:D
I am DAVID.
At the core I have 5
If we talk in roman numeric system, 5 = V
Similarly, 500 stands in the beginning and end
500 = D
I also include the first letter i.e. A and the first number i.e. I (in roman numeric system)
All of them combine to form DAVID. #### D
QUESTION:If n is the product of 3 consecutive integers, which of the following must be true about n?
I. n is a multiple of 2
II. n is a multiple of 3
III. n is a multiple of 4
options: A)I only B)II only C)III only D)I and II E)II and III
SOLUTION:n is the product of 3 consecutive integers.
So, according to the rule, n must be divisible by 3, 2 and 1
So, we already know that statements I and II must be true.
Do we need to check statement III? No.
Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D. #### D
QUESTION:The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000?
options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796.
SOLUTION:30,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option B fulfills the condition and hence is the answer #### B
QUESTION:Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
options: A)3 hours B)6 hours C)4 hours D)8 hours E)10 hours
SOLUTION:Number of pages typed by Ronald in one hour = 32/6 = 16/3
Number of pages typed by Elan in one hour = 40/5 = 8
Number of pages typed by both in one hour = ((16/3) + 8) = 40/3
Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours.
ANSWER:D #### D
QUESTION:Pencils, Pens and Exercise books in a shop are in the ratio of 14: 4 : 3. If there are 140 pencils, the number of exercise books in the shop is:
options: A)30 B)27 C)35 D)33 E)37
SOLUTION:Explanation :
Let Pencils = 14x, Pens = 4x & Exercise books = 3x.
Now, 14x = 140
hence x = 10
Number of exercise books = 3x = 30
Answer : A #### A
QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
options: A)230 B)783 C)291 D)112 E)221
SOLUTION:Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer:A #### A
QUESTION:Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 30ft how many poles do he need?
options: A)20 B)30 C)40 D)50 E)60
SOLUTION:If each side is 120 feet..then total perimeter is 150*4=600
poles every 20 feet hence no of poles= 600/20=30
ANSWER:B #### B
QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 15 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
options: A)25 pounds B)46 pounds C)150 pounds D)100 pounds E)146 pounds
SOLUTION:Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*15 --> x = 150.
Answer: C. #### C
QUESTION:The workforce of Company Samsung is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers?
options: A)180 B)170 C)160 D)150 E)145
SOLUTION:let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added
06x/(0.4x +20) = 50/100 or 60x = 50*( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125
total worker = 125+20= 145
E #### E
QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres?
options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these
SOLUTION:Explanation:
As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute
To climb 26 metres, the time required is:
The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes
Also, the last 5 metres it climbs in another 1 minute
Hence, total time required = 14 + 1 = 15 minutes
ANSWER C #### C
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
options: A)356 B)250 C)127 D)279 E)150
SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 250 m
Answer: B #### B
QUESTION:How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible?
options: A)4C3+4 B)4C3+9 C)4C3+2 D)4C3 E)4C3+6
SOLUTION:So 4C3 for abcd - 4 choices
3 more for dd(b,c or a)
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 4C3+9
Ans : B #### B
QUESTION:What is the smallest positive integer x such that 108x is the cube of a positive integer?
options: A)2 B)4 C)8 D)10 E)7
SOLUTION:Given 108x is a perfect cube
so we will take 216 = 6*6*6
108x = 216
x = 216/108 = 2
correct option is A #### A
QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?
options: A)4 B)5 C)6 D)9 E)7
SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even.
1) 2(6 times)
2) 2(3 times) + 3(2 times)
3) 2(2 times) + 3 + 5
4) 2 + 3 + 7
5) 2 + 5 + 5
6) 3(4 times)
7) 5 + 7
Answer: E #### E
QUESTION:In how many ways can five boys and three girls sit in a row such that all boys sit together?
options: A)A)2888 B)B)2885 C)C)2880 D)D)2876 E)E)2224
SOLUTION:Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements = 4! * 5! = 24 * 120 = 2880.
Answer:C #### C
QUESTION:18 balls are numbered 1 to 18. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
options: A)2/9 B)4/17 C)6/29 D)8/35 E)10/43
SOLUTION:P(1st ball is even) = 9/18
P(2nd ball is also even) = 8/17
P(both balls are even) = 9/18 * 8/17 = 4/17
The answer is B. #### B
QUESTION:Divide Rs. 1300 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
options: A)346 B)368 C)375 D)337 E)325
SOLUTION:A+B+C = 1300
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1300 => 325
Answer:E #### E
QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
options: A)20 B)34 C)38 D)40 E)46
SOLUTION:We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 40
Hence answer is D #### D
QUESTION:Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent?
options: A)16% B)17% C)18% D)58% E)23%
SOLUTION:Total CP = Rs. 36000 + Rs. 15000
= Rs. 51000 and SP = Rs. 62900
Profit(%)
= (62900 - 51000)/51000 * 100
= 23%
Answer: E #### E
QUESTION:If -1 < x < 0, which of the following must be true? I. x^8 < x^3 II. x^4 < 1 – x III. x^3 < x^2
options: A)III only B)II only C)I only D)I,II,III only E)II,III only
SOLUTION:Answer : D #### D
QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the
second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take
both the punctures together to make it flat ?
options: A)315min B)325min C)335min D)345min E)None of these
SOLUTION:Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st
puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(19+16)=(518)
So both punctures will make the type flat in
(185)mins=335mins
Answer: C #### C
QUESTION:There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic?
options: A)70 % B)75 % C)80 % D)85 % E)90 %
SOLUTION:Chance of no picnic+chance of picnic= 100% ... (i)
Chance of picnic=100%-Chance of no picnic ... (ii)
Chance of no picnic= 50% of 30%= 15%
Therefore, According to (ii), Chance of picnic= 100%-15%= 85%.
Answer D #### D
QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work?
options: A)2days B)4days C)6days D)7days E)10days
SOLUTION:The required answer = (15-5)*9 / 15 = 40/10 = 6days
Answer is C #### C
QUESTION:In a consumer survey, 88% of those surveyed liked at least one of three products: 1, 2, and 3. 55% of those asked liked product 1, 40% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
options: A)15 B)20 C)25 D)30 E)35
SOLUTION:55 + 40 + 20 = 115
This number includes some people counted twice and some people counted three times.
115 - 88 = 27, and this number represents people counted twice or three times.
7% of the people are counted two extra times.
The percentage of people counted one extra time is 27 - 7(2) = 13.
The percentage of people who liked more than one product is 7% + 13% = 20%.
The answer is B. #### B
QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches?
options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0
SOLUTION:Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.3
x = 4.8
Alternate solution: Try to backsolve.
Initial volume = 4.8
After one hour --> (1/4)4.8 = 1.2
After two hours --> (1/4)1.2 = 0.3
Answer: C #### C
QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
options: A)277 B)277 C)120 D)882 E)272
SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C #### C
QUESTION:Which of the following inequalities is equivalent to 11 - 11x > 133?
options: A) x > -2 B) x > -1 C) x > -3 D) x > -11 E) x > -5
SOLUTION:You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide by a negative number, the sign of the inequality flips.
To illustrate,
11 - 11x > 133
11x > -122 (Correct)
x > -11 (Correct)
the correct option is D #### D
QUESTION:Two pipes A and B can fill a cistern in 20 and 40 minutes respectively, and a third pipe C can empty it in 80 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
options: A)19 1/7 min B)15 1/7 min C)17 1/7 min D)7 1/7 min E)16 min
SOLUTION:1/20 + 1/40 - 1/80 = 5/80
80/5 = 16
ANSWER:E #### E
QUESTION:8^100 is divisible by 17. Find the remainder?
options: A)10 B)12 C)16 D)18 E)20
SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 = (816)6×8417
Now this problem simply boils down to (1)6×8417 = 8417
84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.
C #### C
QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce?
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Going down = 16 m
Going Up = 8 --> Total = 24
Going down = 8 --> Total = 32
Going Up = 4 --> Total = 36
Going down = 4 --> Total = 40
Going up = 2 --> Total = 42
Going down = 2 --> Total = 44
Going up = 1 --> Total = 45
Going down = 1 --> Total = 46
Going up = 0.5 --> Total = 46.5 (Caught)
No of going downs = 5 ..
ANSWER:A #### A
QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58
options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1
SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300
Sum of the marks for the class of 48 students = 48 * 58 = 2784
Sum of the marks for the class of 103 students =
3300 + 2784 = 6084
Average marks of all the students = 6084/103
= 59.1
Answer:E #### E
QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2!
SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 boys are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 boys do not sit together would be: 7!-3!5!.
Answer: D). #### D
QUESTION:The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly
options: A)24.64 B)24.69 C)24.62 D)24.6 E)24.61
SOLUTION:Explanation:
For 1st year S.I =C.I.
Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200
i.e S.I on the principal for 1 year is Rs.200
Principle = = Rs.2500
Amount for 2 years, compounded half-yearly
C.I = Rs.424.64
Also,
Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64
Answer:A #### A
QUESTION:Evaluate 35 / .07
options: A)400 B)500 C)505 D)None of these E)506
SOLUTION:Explanation:
35/.07 = 3500/7 = 500
Option B #### B
QUESTION:How many 4 letter words can we make from the letters in an alphabet?
options: A)358800 B)358802 C)358801 D)358809 E)358810
SOLUTION:There are 26 letters in an alphabet
to choose 4 from these 26 would mean
26P4 = 26!/(26-4)!
We take Permutation and not Combination since the arrangement of letters matter in forming a word. Like MAPS and PAMS both are different words.
Therefore the answer is 26!/ 22! = 26*25*24*23 = 358800
Answer:A #### A
QUESTION:In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women?
options: A)10 B)20 C)30 D)40 E)50
SOLUTION:6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20
B) #### B
QUESTION:If (-12x)^(4x) = 12x^(15 - x) and x is an integer, what is the value of x ?
options: A)5 B)4 C)3 D)2 E)-2
SOLUTION:Since x is an integer, (-12x)^(4x) is always positive.
So, 12x^4x = 12x^(15 - x)
4x = 15 - x
5x = 15
x = 3
Answer: C #### C
QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes T, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
options: A) 6 B) 9 C) 10 D) 12 E) 15
SOLUTION:This is an inverse proportional problem......
5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15
So, T=15-5 = 10.C #### C
QUESTION:In a group of 3 boys and 2 girls can be formed out of a total of 4 boys and4 girls?
options: A)20 B)22 C)24 D)26 E)29
SOLUTION:Solution: Total number of ways = (select 3 boys from group of 4 boys) * (2 girls from group of 4 girls)
=> (4c3) * (4c2) = 24
C #### C
QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 6 years hence?
options: A)22 B)77 C)70 D)98 E)72
SOLUTION:A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
6 years, their ages will be 46 and 26.
Sum of their ages = 46 + 26 = 72.
Answer: E #### E
QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
options: A)3 1/5 Km B)4 Km C)4 1/5 Km D)3 2/5 Km E)3 3/5 Km
SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A #### A
QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate?
options: A)576 B)425 C)215 D)321 E)None of these
SOLUTION:Explanation :
In a circle, 5 boys can be arranged in 4! ways
Given that the boys and the girls alternate.
Hence there are 4 places for girls which can be arranged in 4! ways
Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A
QUESTION:Scott's average (arithmetic mean) golf score on his first four rounds was 58.What score does he need on his fifth round to drop his average score by 2 points?
options: A)48 B)72 C)78 D)88 E)312
SOLUTION:Average score for first 4 rounds = 58
Average score after 5 rounds = 56
Score Scott needs on his 5th round to drop average score by 2 points = 58 - (2*5) = 48
Answer A #### A
QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is?
options: A)11 B)72 C)36 D)99 E)27
SOLUTION:Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240)/12 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72 km/hr.
Answer: B #### B
QUESTION:(0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is:
options: A)0.8 B)0.4 C)0.96 D)0.69 E)0.76
SOLUTION:Given expression
= (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.5 - 0.1)
= 0.4
Answer is B #### B
QUESTION:A committee of 6 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee?
options: A)1/28 B)3/28 C)1/14 D)360/14 E)3/14
SOLUTION:3/8*4/7*1/6*6! = 3/14. We are multiplying by 6! because we can choose secretary,economist, and accountant is several way:
Answer: D. #### D
QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3%
SOLUTION:Explanation:
Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens = Rs. 33
Profit% = 33/99 * 100 = 33 1/3%
Answer: A #### A
QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly?
options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20
SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/5*1/4 = 9/10.
Answer: D. #### D
QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?
options: A)30 B)42 C)120 D)360 E)720
SOLUTION:5 people ,7 seats, only 2 can drive
if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways
since any one can drive total ways = 24 *2= 48 ways
4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways
48*15=720
ANSWER:E #### E
QUESTION:There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
options: A)1/9 B)2/9 C)5/9 D)4/9 E)2/3
SOLUTION:total 9 from take one.
9c1=9
red 5 from one
5c1=5
5/9
ANSWER:C #### C
QUESTION:It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn
options: A)16 B)45 C)36 D)20 E)90
SOLUTION:1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min..
only A and B are left..
if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins..
ans 20 D #### D
QUESTION:How many different possible permutations can be made from the word ‘VULLAT’ such thatthe vowels are never together?
options: A)120 B)200 C)240 D)260 E)270
SOLUTION:The word ‘BULLAT’ contains 6 letters of which 1 letter occurs twice = 6! / 2! = 360
No. of permutations possible with vowels always together = 5! * 2! / 2! = 120
No. of permutations possible with vowels never together = 360-120 = 240.
C #### C
QUESTION:The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 5 hours. If at 06:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
options: A)16:00. B)18:00. C)20:00. D)22:00. E)24:00.
SOLUTION:Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 5 hours
Time taken by both buses to meet again in St. Louis will be LCM of 2 and 5 = 10
If the buses start at 06:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours
Answer A #### A
QUESTION:If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before?
options: A)A)3/22% B)B)10% C)1/9 % D)1/11 % E)%
SOLUTION:100 – 12 = 88
88------12
100------? => 11 3/22%
ANSWER:A #### A
QUESTION:1 quarter Kg of potatoes cost 60 paise. Calculate the cost of 200 grams
options: A)48 paise B)77 paise C)96 paise D)66 paise E)55 paise
SOLUTION:Explanation:
Let 200 gm potato cost X paise
According to question,
Cost of 1/4 Kg potato = 60 Paise
=> Cost of 250 gm potato = 60 Paise
=> 1 Kg = 1000 gm
=> 1/4 Kg = 1000/4 gm = 250 gm
By direct proportion, more quantity, more cost
200 grams : 250 grams = X : 60
=> 200*60 = 250 X
=> 12000 = 250 X
=> X = 48
=> Thus, the cost of 200 grams is 48 paise.
ANSWER: A #### A
QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance?
options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr
SOLUTION:Total distance traveled = 100+200+300+100 = 700km
Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs
Average speed = 700/16.67 = 42km/hr approximately ;
Answer is B #### B
QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
options: A)17 Kmph B)78 Kmph C)72 Kmph D)18 Kmph E)19 Kmph
SOLUTION:Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C #### C
QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her
options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger
SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1997 has to be the ring finger
Answer is (D) #### D
QUESTION:What is the units digit of (52^5)(37^3)(71^9)?
options: A)3 B)4 C)6 D)7 E)8
SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2.
The units digit of 37^3 is the units digit of 7^3 which is 3.
The units digit of 71^9 is the units digit of 1^9 which is 1.
The units digit of 2*3*1 is 6.
The answer is C. #### C
QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740
SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All two
2. One symmetry and other two non
4. All the two letters can be arranged in 2 ways
( 11c2+ 11c1 * 15c2) *2
( 11*10/ 2 + 11 * 15 * 14 / 2 ) * 2
2420
IMO option D is the correct answer..
OA please...will correct if I missed anything..D #### D
<<<Examples ends
QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3
SOLUTION:distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr
Answer is B. #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
options: A)14 B)144 C)777 D)992 E)221
SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer:B #### B
QUESTION:A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
options: A)10 B)20 C)50 D)30 E)40
SOLUTION:Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 15 - 2.5 = 12.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 12.5 - 2.5 = 10 km/hr
Answer is A. #### A
QUESTION:Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
options: A)8 kmph B)10 kmph C)12 kmph D)16 kmph E)18 kmph
SOLUTION:Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C #### C
QUESTION:A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
options: A)72 B)67 C)108 D)26 E)27
SOLUTION:Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
Answer:C #### C
QUESTION:If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor S of 2x and 3y?
options: A)1 B)S=Cannot be determined C)S=2 D)5 E)6
SOLUTION:My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B #### B
QUESTION:Complete the series:
16, 06 , 68 , 88 , ? , 98
options: A)L8 B)B6 C)S5 D)E8 E)M5
SOLUTION:A
L8
To know why, just read the number series upside down and you will find that the numbers are 91, 90, 89, 88, __, 86
So L8 when read upside down reads as 87. #### A
QUESTION:A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is?
options: A)6 km B)3 km C)9 km D)5 km E)1 km
SOLUTION:Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 47/60
47x/60 = 47/60 => x = 1.
Total distance = 3 * 1 = 3 km.
Answer: B #### B
QUESTION:A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |Y|<3?
options: A)1/7 B)3/7 C)2/5 D)3/11 E)4/7
SOLUTION:|X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
B #### B
QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?
options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c
SOLUTION:Answer D - m, c, w
c ~ 1/3
w ~ 1/2
and m+w+c = 1 hence m ~ 1/6
Hence increasing order would be m -> c -> w
Aswer D #### D
QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red?
options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15
SOLUTION:P(Both are red),
=6C213C2=6C213C2
=5/26
C #### C
QUESTION:Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm.
options: A)227 B)299 C)300 D)161 E)212
SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (22 + 18) * (15)
= 300 cm2
Answer: C #### C
QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
options: A)80% B)107% C)116.7% D)120% E)140%
SOLUTION:Kim purchased 20 gallons of gas. She paid for 5 + 0.9*15 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%.
Isabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%.
8 is 8/7.5*100 = 107% of 7.5.
Answer: B. #### B
QUESTION:Narendra started a business, investing 45000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra?
options: A)A)Rs.7000 B)B)Rs.8000 C)C)Rs.8571 D)D)Rs.8600 E)E)Rs.8700
SOLUTION:The ratio of their investments = 45000 × 12 : 15000 × 6 = 6 : 1.
:. Narendra’s share on profit of Rs.10000 = 10000 × 6/7 = Rs.8571.
C) #### C
QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
options: A)100 B)250 C)260 D)416 E)None of these
SOLUTION:Explanation:
Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 × 32 = 416.
Answer: D #### D
QUESTION:Calculate the percentage increase in the area of a square if each of its sides is increased by 15%?
options: A)32.25% B)39.25% C)36.25% D)35.25% E)31.25%
SOLUTION:Assume original length = 100m by 50m
original area = 100*50= 5000
15% increase on each side
l = 100 + 15 = 115
w = 50 + 7.5 = 57.5
new area = 115*57.5= 6612.5
increase in area = 6612.5 - 5000 = 1612.5
%increase =21%
Answer A #### A
QUESTION:Find the circumference and area of radius 13 cm.
options: A)124 cm² B)531 cm² C)354 cm² D)584 cm² E)594 cm²
SOLUTION:Area of circle = πr²
= 22/7 × 13 × 13 cm²
= 531 cm²
ANSWER:B #### B
QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded?
options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these
SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :-
letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..)
Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get
IDAATRE
ANSWER:D #### D
QUESTION:What percent of 200 is 55?
options: A)0.25% B)4% C)25% D)27.5% E)250%
SOLUTION:200*x /100 = 55
x = 27.5
Ans: D #### D
QUESTION:A person travelled from his house to office at 45km/hr and office to house at 55km/hr. Then find the average speed?
options: A)49km/hr B)49.5km/hr C)50km/hr D)50.5km/hr E)51km/hr
SOLUTION:Average speed = (2*45*55)/(45+55)
= 49.5km/hr
Answer is B #### B
QUESTION:A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week?
options: A)605 B)505 C)105 D)100 E)200
SOLUTION:earning 35 surveys using her cell phone = 13*35 = 455
balance 15 surveys = 10 x 15 = 150
Total = 455+150 = 605
Answer : A #### A
QUESTION:What should be added to 4750 so that it may become a perfect square?
options: A)11 B)15 C)16 D)17 E)18
SOLUTION:69x69=4761
4761-4750 = 11
If added to 11 get perfect square
answer =A #### A
QUESTION:The number of arrangements that can be made with the letters of the word LUCK so that the vowels occupy the even places?
options: A)5 B)3 C)6 D)1 E)2
SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways.
Hence the total ways are 1 * 6 = 6.
Answer:C #### C
QUESTION:Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time W will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did?
options: A)2 minute and 12 seconds. B)two minutes. C)44 seconds. D)20 seconds. E)12 seconds.
SOLUTION:Tom is running alone for 20 seconds.
So he will cover a distance of 20*2.5 = 50 m in 20 seconds=W
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side
D is the answer #### D
QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots?
options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M
SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours.
The answer is A. #### A
QUESTION:(178% of 1265) ÷ 5.96 = ?
options: A)125 B)175 C)225 D)375 E)524
SOLUTION:Explanation :
? = (178 x 1265/100) ÷ 6 = 2250/600 = 375
Answer : Option D #### D
QUESTION:A certain office supply store stocks 2 sizes of self-stick notepads, each in 8 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
options: A)6 B)8 C)16 D)124 E)128
SOLUTION:Notepads of the same color = 8 (we have 8 colors). As we have two sizes then total for the same color=8*2=16
Notepads of the different colors = 8C3=56 (we should choose 3 different colors out of 8). As we have two sizes then total for the different color=56*2=112
Total=112+16=128
Answer: E. #### E
QUESTION:An article is bought for Rs.600 and sold for Rs.900, find the gain percent?
options: A)50% B)63 1/3% C)33 1/3% D)93 1/3% E)33 1/3%
SOLUTION:Explanation:
600 ---- 300
100 ---- ? => 50%
Answer:A #### A
QUESTION:In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ?
options: A)35 B)39 C)48 D)50 E)52
SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C #### C
QUESTION:Find the odd man out
4, 16, 25, 36, 42, 64
options: A)36 B)25 C)42 D)95 E)4
SOLUTION:2^2 = 4
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
ANSWER:C #### C
QUESTION:If log1087.5 = 5.9421, then the number of digits in (875)10 is?
options: A)30 B)70 C)27 D)26 E)25
SOLUTION:X = (875)10 = (87.5 x 10)10
Therefore, log10X = 10(log1087.5 + 1)
= 10(5.9421 + 1)
= 10(6.9421) = 69.421
X = antilog(69.421)
Therefore, number of digits in X = 70.
ANSWER:B #### B
QUESTION:In "Clash Royal" App Game, Warrior "The Bomber" is a very good defensive options. It can be purchased from the card shop.
The cost of the bomber is quite interesting.
The Cost of 1st bomber is: 2
The Cost of 2nd bomber is: 4
The Cost of 3rd bomber is: 6
The Cost of 4th bomber is: 8
The Cost of 5th bomber is: 10
i.e to buy 5 bombers you need 2+4+6+8+10 = 30 coins.
How many bombers can you buy using 1000 coins ? ?
options: A)61 B)62 C)63 D)64 E)65
SOLUTION:Solution
62
The Cost of 1st bomber is: 2 i.e Total coins spend: 2
The Cost of 2nd bomber is: 4 i.e Total coins spend: 6
The Cost of 3rd bomber is: 6 i.e Total coins spend: 12
The Cost of 4th bomber is: 8 i.e Total coins spend: 20
The Cost of 5th bomber is: 10 i.e Total coins spend: 30
The Cost of 6th bomber is: 12 i.e Total coins spend: 42
The Cost of 7th bomber is: 14 i.e Total coins spend: 56
The Cost of 8th bomber is: 16 i.e Total coins spend: 72
The Cost of 9th bomber is: 18 i.e Total coins spend: 90
The Cost of 10th bomber is: 20 i.e Total coins spend: 110
The Cost of 11th bomber is: 22 i.e Total coins spend: 132
The Cost of 12th bomber is: 24 i.e Total coins spend: 156
The Cost of 13th bomber is: 26 i.e Total coins spend: 182
The Cost of 14th bomber is: 28 i.e Total coins spend: 210
The Cost of 15th bomber is: 30 i.e Total coins spend: 240
The Cost of 16th bomber is: 32 i.e Total coins spend: 272
The Cost of 17th bomber is: 34 i.e Total coins spend: 306
The Cost of 18th bomber is: 36 i.e Total coins spend: 342
The Cost of 19th bomber is: 38 i.e Total coins spend: 380
The Cost of 20th bomber is: 40 i.e Total coins spend: 420
The Cost of 21st bomber is: 42 i.e Total coins spend: 462
The Cost of 22nd bomber is: 44 i.e Total coins spend: 506
The Cost of 23rd bomber is: 46 i.e Total coins spend: 552
The Cost of 24th bomber is: 48 i.e Total coins spend: 600
The Cost of 25th bomber is: 50 i.e Total coins spend: 650
The Cost of 26th bomber is: 52 i.e Total coins spend: 702
The Cost of 27th bomber is: 54 i.e Total coins spend: 756
The Cost of 28th bomber is: 56 i.e Total coins spend: 812
The Cost of 29th bomber is: 58 i.e Total coins spend: 870
The Cost of 30th bomber is: 60 i.e Total coins spend: 930
The Cost of 31st bomber is: 62 i.e Total coins spend: 992
Answer B #### B
QUESTION:Which of the following inequalities is equivalent to −4 < x < 8?
options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above
SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format
-4+y < x+y < 8+y
Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2
Thus, -6< x-2 < 6 => |x-2| < 6.
Hence, answer is D #### D
QUESTION:When 4 dice are thrown, what is the probability that the same number appears on each of them?
options: A)1/36 B)1/18 C)1/216 D)1/5 E)1/4
SOLUTION:Sample space (Denominator): When 4 dice are thrown simultaneously, then the total number of possible outcomes is 64 = 1296.
Event (Numerator): The chances that all the dice show same number (1,1,1,1),
(2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)} is 6.
Probability = Event/ Sample space = 6/64 = 1/63 = 1/216.
ANSWER:C #### C
QUESTION:Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average score for all the three classes, taken together?
options: A)81 B)81.5 C)82 D)84.5 E)None of these
SOLUTION:Explanation :
Let the number of students in classes X, Y and Z be a,
b and c respectively. Then
Total of X = 83a
Total of Y = 76b
Total of Z = 85c
And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b.
Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b.
Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a.
Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c).
=> 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a .
=> 978/12
=> 81.5
Answer : B #### B
QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum Q of even integers from 102 to 200 inclusive?
options: A)5100 B)7550 C)10100 D)15500 E)20100
SOLUTION:My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
Q=2550+(100*50)=7550.B #### B
QUESTION:Two hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?
options: A)20% B)25% C)40% D)50% E)80%
SOLUTION:Two hundred multiples of seven will have 100 even and 100 odd numbers
300 multiples of eight will have ALL even (being multiple of 8)
Probability of number selected being odd = Total Odd Numbers / Total available numbers
Probability = 100/500 = 0.2 = 20%
Answer: Option A #### A
QUESTION:If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?
options: A)9 B)10 C)11 D)12 E)13
SOLUTION:0.003^5= (3*10^-3)^5 = 243*10^-15 = 0.243*10^-12 which would have 12 zeros to the right of the decimal point. The answer is D. #### D
QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent?
options: A)200 B)100 C)276 D)280 E)279
SOLUTION:Profit on first article = 10% of 1000 = 100.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: B #### B
QUESTION:In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ?
options: A)30 B)45 C)42 D)72 E)75
SOLUTION:Let the number of benches in the class be x.
Then, 6(x + 1) = 7x - 5
x = 11.
Hence, number of students in the class = 6 ( x + 1)
= 6 x 12
= 72.
ANSWER:D #### D
QUESTION:Find the value of a from (15)^2 x 8^3 ÷ 256 = a.
options: A)250 B)420 C)440 D)650 E)450
SOLUTION:Given Exp. =(15)^2 x 8^3 ÷ 256 = a
= 225 x 512 ÷ 256 =
450
E #### E
QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
options: A)897 B)164,850 C)164,749 D)149,700 E)156,720
SOLUTION:Explanatory Answer
Step 1: Identify the series
The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.
The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107.
The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.
It is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2).
So, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3.
Step 2: Compute the sum
Sum of an Arithmetic Progression (AP) = [first term + last term/2]n
We know the first term: 101
We know the last term: 998.
The only unknown is the number of terms, n.
In an A.P., the nth term an = a1 + (n - 1)*d
In this case, therefore, 998 = 101 + (n - 1)* 3
Or 897 = (n - 1) * 3
(n - 1) = 299 or n = 300.
Sum of the AP will therefore, be [101+998/2]∗300 = 164,850
Choice B is the correct answer. #### B
QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16
SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C #### C
QUESTION:A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
options: A)5/8 B)6/13 C)5/16 D)5/13 E)5/11
SOLUTION:Two balls can be picked from thirteen balls in 13Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (9 * 4) = 36/78 = 6/13
Answer: B #### B
QUESTION:The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 360 m, its area is?
options: A)180 B)882 C)277 D)261 E)281
SOLUTION:5x + 12x + 13x = 360 => x = 12
a = 60, b = 144, c = 156
S = (60 + 144 + 156)/2 = 180
Answer: A #### A
QUESTION:385, 462, 572, 396, 424, 671, 264
options: A)385 B)424 C)671 D)264 E)None of these
SOLUTION:Solution
In each number except 424,the middle digit is the sum of the other two. Answer B #### B
QUESTION:find out the probability to get 1Rs coin head, 2Rs coin Tail and 5Rs coin head??
options: A)1/2 B)1/8 C)1/16 D)1/4 E)None of these
SOLUTION:1Rs coin head=1/2
2Rs coin Tail=1/2
5Rs coin head=1/2
=(1/2)*(1/2)*(1/2)
=1/8
ANSWER:B #### B
QUESTION:P, Q and R can do a work in 6 , 9 and 12 days respectively. They completed the work and got Rs.195. What is the share of P?
options: A)80 B)70 C)85 D)90 E)95
SOLUTION:The ratio of their working rates = 1/6 : 1/9 : 1/12 = 6 : 4 : 3.
Since, they work together, the share of P
= 6/13 * 195 = Rs.90
Answer: D #### D
QUESTION:In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
options: A)3.5% B)2.4% C)10.2% D)5% E)2.6%
SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
Now, the area obtained with wrong measurements would be 116*95=11,020, which is 10.2% greater than the actual area.
Answer: C. #### C
QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible?
options: A)90 B)79 C)64 D)57 E)36
SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible.
Total Options: 64
Final Answer:
C #### C
QUESTION:If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers?
options: A)108 B)99 C)128 D)135 E)143
SOLUTION:Let the 2 positive numbers x and y
x+ y = 20 -- 1
x^2 - y^2 = 40
=> (x+y)(x-y)=40 -- 2
Using equation 1 in 2 , we get
=> x-y = 2 -- 3
Solving equation 1 and 3 , we get
x= 11
y= 9
Product = 11*9 = 99
Answer B #### B
QUESTION:If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
options: A)3⁄7 B)4⁄7 C)3⁄4 D)4⁄3 E)7⁄4
SOLUTION:Should be a sub-600 level Q..
volume= {3/7}/{4/7}=3/4
ANSWER:C #### C
QUESTION:The sum of three consecutive odd natural numbers, each divisible by 3 is 90. What is the largest among them?
options: A)21 B)24 C)27 D)33 E)45
SOLUTION:Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 = 90
3X = 81
X = 27
The numbers are 27, 30, 33
Therefore the largest number is 33
Answer D. #### D
QUESTION:A bicyclist's wheel has a circumference of 6 meters. if the bicyclist covers 180 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour.
To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.=180/6*5 =6
Answer (E) #### E
QUESTION:What is the prime factors’ number of 36?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 24 = 2^2*3^2
prime factors’ number will be 2+2 = 4.
Hence, answer is C. #### C
QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
options: A)8% B)7% C)10% D)12% E)4%
SOLUTION:Option E
Explanation:
65*(90/100)*((100-x)/100) = 56.16
x = 4% #### E
QUESTION:if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no.
options: A)24 B)25 C)26 D)27 E)28
SOLUTION:25 m^3 = (3+1)(3+1) = 16
then m^4 = (4+1)(4+1)=25
ANSWER:B #### B
QUESTION:If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b =
options: A) −48 B) −2 C) 2 D) −7 E) 48
SOLUTION:a(a + 7) = 18 and b(b + 7) = 18
=> a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively
=> a+b = -7
Ans: D #### D
QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction?
options: A)5hours B)10hours C)8hours D)10hours E)12hours
SOLUTION:To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 20 =10 hours
Answer is B #### B
QUESTION:What is the place value of 7 in the numeral 2734?
options: A)450 B)500 C)700 D)800 E)840
SOLUTION:Option 'C'
7 * 100 = 700 #### C
QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls?
options: A)12 B)32 C)5 D)28 E)30
SOLUTION:number of kids playing with white color balls = 26
total number of kids in the play school = 35
number of kids playing with both white and yellow color balls = 19
we have to find,
number of kids playing with yellow color balls
35 = 26 + n(B) - 19
35 + 19 - 26 = 28
Hence, Answer is 28 kids play with yellow color
balls. ANSWER D #### D
QUESTION:121,112,...?..,97,91,86
options: A)99 B)104 C)102 D)108 E)100
SOLUTION:121. 112. 104. 97. 91. 86
the decreasing difference is reducing by 1 at each step
so,missing no. will be 104
answer B #### B
QUESTION:An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang two on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
options: A)18 B)30 C)56 D)120 E)216
SOLUTION:Arrangment means permutations questions..
8P2 = 8!/2! = 56.
IMO option C is correct answer.. #### C
QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years. The age of the 15th student is
options: A)9 years B)11 years C)17 years D)21 years E)25 years
SOLUTION:Solution
Age of the 15th student =[15x15-(14x8+16x6)]
= (225 - 208)
= 17 years.
Answer C #### C
QUESTION:The length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
options: A)50 m B)60 m C)65 m D)75 m E)80 m
SOLUTION:Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B #### B
<<<Examples ends
QUESTION:By how much is 50% of 250 greater than 25% of 400.
options: A)25 B)26 C)29 D)39 E)26
SOLUTION:(50/100) * 250 – (25/100) * 400
125 - 100 = 25
Answer:B #### B
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Which one the following fractions has the biggest value?
options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711
SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D
QUESTION:Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
options: A)$140 B)$141 C)$142 D)$147 E)$145
SOLUTION:Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 147.
So after completing the 1st week she will get $ (x+147).
Similarly after completing the 2nd week she will get $ (x + 147) + $ 147.
= $ (x + 147 + 147)
= $ (x + 294)
So in this way end of every week her salary will increase by $ 147.
correct answer D)$147 #### D
QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is
options: A)2970 B)297 C)2997 D)300 E)30
SOLUTION:(1/10)*3000 - (1/10)%*3000 =
300 - (1/1000)*3000 =
300 - 3 = 297
The answer is B. #### B
QUESTION:In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?
options: A)25 B)30 C)45 D)20 E)50
SOLUTION:6p2 = 6 x 5 = 30
B) #### B
QUESTION:The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is:
options: A)89.25 km/hr. B)77 km/hr. C)90.25 km/hr. D)94.25 km/hr. E)96.25 km/hr.
SOLUTION:Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (440/5) = 88
x = (88/8) = 11
Hence, speed of first bullet train = (7 x 11) km/hr = 77 km/hr.
B #### B
QUESTION:A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 45 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
options: A)40 B)45 C)50 D)55 E)60
SOLUTION:A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 45 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
45 = 180/4t
t = 60
B-C = 60 mph
Answer E #### E
QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
options: A)2.5 sec B)2.9 sec C)3.5 sec D)7.5 sec E)5 sec
SOLUTION:Speed = 144 * 5/18 = 40 m/sec
Time taken = 200/40
= 5 sec.
Answer: E #### E
QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train?
options: A)7:00 B)8:00 C)9:00 D)10:00 E)11:00
SOLUTION:In one hour and thirty minutes the first train travels 105 km.
The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h.
The second train will catch the first train in 105/10 = 10.5 hours, so at 9:00 pm.
The answer is C. #### C
QUESTION:If the two hands in a clock are 11 minutes divisions apart,then the angle between them is
options: A)66° B)18° C)24° D)60° E)None of these
SOLUTION:In a clock, each minute makes 6°
∴ 11 minutes will make 6 × 11 = 66°
Answer A #### A
QUESTION:If a certain manager had received a 5% raise instead of the 8% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise?
options: A)55,000 B)58,806 C)59,290 D)62228.52 E)61,620
SOLUTION:No need of getting involved with decimals ..just work in fractions ..
salary(let X) included 5% increase can be written as
(1+5/100)X=60500
X=60500/1.05------>57619.05
if there is 8% rise in 57619.05
then the salary now is 8% of 57619.05
8*57619.05/100=4609.52
then toal salary after increment=57619.05+4609.52----->62228.52
Ans D #### D
QUESTION:Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 18 hours. If all the three pipes are opened together, then the tank will be filled in?
options: A)3 9/97 hrs B)4 2/4 hrs C)3 9/17 hrs D)3 9/27 hrs E)3 9/19 hrs
SOLUTION:Net part filled in 1 hour = 1/9 + 1/6 - 1/18
= 4/18
The tank will be full in 18/4 hrs, i.e., 4 2/4 hrs.
Answer:B #### B
QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rakesh ?
options: A)1000 B)1100 C)1125 D)1200 E)1050
SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000
=>4:5:3
=>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...]
=> 12:5:6
Share of Rajan => 4600*12/23 = 2400
Share of Rakesh => 4600*5/23 = 1000
ANSWER:A #### A
QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
options: A)Rs.81.60 B)Rs.160 C)Rs.172 D)Rs.727 E)Rs.728
SOLUTION:SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer:A #### A
QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold?
options: A)6 B)4 C)8 D)10 E)12
SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies;
14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22
# of paperback copies sold is 30-22=8
Answer: C #### C
QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
options: A)35.2 B)36.1 C)36.5 D)39.1 E)None
SOLUTION:Sol.
Therefore correct sum
= ( 36 × 50 + 48 – 23)
= 1825.
Therefore correct mean
= 1825 / 50
= 36.5.
Answer C #### C
QUESTION:If log10 2 = 0.3010, the value of log10 80 is:
options: A)1.5252 B)1.903 C)3.9252 D)3.903 E)2.5252
SOLUTION:= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
ANSWER B #### B
QUESTION:72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand?
options: A)Rs. 3.23 B)Rs. 5.11 C)Rs. 5.51 D)Rs. 7.22 E)None
SOLUTION:Explanation :
The best way to solve this question is to multiply the alternatives by 72 and find which one gives the middle three digits 96.7.
To cut time, you can choose to multiply 72 by integer values only, e.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504.
It must be remembered that the decimal part of the answer will be multiplied by 72 and the actual answer will increase .
Let us now roughly multiply the decimal values of the options also by 72,
e.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2 and 72 × 0.5 = 36.
So, option (1) will yield (216 + 14) = 230 (approximately),
option(2) will yield (360 + 7) = 367 (approximately),
option(3) will yield (360 + 36) = 396 (approximately),
and option(4) will yield (504 + 14) = 528 (approximately).
Of these only option (3) satisfies our requirement of 2nd and 3rd digits being 96.
Answer : C #### C
QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
options: A)35 B)36 C)37 D)43 E)39
SOLUTION:James worked for 41 hours hence he earned 40*x+5*2x=50x dollars;
We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours.
Answer: D. #### D
QUESTION:Claire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?
options: A)39 B)50 C)66 D)57 E)60
SOLUTION:G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300
G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66
C #### C
QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2.
options: A)Cannot be determined B)1 C)2 D)3 E)4
SOLUTION:take square of any prime number
remainder will be 1
Ans B #### B
QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
options: A)3 B)7 C)8 D)5 E)1
SOLUTION:S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C #### C
QUESTION:A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
options: A)30days B)35days C)40days D)44days E)45days
SOLUTION:Explanation:
(A+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5
A complete remaining work in 2/5*50 = 20
Total work = 10+20= 30days
Answer: Option A #### A
QUESTION:There is a biased dice..wen d dice is thrown. probability of occurrence of odd numbers is thrice that of even numbers. If the dice is thrown twice..find the probability of the products of the numbers appeared being odd.
options: A)8/16 B)9/16 C)10/16 D)11/16 E)7/16
SOLUTION:since, p(odd)=3p(even)
and p(odd)+p(even)=1
hence p(odd)=3/4
now only odd*odd=odd
hence two odd i s p(odd)=3/4*3/4=9/16
ANSWER:B #### B
QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.6400?
options: A)8100 B)3388 C)7767 D)2009 E)22888
SOLUTION:6400* 9/8 * 9/8
= 8100
Answer: A #### A
QUESTION:A man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack?
options: A)106 B)301 C)309 D)400 E)450
SOLUTION:Explanation:
Clearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (L.C.M of 3, 4, 5, 6) x + 1 i.e., (60x + 1 ) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So the number is 301.
Answer: B) 301 #### B
QUESTION:In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 80 and a standard deviation of 14, which of the following is exactly 2.60 standard deviations more than the mean?
options: A)a) 43.6 B)b) 60 C)c) 72 D)d) 77.5 E)e) 81
SOLUTION:Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 80
2) The standard deviation of the group is 14
If you go 1 SDupfrom the average, you hit.....80+14 = 94
If you go 1 SDdownfrom the average, you hit.....80-14 = 66
If you go 2 SDsupfrom the average, you hit.....80+2(14) = 108
If you go 2 SDsdownfrom the average, you hit.....80-2(14) = 52
Etc.
Here, we're asked for the number that is EXACTLY 2.60 SDs above the mean....
2.60 SDsupwould be.....80 + 2.60(14) = 43.6
A #### A
QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
options: A)4% B)8% C)4.2% D)4.8% E)5%
SOLUTION:Let's say there is a TOTAL of100students at this college.
60 percent of the total number of students are freshmen.
# of freshmen = 60% of 100 =60
40 percent of the fresh-men are enrolled in the school of liberal arts...
Number of liberal arts freshmen = 40% of 60 =24
...and, of these, 20 percent are psychology majors...
Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8
What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
4.8/100= 4.8%
Answer:D #### D
QUESTION:Convert 0.30 in to a vulgar fraction ?
options: A)18/50 B)16/50 C)3/10 D)19/50 E)None
SOLUTION:Answer
0.30 = 30/100 = 3/10
Correct Option: C #### C
QUESTION:Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Six years ago Jim was 7 times as old as Sam. How old is Jim now?
options: A)8 B)12 C)16 D)20 E)24
SOLUTION:We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 2 years younger than Fred
3) Six years ago, Jim was 7 times as old as Sam.
let's TEST Answer D: 20
IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 8 years old
6 years ago, Jim was 14 and Sam was 2, so Jim WAS 7 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
D #### D
QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
options: A)2/7 B)3/8 C)3/10 D)4/11 E)5/13
SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C #### C
QUESTION:It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish?
options: A)20 B)22 C)24 D)26 E)28
SOLUTION:The bacteria doubles each day, so after 29 days, the dish was half full.
After 28 days, the dish was one quarter full.
After 27 days, the dish was one eighth full.
After 26 days, the dish was one sixteenth full.
After 25 days, the dish was 1/32 full.
After 24 days, the dish was 1/64 full.
The answer is C. #### C
QUESTION:Two dice are rolled. The probability of getting a sum of at least 9 is
options: A)13/36 B)5/18 C)35/36 D)11/36 E)15/36
SOLUTION:Sum of 9 = {(3,6) (6,3)} = 2ways.
Sum of 10 = {(5,5) (6,4) (4,6) (5,5)} = 4 ways.
Sum of 11 = {(6,5) (5,6)} = 2 ways.
Sum of 12 = {(6,6) (6,6)} = 2 ways.
Therefore, Favourable cases = 10
Total cases = 6 x 6 = 36.
Therefore, Probability = 10/36 = 5/18.
ANSWER:B #### B
QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
options: A)$18,400 B)$19,500 C)$20,200 D)$20,400 E)$21,100
SOLUTION:Important point to notice- 2.5% decrease from the original price
2.5% of 22,000= 550
Total reduction in 6 years= 550*6= 3300
Final price= 22,000 +1500 - 3300= 20,200
C is the answer #### C
QUESTION:A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a red ball is selected?
options: A)x/(x + 4) B)y/(x + 5) C)(x + 5)/(x + y + 9) D)(y + 4)/(x + y + 9) E)(x + 4)/(x + y + 9)
SOLUTION:x red balls
y green balls
x+4+y+5 is the total
=x+y+9
x+5 is the number of red balls
so (x + 5)/(x + y + 9)
the answer is C #### C
QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/4 meter, and then if the cable were cut at each mark, how many different size length of cable would result?
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:In this particular example length (10 meter) is just extraneous information.
The location of the marks for 1/3 meter would be 4/12, 8/12, 12/12, etc...
The location of the marks for 1/4 meter would be 3/12, 6/12, 9/12, 12/12, etc...
The distances between marks are 3/12, 1/12, and 2/12.
The answer is C. #### C
QUESTION:A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
options: A)19 cm2 B)30 cm2 C)17 cm2 D)18 cm2 E)12 cm2
SOLUTION:The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5
= 30 cm2
Answer:B #### B
QUESTION:If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is?
options: A)A)15 B)B)10 C)C)14 D)D)12 E)E)11
SOLUTION:2 * 22/7 * 14 * x = 880 => x = 10
ANSWER:B #### B
QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 6 rows or 4 rows or 8 rows, then no tree will be left. Find the least number of trees required
options: A)24 B)60 C)28 D)76 E)21
SOLUTION:Explanation:
The least number of trees that are required = LCM(6,4,8) = 24
Answer: A #### A
QUESTION:Find the value of a from (15)^2 x 8^3 ÷ 256 = a.
options: A)250 B)420 C)440 D)650 E)450
SOLUTION:Given Exp. =(15)^2 x 8^3 ÷ 256 = a
= 225 x 512 ÷ 256 =
450
E #### E
QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
options: A)32 Yrs B)36 Yrs C)40 Yrs D)48 Yrs E)None
SOLUTION:Explanation:
Let the mother's present age be x years.
Then, the person's present age = (2/5)*x years.
((2/5)*x)+8 = (1/2)(x+8)
2(2x + 40) = 5(x + 8)
x = 40.
Answer: C #### C
QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
options: A)14355 B)15432 C)17576 D)18543 E)16878
SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C #### C
QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
options: A)90 B)2,700 C)3,300 D)5,400 E)324,000
SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 110*30=3,300 copies.
Answer: C. #### C
QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least?
options: A)John B)Susan C)Sam D)Mark E)Lynn
SOLUTION:Let J – John’s weight
S – Susan’s weight
M – Mark’s weight
A – Sam’s weight
L – Lynn’s weight
J = 2S
S = 0.6A
M = 0.5L
L = 1.9J
Let us convert these weights to one variable
S = J/2
A = S/0.6 = J/1.2 = 5J/6
L = 1.9J
M = 0.5 * 1.9J = 0.95J
So Susan has the least weight.
Answer - B #### B
QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination.
options: A)15 B)21 C)17 D)19 E)21
SOLUTION:Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 36 - X
Now,
50*X + 500 * (36 - X) = 10350
50X + 18000 - 500X = 10350
- 450X = - 7650
X = 17.
No. of 50 rupees note = 17.
Answer: Option C #### C
QUESTION:The fourth proportional to 12, 16 and 18 is?
options: A)21 B)24 C)88 D)99 E)26
SOLUTION:(16*18)/12 = 24
Answer: B #### B
QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 16 hours a day, the number of men required is:
options: A)4 B)5 C)6 D)8 E)9
SOLUTION:Explanation :
Let the required number of men be x.
Less days, More men (Indirect Proportion)
More working hrs per day, Less men (Indirect Proportion)
Days 8 : 10
Working Hrs 16: 8 :: 12 : x
=> 12 x 16 x x = 10 x 8 x 12
=> x = 10 x 8 x 12 / (12 x 16)
=> x = 5
Answer : B #### B
QUESTION:How many ways could two people sit at a table with four seats in which two of the four seats will remain empty?
options: A)60 B)12 C)112 D)118 E)120
SOLUTION:ways in which 2 seats out 4 can be selected = 4C2
ways in which 2 people can be arranged in 2 seats = 2!
Total ways of arrangement = 4C2*2!
=4*3
=12
Ans = B #### B
QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone?
options: A)4 2/3 B)7 C)9 D)24 E)21
SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 6 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/7+6*1/x=1
5x+42=7x
2x=42
x=21 days.
Ans:E #### E
QUESTION:If x and y are perfect squares, then which five of the following is not necessarily a perfect square?
options: A)x^2 B)xy C)4x D)x+y E)x^5
SOLUTION:If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square.
Answer: A. #### A
QUESTION:Find the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114.
options: A)2 or ½ B)2/3 or 3/2 C)¾ or 4/3 D)4 or ¼ E)5 or 1/5
SOLUTION:Let the terms be a/r, a , ar
a/r *a * ar = a 3 =216, a =6
(a/r*a )+ (a*ar) + (ar*a/r ) =114, a 2/r + a 2 r + a 2 =114
a 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114
6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0,
On solving, r = 2/3 or 3/2
ANSWER:B #### B
QUESTION:At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock
options: A)47 B)76 C)28 D)66 E)99
SOLUTION:Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 45/5 = 9 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 9 = 99 secs.
Answer: E #### E
QUESTION:If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips?
options: A)1/4 B)1/8 C)1/2 D)1/16 E)1/32
SOLUTION:(1/2) * (1/2) * (1/2) * (1/2) = 1/16 Answer: D #### D
QUESTION:When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[8] = ?
options: A)[22] B)[44] C)[75] D)[88] E)[90]
SOLUTION:[7]*[8]=(7*2+1)(8/2+1)
=[75].
Ans -C #### C
QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ?
options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these
SOLUTION:solution:
Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)]
=23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4.
∴ Required average =8.4/2 = 4.2 Answer B #### B
QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners.
Conclusions:
1) 80% of the team consists of spinners.
2) The opening batsmen were spinners.
options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow
SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow.
D #### D
QUESTION:On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is:
options: A)364724 B)365387 C)365737 D)366757 E)366767
SOLUTION:Required number= 999*366+103
= (1000-1)*366+103
= 366000-366+103
= 365737.
ANSWER:C #### C
QUESTION:What number should replace the question mark?
16, 23, 19, 19, 22, 15, 25, ?
options: A)11 B)12 C)13 D)14 E)15
SOLUTION:A
11
There are two alternate sequences + 3 and - 4 #### A
QUESTION:If 45-[28-{37-(15-*)}]= 56, then * is equal to:
options: A)-29 B)-19 C)17 D)29 E)39
SOLUTION:45-[28-{37-(15-*)}]= 56 => 45-[28-{37-15+*}]=56
45-[28-37+15-*]=56 => 45[43-37-*]=56
45-[6-*]=56 => 45-6+*=56
39+*=56 => *=56-39
= 17
ANSWER:C #### C
QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required?
options: A)34 B)40 C)68 D)88 E)26
SOLUTION:We have: l = 20 ft and lb = 60 sq. ft.
So, b = 3 ft.
Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft.
ANSWER:E #### E
QUESTION:A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is?
options: A)5 B)6 C)10 D)8 E)9
SOLUTION:US = 15
DS = 35
M = (35 - 15)/2 = 10
Answer: C #### C
QUESTION:probability that guy1 will succesfully hit a shot is 2/3. probabilty of guy2 succesfully hitting a shot is 2/3. if they shoot two shots each, what is the probability that they have equal number of hits?
options: A)9/27 B)10/27 C)11/27 D)12/27 E)11/26
SOLUTION:(1/3*1/3)[guy1]*(1/3*1/3)[guy2]
for 1 hit each: (4 ways)
(2/3*1/3)*(2/3*1/3), (2/3*1/3)*(1/3*2/3), (1/3*2/3)*(2/3*1/3), (1/3*2/3)*(1/3*2/3)
for 2 hits each:(1 way)
(2/3*2/3)*(2/3*2/3)
Add all these cases, you will get answer as 11/27.
ANSWER:C #### C
QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube.
options: A)36 B)48 C)45 D)360 E)55
SOLUTION:16200 = 23 * 34 * 52
A perfect cube has a property of having the indices of all its prime factors divisible by 3.
Required number = 32 * 5 = 45.
ANSWER:C #### C
QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove?
options: A)$240 B)$260 C)$280 D)$300 E)$320
SOLUTION:J+K=700 so K=700-J
2J=K+80
2J=(700-J)+80
3J=780
J=260
The answer is B. #### B
QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class?
options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25
SOLUTION:the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C) #### C
<<<Examples ends
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
options: A)120 metres B)180 metres C)324 metres D)150 metres E)180 metres
SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec.
Length of the train = (Speed x Time).
Length of the train = 50 x 9/3 m = 150 m.
ANSWER : OPTION D #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A fruit seller had some oranges. He sells 20% oranges and still has 380 oranges. How many oranges he had originally?
options: A)475 B)700 C)220 D)400 E)None of these
SOLUTION:Explanation :
He sells 20% of oranges and still there are 380 oranges remaining
=> 80% of oranges = 380
⇒ (80 × Total Oranges)/100 = 380
⇒ Total Oranges/100 = 4.75
⇒ Total Oranges = 4.75 × 100 = 475
Answer : Option A #### A
QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
options: A)10hours B)12hours C)8hours D)5hours E)15hours
SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10
The leak will empty the tank in 10hours
Answer is A #### A
QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest.
options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23
SOLUTION:R = 100 I / PT
=> R = (100 * 7200)/ (15000 * 5) = 9.6%
CI = P{ [1 + R /100]n - 1}
= 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24
Answer:D #### D
QUESTION:When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these
SOLUTION:Let the first and the second numbers be x and y respect then
y + 30% of x = 140% of y
or, y + 0.3x = 1.4y
or, 0.3x = 0.4y
∴ x : y = 0.4 : 0.3 = 4 : 3
Answer B #### B
QUESTION:Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 0.5. What value is exactly 2 standard deviations less than the mean?
options: A) 10.5 B) 11 C) 11.5 D) 12 E) 12.5
SOLUTION:The value which is exactly two SD below the mean is: mean-2*SD=13.5-2*0.5=12.5.
Answer: E. #### E
QUESTION:Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
options: A)76 seconds B)16 seconds C)18 seconds D)27 seconds E)19 seconds
SOLUTION:Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.
Answer: D #### D
QUESTION:A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
options: A)227 B)400 C)230 D)288 E)271
SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 42 = 50/3
3(x + 300) = 2100 è x = 400m.
Answer: B #### B
QUESTION:If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is
options: A)40 B)49 C)80 D)88 E)90
SOLUTION:Sol.
Let the numbers be x and y.
Then, (x+y) = 22 and x2 + y2 = 386.
Now, 2xy = (x+y)2 - (x2 + y2)
= (22)2 - 386= 484 - 386= 98
xy = 49.
Answer B #### B
QUESTION:For each positive integer,the quantitySn is defined such thatSn+1=(Sn)^2 -S(n+1).in addition ,S2=1.then which of the following must be true.
options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7
SOLUTION:Since all the answers include S4, let's start from there.
S4=S2^2-S3
S3=S1^2-S2
Substituting S3 into the first equation we get:
S4=S2^2-(S1^2-S2)
Since S2=1
S4=1-(S1^2-1)
S4=2-S1^2
We need S1^2 in order to calculate S4.
E) provides S1 and from there we can calculate S4:
S4=2-(-3)^2
S4=-7
Correct.
As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.
For example:
If S4=-7 then S1=3 :
if we substitute S4 with - 7 we get:
-7=2-S1^2
S1^2=9
now S1 can be +/-3 !!
A #### A
QUESTION:A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder?
options: A)9 B)8 C)7 D)6 E)5
SOLUTION:Number = ( 779 x a) + 47, where "a" is the quotient
= (19 x 41 x a) + (19 x 2) + 9
= 19 x (41a + 2) + 9
= 19 x (New quotient) + 9
\inline \fn_jvn \therefore Required remainder = 9
Answer:A #### A
QUESTION:In a mixture of 60 liters, the ratio of milk and water is 4:1. What amount of water must be added to make the ratio of milk and water as 1:4?
options: A)60 liters B)42 liters C)68 liters D)65 liters E)62 liters
SOLUTION:4:1 --- 60
1:4
2:8
---------------
5
5 ----------- 60
5 ----------- ? => 60 liters
ANSWER:A #### A
QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years?
options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11
SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320
C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5
Difference = (360.5 - 320) = Rs. 40.5
Answer: C #### C
QUESTION:8k8
+ k88
--------
1,6w6
If k and w represent non-zero digits within the integers above, what is w?
options: A)6 B)7 C)8 D)9 E)17
SOLUTION:8k8
k88
--------
16w6
Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and w=6.
Answer: A. #### A
QUESTION:Goldenrod and No Hope are in a horse race with 6 contestants. How many different L arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
options: A) 720 B) 360 C) 120 D) 24 E) 21
SOLUTION:no hope finishing before goldenrod= 1/2 of the times
therefore the different L arrangements are 1/2* 6! = 360 = B #### B
QUESTION:Let X be the smallest positive integer such that 10 and 14 are factors of 250 + X, so the value of X is:
options: A)0 B)10 C)20 D)30 E)40
SOLUTION:You can calculate the LCM (10,14) = 70.
After that you should check which of the possible X values will result in a number divisible by 70.
The only possibility for this is 30 ( because 250 + 30 = 280 = 70*4)
Answer D #### D
QUESTION:A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
options: A)5 kmph B)7 kmph C)9 kmph D)8 kmph E)1 kmph
SOLUTION:Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer:D #### D
QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test.
You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it?
options: A)48% B)55% C)60% D)71% E)80%
SOLUTION:C
60%
In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability.
In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already.
Therefore, P(Second/First) = P (First and Second)/ P (First)
= 0.25/0.42
=0.60
=60 % #### C
QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51 kmph, find the speed of the stream?
options: A)12 kmph B)13 kmph C)14 kmph D)15 kmph E)17 kmph
SOLUTION:The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 51/3 = 17 kmph
ANSWER:E #### E
QUESTION:The diameter of a garden roller is 1.4 m and it is 4 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7)
options: A)80 m2 B)84 m2 C)88 m2 D)86 m2 E)None of these
SOLUTION:Required area covered in 5 revolutions
= 5 × 2Ï€rh = 5 × 2 × 22â„7 × 0.7 × 4 = 88 m2
Answer C #### C
QUESTION:In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true?
I) k=0
II) k=−1
III) k=−3
options: A)I only B)III only C)I and II only D)II and III only E)I and III only
SOLUTION:Please format the question properly.
Per the question, x^2+kx+1=0 with k=constant.
For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges.
B is the correct answer. #### B
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
options: A)7 B)9 C)8 D)4 E)5
SOLUTION:25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 8
Answer:C #### C
QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 39.6. The difference between the unit digit and hundreds digit of that number is :
options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 0
SOLUTION:Since the average increased by 39.6 and there were a total of 10 numbers, it means the incorrect number was 396 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 396
99c - 99a = 99(c - a) = 396
396 = 99*4 = 99(c - a)
So c - a = 4
Answer (A #### A
QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
options: A)16 km/hr B)17 km/hr C)60 km/hr D)15 km/hr E)19 km/hr
SOLUTION:Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer: C #### C
QUESTION:The remainder when 1!+2!+3!...+50! divided by 8! will be
options: A)21 B)5193 C)77 D)9275 E)19
SOLUTION:The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!.
So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!.
So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320)
So remainder is 5193.
Answer:B #### B
QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is?
options: A)1994 B)1494 C)1349 D)1496 E)1500
SOLUTION:LCM = 1400
1400 - 6 = 1394
ANSWER:C #### C
QUESTION:A car travels at a speed of 65 miles per hour. How far will it travel in 8 hours?
options: A)125 miles B)225 miles C)520 miles D)425 miles E)525 miles
SOLUTION:During each hour, the car travels 65 miles. For 8 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 + 65 + 65 = 8 × 65 = 520 miles
correct answer is C) 520 miles #### C
QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total?
options: A)16 B)12 C)18 D)22 E)08
SOLUTION:2*6=12.Answer is B. #### B
QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered?
options: A)60% B)28% C)30% D)56% E)73%
SOLUTION:Let C.P. be Rs. 100.
Then, S.P. = Rs. 121.60
Let marked price be Rs. x. Then, 95/100 x = 121.60
x = 12160/95 = Rs. 128
Now, S.P. = Rs. 128, C.P. = Rs. 100
Profit % = 28%.
Answer: B #### B
QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 54 years now, the son's age 8 years back was?
options: A)12yr B)19yr C)14yr D)10yr E)20yr
SOLUTION:Let the son's present age be x years
Then, 54-x = x
x = 27
Son's age 8 years back = 27-8= 19years
Answer is B #### B
QUESTION:In how many different number of ways 9 men and 2 women can sit on a shopa which can accommodate persons?
options: A)A)160 B)B)170 C)C)190 D)D)210 E)E)1663200
SOLUTION:11p7 = 11 x 10 x 9 x 8 x 7 × 6 × 5 = 1663200
Option 'E' #### E
QUESTION:How much interest will $8,000 earn in 9 months at an annual rate of 6%?
options: A)$250 B)$350 C)$360 D)$550 E)$650
SOLUTION:Soln:-
9 months = 3/4 of year;
6% = 6/100=3/50;
$8,000(principal)*3/50(interest rate)*3/4(time)=$360.
ANSWER:C #### C
QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
options: A)1236 B)1345 C)1358 D)1321 E)1365
SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E #### E
QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph
SOLUTION:Speed downstream = 50 + 20 = 70 kmph
Speed upstream = 50 - 20 = 30 kmph
Answer: C #### C
QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
options: A) 5/6*d B) 7/3*d C) 10/3*d D) 7/2*d E) 9/2*d
SOLUTION:Favid has d books;
Jeff has d/3 books;
Paula has 2d books;
Total = d+d/3+2d=10d/3.
Answer: C. #### C
QUESTION:A square with sides of 15 units each. What would be the area of the square. Consider a square as a combination of two right angled triangles.
options: A)100 B)256 C)225 D)81 E)144
SOLUTION:A square can be considered as a set of two right angled triangles joined from the hypotenuse.
Since the sides are 10 units each. The height and base of both the triangles is 10 each.
Area of a right angled triangle is 1/2 * base * height
Area of both the triangles is 2 * 1/2 * base * height. Since both triangles are similar.
= base * height
= 15*15 =225
Ans: C #### C
QUESTION:Working together, Jose and Jane can complete an assigned task in 5 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 15 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose
options: A)26 days B)15 days C)60 days D)65 days E)36 days
SOLUTION:Assume:
Jose does 1 job in x days, so Jose does 1/x job in a day
Jane does 1 job in y days, so Jane does 1/y job in a day
Together, they does (x+y)/xy job in a day. This is equals to 1/20. So
(x+y)/xy = 1/5
5(x+y) = xy
Next, we're told 1 job takes 15 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.
x/2 + y/2 = 15
x+y = 30
So
xy = 150
The answer choices are:
26 days
15 days
60 days
65 days
36 days
From the answer choices, So I'll go for 15 days for Jose and 10 days for Jane.
Answer : B #### B
QUESTION:What should come in place of the question mark (?) in the following equation?
45789+ 34567 = 610+ ?
options: A)96543 B)13678 C)23456 D)56789 E)79746
SOLUTION:45789+ 34567 = 610+ ?
45789+ 34567 – 610 = 79746
Answer E #### E
QUESTION:In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
options: A)3 B)5 C)8 D)13 E)15
SOLUTION:Total # of students = 40
Avg # of books per student = 2
Total # of books = 40*2 = 80
# of student borrowed at least 3 books = 40-2-12-10 = 16
# of books borrowed by above 16 students = 80-(12*1)-(10*2) = 48
Considering that 15 out of above 16 students borrowed only 3 books, # of books borrowed = 15*3 = 45
So maximum # of books borrowed by any single student = 48-45 = 3
option A #### A
QUESTION:A man can row at 4 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
options: A)2.4 km B)2.9 km C)3.4 km D)1.9 km E)5.6 km
SOLUTION:Explanation:
Speed in still water = 4 kmph
Speed of the current = 1 kmph
Speed downstream = (4+1) = 5 kmph
Speed upstream = (4-1) = 3 kmph
Let the required distance be x km
Total time taken = 1 hour
⇒ x/5+x/3=1
⇒3x+5x=15
⇒8x=15
⇒x=1.9 km
Answer: Option D #### D
QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average
options: A)5 B)6 C)7 D)8 E)9
SOLUTION:Let the sequence have N terms starting 18*K
--> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence.
The sum of the sequence is
---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2).
So the average is
153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*).
On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**).
By *), **) we have K=2, N=14.
Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms R which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C. #### C
QUESTION:What is the value of x if (64^2)-(36^2)=20*x?
options: A)120 B)100 C)140 D)130 E)115
SOLUTION:20*x=(64+36)(64-36)
20*x=100*28
x=(100*28)/20
x=5*28
x=140
Option C #### C
QUESTION:Forks, Spoons, and Knives in drawer are in the ratio of 4: 4 : 3. If there are 16 Forks, the number of Knives in the drawer is:
options: A)8 B)4 C)12 D)16 E)14
SOLUTION:Explanation :
Let Forks = 4x, Spoons = 4x & Knives = 3x. Now, 4x = 16 hence x = 4.
Number of Knives = 3x = 12.
Answer : C #### C
QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in
options: A)6 days B)2 days C)3 days D)5 days E)4 days
SOLUTION:That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
C #### C
QUESTION:The cost price of 14 articles is equal to the selling price of 11 articles. Find the profit percent?
options: A)18 2/91% B)18 2/11% C)27 3/11% D)18 2/91% E)12 2/11%
SOLUTION:14 CP = 11 SP
11 --- 2 CP
100 --- ? =>27 3/11%
Answer:C #### C
QUESTION:Find the smallest number which should be multiplied with 520 to make it a perfect square
options: A)337 B)297 C)266 D)116 E)130
SOLUTION:Explanation:
520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5
Required smallest number = 2 * 13 * 5 = 130
130 is the smallest number which should be multiplied with 520 to make it a perfect square.
Answer: E #### E
QUESTION:Sandy can do a job in 12 days and Molly can do the same job in 24 days. If they work together, in how many days will they complete the job?
options: A)6 B)7 C)8 D)9 E)10
SOLUTION:Sandy can do 1/12 of the job each day.
Molly can do 1/24 of the job each day.
The combined rate is 1/12 + 1/24 = 1/8 of the job each day.
The job will take 8 days.
The answer is C. #### C
QUESTION:Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?
options: A)1 B)2 C)4 D)5 E)6
SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) = 5 (x + 8)
2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2.
B #### B
QUESTION:A woman swims downstream 54 km and upstream 6 km taking 6 hours each time, what is the speed of the woman in still water?
options: A)2 B)3 C)4 D)5 E)6
SOLUTION:54 --- 6 DS = 9
? ---- 1
6 ---- 6 US = 1
? ---- 1 M = ?
M = (9 + 1)/2 = 5
Answer:D #### D
QUESTION:Two trains leave the same train station at 6:00 am and 6:45 am and they travel at 100 kph and 125 kph respectively. How many kilometers from the train station will the two trains be together?
options: A)300 B)325 C)350 D)375 E)400
SOLUTION:At 6:45, the first train is 75 km ahead.
The second train gains 25 km each hour.
The time it takes the second train to catch the first train is 75 / 25 = 3 hours.
In this time, the second train travels 3*125=375 km.
The answer is D. #### D
QUESTION:The average of first 13 even numbers is?
options: A)10 B)11 C)12 D)13 E)14
SOLUTION:Sum of 13 even numbers = 13 * 14 = 110
Average = 182/13 = 14
ANSWER:E #### E
QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0
SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B , if you put x = -5, you get -ve value for y co-ordinate.
Answer must be (B) #### B
QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?
options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31
SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 2/7 + 2/5 * 5/7
= 16/35
Answer:A #### A
QUESTION:Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work?
options: A)6 days B)7.2 days C)9.5 days D)12 days E)13 days
SOLUTION:EXPLANATION:
Hint:
A's one day work = 1/12
B's one day work = 1/18
(A + B)'s one day work = 1/12 + 1/18 = (18 + 12)/(12 x 18)= 30/216= 1/7.2
Together, A & B will finish the work in 7.2 days.
ANSWER IS B #### B
QUESTION:The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be social teachers?
options: A)2/3 B)1/12 C)2/9 D)1/2 E)1/24
SOLUTION:Probability of first member an English teacher = 3/9
Probability of second member an English teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (B) #### B
QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is :
options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7
SOLUTION:Explanation:
We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.
Now. .
Answer: B) 3 M^2 #### B
QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
options: A)248 m B)210 m C)277 m D)765 m E)176 m
SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x
= 210 m.
Answer: B #### B
QUESTION:Find the total number of divisors of 1728(including 1 and 1728)
options: A)28 B)29 C)30 D)31 E)32
SOLUTION:1728=2^6*3^3
no. of divisors = (6+1)*(3+1)=28
ANSWER:A #### A
QUESTION:A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
options: A)76 seconds B)18 seconds C)40 seconds D)19 seconds E)44 seconds
SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 410+140 = 550 meter
Time = Distance/speed
= 550 * (2/25)
= 44 seconds
Answer: E #### E
QUESTION:From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond?
options: A)238/5525 B)176/5534 C)253/5523 D)234/5525 E)1/5525
SOLUTION:Solution
Let S be the sample space. Then,
n(S) = 52C3 = 22100
Let E = event of getting 1 face card.
n(E) = number of ways of choosing 1 face card out of 26
=13C1 * 13C2= 13*72 = 936
P(E) = n(E) / n(S) = 936 / 22100 = 234/5525
= 234/5525.
Answer D #### D
QUESTION:There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family
options: A)1 B)2 C)3 D)4 E)5
SOLUTION:Let the number of men be m and so the number of women = 15-m
Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.
Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).
Let the total work be 360 units (LCM of 180 and 120).
1 man does 360/120 = 3 units per day
1 woman does 360/180 = 2 units per day
Based on above facts,
Total work by men + women in these 17 days = 360 units
m*9*3 + (15-m)*6*2 = 360,
27m + 180 -12m = 360, Solving m=12.
Num of men = 12 and number of women = 15-12 = 3
ANSWER:C #### C
QUESTION:If a/b = 6/5, Then (5a + 4b) / (5a - 4b) = ?
options: A)4 B)7 C)5 D)3 E)6
SOLUTION:Answer
Dividing numerator as well as denominator by b, we get
Given Exp. = (5a + 4b) / (5a - 4b) = (5a/b + 4) / (5a/b - 4)
Since a/b = 6/5
this implies that
=[(5*6)/5 +4]/[(5*6)/5 -4)]
= (6 + 4) / (6 - 4)
= 5
Option: C #### C
QUESTION:The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is
options: A)51:53 B)52:53 C)53:54 D)54:55 E)None of these
SOLUTION:Explanation:
Let the Cost price of article is Rs. x
Required ratio = (102% of x) / (106% of x)
=102/106
=51/53 = 51:53.
Answer: A #### A
QUESTION:One train is traveling 72 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
options: A)5:4 B)5:6 C)2:1 D)5:4 E)5:1
SOLUTION:72 * 5/18 = 10
20:10 => 2:1
Answer: C #### C
QUESTION:For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
options: A)Rs. 8000 B)Rs. 9000 C)Rs. 9900 D)Rs. 98900 E)Rs. 10000
SOLUTION:Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E #### E
<<<Examples ends
QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor?
options: A)14 B)16 C)18 D)20 E)22
SOLUTION:d = (D-R)/Q
= (122 - 2)/6
= 122/6 = 20
D) #### D
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively
options: A)19 B)17 C)13 D)9 E)18
SOLUTION:Explanation:
Answer will be HCF of (28-10, 128-2, 147-3)
HCF of (18, 126, 144) = 18
Option E #### E
QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities?
options: A)48 B)72 C)96 D)120 E)192
SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance Q to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E #### E
QUESTION:If “GREEN” is given number code as 49, what is the difference between the number codes of “VIOLET” and “PINK” ?
options: A)55 B)45 C)33 D)60 E)40
SOLUTION:Explanation:
Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
GREEN = 7 + 18 + 5 + 5 + 14 = 49
Thus we get,
VIOLET = 22 +9 +15+12 + 5 + 20 = 83
PINK = 16 + 9 + 14 + 11 = 50
Thus, difference is 83 – 50 = 33.
ANSWER C #### C
QUESTION:If it is true that x > -3 and x < 7, which of the following must be true?
options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above.
SOLUTION:the range is -3 < x < 7
A. x > 3 - no because x can be between -3 < x < 3
B. x < -7 - no because the values of x are always >-7
C. x < 3 - no because x can be between 3 < x < 7
D. -7 < x < 3 - no because x can be between 3 < x < 7
E. none of the above.
Answer: E #### E
QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more
men joined them. How many days will they take to complete the remaining work?
options: A)3days B)4days C)2days D)8days E)5days
SOLUTION:1 man's 1 day work = 1/108
12 men's 6 days work = 6/9 = 2/3
remaining work = 1 – 2/3 = 1/3
18 men's 1 days work = 18/108 = 1/6
1/6 work is done by them in 1 day
therefore, 1/3 work is done by them in 6/3 = 2 days.
ANSWER C 2days #### C
QUESTION:Three coins are tossed. Find the probability of at least 1 head and 1 tail ?
options: A)1/2 B)1/4 C)3/4 D)7/8 E)1/8
SOLUTION:n(s) = 2^3 = 8 ....(3 coins tossed)
let E is the event of getting at least 1 head and 1 tail
n(E) = TTH , HTT, THT, HHT, HTH, THH = 6
P(E) = n(E) / n(s)
= 6/8
= 3/4
Ans- C #### C
QUESTION:Car A runs at the speed of 60 km/hr and reaches its destination in 8 hours. Car B runs at the speed of 70 km/h and reaches its destination in 4 hours. What is the ratio of distances covered by Car A and Car B?
options: A)3 : 7 B)4 : 9 C)12 : 7 D)5 : 7 E)6 : 11
SOLUTION:Car A travels 60 × 8 = 480 km
Car B travels 70 × 4 = 280 km
The ratio is 480 : 280 = 48 : 28 = 12 : 7
The answer is C. #### C
QUESTION:850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
options: A)a) 162 B)b) 138 C)c) 60 D)d) 17 E)e) 12
SOLUTION:Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 850 = 17
Answer: D #### D
QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce
options: A)100 B)65 C)25 D)11 E)18
SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 10
So, x = 10.
Hence 6x = 6*10 = 60 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/60
= 18
Hence option (E). #### E
QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2
SOLUTION:42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer: C #### C
QUESTION:Mary's income is 70 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?
options: A) 124% B) 102% C) 96% D) 80% E) 64%
SOLUTION:Juan's income = 100 (assume);
Tim's income = 60 (40 percent less than Juan's income);
Mary's income = 102 (70 percent more than Tim's income).
Thus, Mary's income (102) is 102% of Juan's income (100).
Answer: B. #### B
QUESTION:A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders R when the order of the divisors is reversed.
options: A)8,5,3 B)R=4,2,1 C)R=3,2,1 D)R=6,4,2 E)None of above
SOLUTION:My approach would be
Three Divisors : 3, 5, 8
Three Remain: 1, 4, 7
Start from the bottom of the last column i.e. from the third remainder:
Go up diagonally and multiply by the second divisor: 5*7 = 35
Go down and add the second remainder: 35 + 4 = 39
Go up diagonally and multiply by the first divisor: 39* 3 = 117
Go down and add the first remainder: 117 + 1 = 118
Divide 118 by 8, 5, 3
118/8 gives quotient = 14 and remainder = 6
14/5 gives quotient = 2 and remainder = 4
2/3 gives quotient = 0 and remainder = 2
Ans is D i.e. 6,4,2 #### D
QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549
SOLUTION:A+B+C = 2600
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 2600 = Rs.1200
Answer: A #### A
QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?
options: A)4 B)5 C)6 D)9 E)7
SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even.
1) 2(6 times)
2) 2(3 times) + 3(2 times)
3) 2(2 times) + 3 + 5
4) 2 + 3 + 7
5) 2 + 5 + 5
6) 3(4 times)
7) 5 + 7
Answer: E #### E
QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is
options: A)10% B)50% C)25% D)52% E)None of these
SOLUTION:Explanation:
cost price = (225 + 15) = 240 sell price = 300
gain = (60/240)*100 = 25%. Answer: C #### C
QUESTION:If the price of sugar rises from Rs. 3 per kg to Rs. 5 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
options: A)15% B)20% C)25% D)30% E)40%
SOLUTION:Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 3 = x × 5 = x = 60 kg.
∴ Reduction in consumption = 40%.
Answer E #### E
QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered?
options: A)60% B)28% C)30% D)56% E)73%
SOLUTION:Let C.P. be Rs. 100.
Then, S.P. = Rs. 121.60
Let marked price be Rs. x. Then, 95/100 x = 121.60
x = 12160/95 = Rs. 128
Now, S.P. = Rs. 128, C.P. = Rs. 100
Profit % = 28%.
Answer: B #### B
QUESTION:A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
options: A)30.98%loss B)20.98%loss C)20.97%loss D)20.68%loss E)20.98%loss
SOLUTION:81 ---- 17
100 ----- ? è
20.98%loss
Answer: B #### B
QUESTION:If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x?
options: A)x - 8 B)x - 5 C)x - 2 D)x + 2 E)x + 6
SOLUTION:Answer: A
4^(x-4) = 4^(y+4)
Since the base is the same, I isolated the equations and solved for y.
x-4 = y+4
y=x-8 #### A
QUESTION:In how many ways can the integer 120 be expressed as a product of two different positive integers?
options: A)10 B)8 C)5 D)4 E)2
SOLUTION:120=(2^3)*3*5
Since 120 is not a perfect square, no of ways=5
Answer C #### C
QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is
options: A)91 B)910 C)61 D)1911 E)None
SOLUTION:olution
Required number of students.
= H.C.F of 671 and 610.
‹=› 61.
Answer C #### C
QUESTION:There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen?
options: A)2 B)3 C)14 D)16 E)20
SOLUTION:60% of 30 = 18.
So, there are 18 red socks and there are 12 blue socks.
Check out this possible cases once we have selected TWO socks:
case a: 2 red socks, in which case we have a pair of matching socks. DONE!
case b: 2 blue socks, in which case we have a pair of matching socks. DONE!
case c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet.
Since the first 2 cases result in a pair of matching socks, let's focus on case 3 and what happens when we select a 3rd sock.
If we have 1 red sock and 1 blue sock, then the next sock we select will EITHER match the red sock OR match the blue sock.
In both cases, we are guaranteed to have a pair of matching socks.
So, selecting 3 socks guarantees that we have a pair of matching socks.
ANSWER:B #### B
QUESTION:Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
options: A)229 B)270 C)877 D)266 E)281
SOLUTION:Let xx be the total number of pages in the book, then she finished 23⋅x23⋅x pages.
Then she has x−23⋅x=13⋅xx−23⋅x=13⋅x pages left.
23⋅x−13⋅x=9023⋅x−13⋅x=90
13⋅x=9013⋅x=90
x=270x=270
So the book is 270 pages long.
Answer:B #### B
QUESTION:12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
options: A)990 B)495 C)1980 D)none E)Cannot be determined
SOLUTION:Explanation :
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals.
Answer : B #### B
QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3
SOLUTION:distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr
Answer is B. #### B
QUESTION:If one of the followings is the product of the two 3-digit integers 8K5 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be
options: A) 478,823 B) 511,913 C) 531,875 D) 538,424 E) 569,114
SOLUTION:To know the unit digit you can multiply both digit number: 5 x 5 = 25
This eliminates A, B, D, and E, because the number must end with a 5
So the answer is C #### C
QUESTION:Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get?
options: A)57% B)57.3% C)65% D)90% E)80%
SOLUTION:total votes are 20280 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*11620/20280 = 57.3%
ANSWER:B #### B
QUESTION:Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly?
options: A)$645.56 B)$824.32 C)$954.26 D)$2472.96 E)$1020.45
SOLUTION:Principle = $10000
Rate = 2% half yearly = 4 half years
Amount = 30000*(1 + 2/100)^4 = 30000 * 51/50 * 51/50 * 51/50 * 51/50
= $32472.96
C.I. = 32472.96-10000 = $2472.96
Answer is D #### D
QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was
options: A)162 B)108 C)96 D)54 E)None
SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively;
Total students = 2x+3x+4x = 9x.
According to the question,
(2x+12)/(3x+12) = 8/11
24x+96 = 22x+132
Or, 2x = 132-96
Or, x = 36/2 = 18
Hence, Original number of students,
9x = 9*18 = 162.
Answer: Option A #### A
QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
options: A)2388 B)2380 C)2888 D)2663 E)2922
SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer: B #### B
QUESTION:With out any halt a train travels a certain distance with an average speed of 66 km ph , and with halts it covers the same distance at an average speed of 33 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
options: A)48 min. B)12min. C)60min. D)18min. E)19min.
SOLUTION:With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 66/33= 2/1 = 120 minutes
:. 60 minutes is the halting time per hour
ANSWER:C #### C
QUESTION:What is the remainder when 1274 * 1275 * 1277 *1285 is divided by 12?
options: A) 0 B) 6 C) 11 D) 9 E) 7
SOLUTION:1271*1275*1277*1285 = (1272 - 2)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-2)(3)(-7)(1) = 42. Thus the question becomes: what is the remainder upon division of 42 by 12? The answer to this question is 6.
Answer: B #### B
QUESTION:If a man buys 10 lollipops for $90 and sold them for $6 dollars determine his loss.
options: A)50 B)60 C)70 D)20 E)90
SOLUTION:Cost of 10 lollipops = $80
Sold each lollipop for $6
So he sold 10 lollipops for $(10 × 6) = $60
Loss = $(80 – 60) = $20
answer :D
Therefore, loss = $ 20. #### D
QUESTION:Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?
options: A)30 B)36 C)70 D)80 E)150
SOLUTION:Method I: the rates solution
“Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Rane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is
R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12
That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:
T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36
BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Rane and Zane need 36 weeks to make 15 drums.
Answer = B. #### B
QUESTION:On increasing the price of T.V. sets by 40%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
options: A)4 B)5 C)56 D)12 E)7
SOLUTION:Explanation:
Let the price be = Rs.100, and number of units sold = 100
Then, sale value = Rs.(100 × 100) = Rs.10000
New sale value = Rs.(140 × 80) = Rs.11200
Increase% = 1200/10000 × 100 = 12%
Answer: D #### D
QUESTION:A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is :
options: A)16000 B)18000 C)20000 D)30000 E)None of these
SOLUTION:Explanation:
Number of bricks =Courtyard area /1 brick area
=(1800×1200 /12×6)=30000
Option D #### D
QUESTION:In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is :
options: A)12 B)11 C)10 D)27 E)22
SOLUTION:Explanation:
Total employees = \inline \frac{(25-10)\times 20}{10}=30
Hence number of educated employees = 30-20 = 10
Answer: C) 10 #### C
QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min
SOLUTION:A
20 hours 30 min
1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours #### A
QUESTION:A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
options: A)60 km/hr B)50 km/hr C)36 km/hr D)26 km/hr E)87 km/hr
SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 15 = 45 => x = 60 km/hr.
Answer:A #### A
QUESTION:A club wants to mix 15 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
options: A)20 B)30 C)40 D)50 E)60
SOLUTION:Let number of pounds of 5$ candy to be used be w
6 = (15*8 + 5*w)/(15 +w)
=>90 + 6w = 120 + 5w
=> w = 30
Answer B #### B
QUESTION:Two coins are tossed, find the probability that two Tails are obtained
options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3
SOLUTION:The sample space S is given by.
S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two heads are obtained".
E = {(T,T)}
P(E) = n(E) / n(S) = 1/4
B #### B
QUESTION:A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
options: A)1/5 B)2/7 C)2/9 D)3/5 E)4/11
SOLUTION:The total number of ways to choose 2 apples is 7C2 = 21
The number of ways that include the spoiled apple is 6C1 = 6
P(the spoiled apple is included) = 6/21 = 2/7
The answer is B. #### B
QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
options: A)29997 B)28088 C)13500 D)19000 E)2799
SOLUTION:Money paid in cash = Rs. 1500
Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C
QUESTION:Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y?
options: A)15.5 sec B)8.4 sec C)33.6 sec D)31.11 sec E)16.8 sec
SOLUTION:Z--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D #### D
QUESTION:If you add all the numbers on your mobile phone , what is the answer?
options: A)45 B)50 C)55 D)100 E)60
SOLUTION:0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are in your mobile phone.
Therefore 0+1+2+3+4+5+6+7+8+9=45
Answer is A #### A
QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 14 years?
options: A)30 B)34 C)40 D)50 E)60
SOLUTION:Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 14 years = (20 + 14) years =34 years.
Answer : B #### B
QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
options: A)Rs.6620 B)3378 C)2768 D)2999 E)2771
SOLUTION:A = 20000(11/10) 3
= 26620
= 20000
----------
6620
Answer: A #### A
QUESTION:33 1/3% OF 330?
options: A)80 B)90 C)110 D)120 E)130
SOLUTION:33 1/3 % = 1/3
1/3 × 330 = 110
C) #### C
QUESTION:If the sum of the interior angles of a regular polygon measures up to 1440 degrees, then how many sides does the polygon have?
options: A)10 B)16 C)12 D)11 E)14
SOLUTION:one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1440
180n - 360 = 1440
180n = 1800
n = 1800/180 = 10
ANSWER:A #### A
QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
options: A)288 B)165 C)881 D)1277 E)121
SOLUTION:Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 25 = 375 m.
Let the length of the platform be x m . Then,
(x + 375)/36 = 15 => x = 165 m.
Answer: B #### B
QUESTION:Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
options: A)50 B)88 C)77 D)55 E)23
SOLUTION:Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A #### A
QUESTION:If ratio of profit of A and B is 4:5 and they together invested Rs.90,000 then money invested by B is
options: A)Rs.48,000 B)Rs.45,000 C)Rs.30,000 D)Rs.50,000 E)None of the above
SOLUTION:investment by B=(5*90000)/(4+5)
=50000
ANSWER:D #### D
QUESTION:Two pipes can fill a tank in 10 hours & 12 hours respectively. While 3rd pipe empties the full tank n 20 hours. If all the three pipes operate simultaneously,in how much time will the tank be filled?
options: A)6 hrs 43 min B)2 hrs 25 min C)7 hrs 30 min D)6 hrs 32 min E)7 hrs 10 min
SOLUTION:tank filled in 1 hr = 1/10 + 1/12 - 1/20 = 8/60 = 2/15 part
so full tank is filled in 15/2 hrs = 7 hr 30 min..
ANSWER:C #### C
QUESTION:N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N?
options: A)3/2 B)5/3 C)1+1/3 D)1 1/2 E)1 1/3
SOLUTION:N is such that when multiplied by 0.75 gives 1" is written mathematically as
N * 0.75 = 1
Solve for N
N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3
correct answer C #### C
QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents?
options: A)24 B)18 C)32 D)16 E)20
SOLUTION:0.10(x)+0.35(20-x)=2.5
0.10x+7-0.35x=2.5
so x=18
ans is B #### B
QUESTION:In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater?
options: A)600 B)640 C)680 D)720 E)760
SOLUTION:The number of seats in the theater is
15 + (15+2) + ...+ (15+38)=
20(15) + 2(1+2+...+19)=
20(15) + 2(19)(20)/2=
20(15+19) = 20(34) = 680
The answer is C. #### C
QUESTION:A password for a computer uses three digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
options: A)1/32 B)1/16 C)1/8 D)2/5 E)1/2
SOLUTION:To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 = 1,000 possible combinations.
Prime numbers constitute 2, 3 In addition to zero, this is 3 total possibility for each digit. So the number of satisfactory variants is 3× 3 × 3 . So the probability is 1/2 × 1/2 × 1/2 = 1/8.
The right answer is choice (C). #### C
QUESTION:In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?
options: A)17 B)18 C)56 D)21 E)23
SOLUTION:8p2 = 8 x 7 = 56
Answer: C #### C
QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
options: A)80% B)105% C)88% D)124.2% E)138%
SOLUTION:x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,11 = 11/100
x= 80*11/100
x= 8.8
8.8/10 = 0.88 = 88%, Answer C #### C
QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction?
options: A)5hours B)40hours C)8hours D)20hours E)30hours
SOLUTION:To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 40 =20 hours
Answer is D #### D
QUESTION:How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/57 ?
options: A)6 B)3 C)2 D)1 E)5
SOLUTION:There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.
So, we start with
a=1, we get b as -ve. out
a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)
a=3, we get b as 3. Yes (Now we have 3 possible solutions)
a=4, we get b as fraction. Out
a=5, we get b again as some fraction. Out
a=6 already taken.
We have A,B options left. C,D,E are out.
A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.
When a=b, we have only 1 solution = 5. So, one more solution, where a=b is not possible.
So, answer will be E. #### E
QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase?
options: A)80% B)90% C)70% D)60% E)50%
SOLUTION:Ans. Let previous income = Rs. 100
Previous savings = 10% of Rs. 100 = Rs. 10
Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120
Increased savings = 15% of Rs. 120 = Rs. 18
Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8
Therefore, Percent increase in savings = 8/10 x 100 = 80%
Answer A #### A
QUESTION:A part of certain sum of money is invested at 16% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
options: A)5:4 B)1:4 C)3:1 D)3:5 E)3:4
SOLUTION:12:16
= 3:4
ANSWER:E #### E
QUESTION:After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
options: A)Rs.2989 B)Rs.5029 C)Rs.5000 D)Rs.5197 E)Rs.5029
SOLUTION:Given SP = Rs. 6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15)
= Rs. 8000
If SP = Rs. 8000, profit
60%
CP = [SP(100)]/(100 + 60)
= (8000 * 100)/160
= Rs.5000
Answer: C #### C
<<<Examples ends
QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?
options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3%
SOLUTION:Let the price of the article be Rs. 100.
20% of 100 = 20.
New price
= 100 + 20 = Rs. 120
Required percentage
= (120 - 100)/120 * 100
= 20/120 * 100
= 50/3
= 16 2/3%.
Answer:A #### A
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?
options: A)1/18 B)64/4032 C)63/64 D)1/9 E)1/4
SOLUTION:Explanation :
No of ways of selecting two squares from 64 squares on the chess board is 64C2.
Three cases arise:
case 1: when first square is any of the four corner ones
In this case second square can be chosen in 2 ways
no of ways of selecting two squares: 4*2 = 8
case2: when first square is any of the 24 squares on the side of the chess board other than the corner ones
the second square can be chosen in 3 ways
no of ways of selecting two squares: 24*3 = 72
case 3: the first square is any of the 36 remaining squares
the second square can be chosen in 4 ways
no of ways of selecting two squares: 36*4 = 144
Total no of ways of selecting two adjacent squares = 8 + 72 + 144 = 224
So required probability = 224/64C2 = 224/4032 = 1/18
Answer : A #### A
QUESTION:If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2?
options: A)1 B)3 C)5 D)6 E)14
SOLUTION:For unit digit of a^2 to be 9...unit digit of a has to be 3 or 7...
Now for unit digit of (a+1)^2 to be 4..unit digit of a has to be 1 or 7....
From the above two conditions, unit value of a has to be 7, which will satisfy both the conditions...
Now id unit digit of a is 7, unit digit of (a+2)^2 hast to be 1.
ANSWER:A #### A
QUESTION:(a/2)/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression?
options: A)8/2 B)2/4 C)1/8 D)2/4 E)4/6
SOLUTION:(a/2)/(b/c)
= (a*c)/2b
The expression will have the largest value when numerator (a*c) is the largest.
= (2*4)/2*1
=8/2
Answer A #### A
QUESTION:If E is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of E?
options: A)10 B)12 C)14 D)16 E)18
SOLUTION:E = 30!
8
E = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3
3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3
So we have a total of 14 three's ...
Therefore the maximum value of K can be 14 (C) #### C
QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years?
options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 %
SOLUTION:Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11)
= 100/11 = 9.09 %
ANSWER:A #### A
QUESTION:If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1?
options: A)a. 8 B)b. 9 C)c. 12 D)d. 7 E)e. 27
SOLUTION:Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30
We can write 30 as product of two numbers in following ways
1*30
2*15
3*10
5*6
4 cases = 4*2 i.e. 8 factors (including 1)
Factors greater than 1 = 7
Answer: Option D #### D
QUESTION:Consider two statements
Statement 1 => If R is an integer and R=2p+1 where p is not an integer.
Statement 2 => If S is an integer and S=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of R and S respectively
options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined
SOLUTION:answer will be E
R = integer
R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even R would odd
if n odd R would be even
ANSWER IS E #### E
QUESTION:A person spent Rs. 5,040 from his salary on food and 5,000 on house rent. After that he was left with 20% of his monthly salary. What is his monthly salary ?
options: A)22,550 B)32,550 C)52,550 D)62,550 E)12,550
SOLUTION:Total money spent on food and house rent = 5,040+5,000 = 10,040
Which is 100 - 20 = 80% of his monthly salary
∴ His salary = 10040x100/80 = 12550
Answer : E #### E
QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -.
options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7
SOLUTION:3!4! Required probability = 3!4!/6! = 1/5
ANSWER A #### A
QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
options: A)255 B)267 C)225 D)277 E)211
SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m. Answer:C #### C
QUESTION:If n = 2.0254 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n?
options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0046 E) 0.0153
SOLUTION:n*=2.03
n*-n=2.03-2.0254
0.0046
Answer: D #### D
QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
options: A)6 B)9 C)36 D)120 E)144
SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways
Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places
Second Place, Physics Book - in 4 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.
Total no of ways = 4*3*3*2*2*1*1 = 144 ways
E #### E
QUESTION:Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged?
options: A)6 B)48 C)36 D)24 E)12
SOLUTION:Dhoni have to sit at either of the ends.
If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24
David can also sit on the other end, then another 4! ways we can arrange.
So total number of ways = 24+24 = 48
Answer : B #### B
QUESTION:Four person are chosen at random form a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is:
options: A)10/21 B)20/22 C)32/45 D)13/98 E)43/21
SOLUTION:Number of ways of choosing 4 persons out of 9
=9c4
=126
No.of ways of choosing 2 children out of 4 and 2 persons out of (3+2)= (4c2+5c2)
=60
P(E)=60/126
=10/21
ANSWER A #### A
QUESTION:A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere
interest rate is increased by 8%, it would amount to bow mucb ?
options: A)Rs 990 B)Rs 995 C)Rs 997 D)Rs 992 E)Rs 999
SOLUTION:S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _
. R = ((100 x 120)/(800*3) ) % = 5%.
New rate = (5 + 3)% = 8%.
New S.l. = Rs. (800*8*3)/100 = Rs. 192.
:. New amount = Rs.(800+192) = Rs. 992
Answer is D. #### D
QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 36 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
options: A)10 sec B)16 sec C)19 sec D)7.2 sec E)13 sec
SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18
T = 36
D = 36 * 100/18 = 200
RS = 60 + 40 = 100 * 5/18
T = 200 * 18/500 = 7.2 sec
Answer: D #### D
QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?
options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150
SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15.
Hence, the probability that at least one light bulb fails is 1-0.94^15.
Answer: A.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A
QUESTION:Computer completes the first iteration in 10 seconds and then the following iterations are completed in 7 seconds as constants are already loaded. What is the maximum number of completed iterations under 5 minutes?
options: A)41 B)42 C)43 D)44 E)45
SOLUTION:b must be an integer as it is the number of completed iterations at a rate of 7sec/iteration
10 + 7b =5*60
7b = 290
b= 41
The total number of iterations --> 41+1 = 42 and
43rd iteration will be completed at 304seconds which is above 5 minutes
ANSWER: B #### B
QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
options: A)1/48 B)1/42 C)1/40 D)1/41 E)1/43
SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer: B #### B
QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
options: A)0 B)1 C)2 D)3 E)4
SOLUTION:First, reach to the point of getting the equation W: x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D
QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23?
options: A)4 B)3 C)2 D)1 E)0
SOLUTION:Explanation :
1056 ÷ 23 = 45 with remainder = 21
Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be
divisible by 23. Answer : Option C #### C
QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
options: A)69 B)78 C)96 D)56 E)48
SOLUTION:let the digits be x,y
x + y = 15
x - y = 3
2x = 18, x = 9 so y = 6
hence the number is 96
so the correct answer is option C) 96. #### C
QUESTION:What is the sum of all the multiples of 10 between 0 and 75?
options: A)500 B)620 C)450 D)340 E)280
SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280.
Final Answer:
E #### E
QUESTION:What is the rate percent when the simple interest on Rs.1600 amount to Rs.200 in 4 Years?
options: A)4% B)3.125% C)5% D)6% E)7%
SOLUTION:Interest for 1 year = 200/4 = 50
Interest on Rs 1600 p/a = 50
interest rate = 50/1600*100 = 3.125%
Answer : B #### B
QUESTION:One boy forgot the last digit of a 7 digit no. If he randomly dialthe final 3 digits aftercorrectly dialing the 1st 4, then what is the chance of dialing the correct no.?
options: A)1/890 B)2/465 C)1/1000 D)1/3453 E)2/1454
SOLUTION:it is given that last 3 digits are randomly dialed
Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability
= 1/(10)3 = 1/1000
C #### C
QUESTION:By how much is 50% of 250 greater than 25% of 400.
options: A)25 B)26 C)29 D)39 E)26
SOLUTION:(50/100) * 250 – (25/100) * 400
125 - 100 = 25
Answer:B #### B
QUESTION:A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price
options: A)Rs.450/- B)Rs.451/- C)Rs.440/- D)Rs.455/- E)Rs.445/-
SOLUTION:Loss = 500*10/100 = 50
S.P = C.P - Loss
= 500- 50
=Rs.450/-
Answer : A #### A
QUESTION:Two water pumps, working simultaneously at their respective constant rates, took exactly six hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
options: A)8 B)10 C)12 D)14 E)16
SOLUTION:Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump.
Both pumps together can fill 1/6 of the pool each hour.
2.5x = 1/6
x = 1/15
1.5x = 1.5/15 = 1/10
The faster pump could fill the pool in 10 hours.
The answer is B. #### B
QUESTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
options: A)2443200 B)3643200 C)5443200 D)1443200 E)2163200
SOLUTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216
Choosing the digit for p - 9 ways;
Choosing the digit for q - 8 ways;
Choosing the digit for r - 7ways;
Choosing the digit for s - 6ways;
Choosing the digit for t - 5ways;
# of permutations of 3 digits in ppqrst - 6!/2!
Total: 9*8*7*6*5*6!/2!=5443200.
Answer: C. #### C
QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
options: A)165 B)771 C)245 D)177 E)121
SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C #### C
QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses?
options: A)5 B)7 C)8 D)10 E)11
SOLUTION:Q=7 is the correct answer.
Good solution Buneul.B #### B
QUESTION:Arjun started a business with Rs. 40,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally?
options: A)3 B)4 C)5 D)6 E)7
SOLUTION:Suppose Anoop joined after 3 months.
Then, 40000 * 12 = 80000 * (12 – x)
=> x = 6.
ANSWER:D #### D
QUESTION:$500 will become $1000 in 6 years find the rate of interest?
options: A)A)16.67% B)B)20% C)C)25% D)D)30% E)E)50%
SOLUTION:SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*6 =16.67%
Answer is A #### A
QUESTION:On flipping 3 coins together what is the outcomes for exactly one head and one tail?
options: A){HHH, HTH, THH, TTH, THT, HTT} B){HHT, HTH, THH, TTH, THT, TTT} C){HHT, HTH, THH, TTH, THT, HTT} D){HHT, HTH, THH, TTH, THT, TTT} E)None
SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for one head and one tail and favorable outcomes for more than one head and one tail.
= {HHT, HTH, THH, TTH, THT, HTT}
C #### C
QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
options: A)1/45 B)1/42 C)1/46 D)1/48 E)1/43
SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer:B #### B
QUESTION:Each of the positive integers a and c is a four-digit integer. If each of the digits 0 through 9 appears in one of these three integers, what is the maximum possible value of the sum of a and c?
options: A)18695 B)18325 C)18365 D)18395 E)18485
SOLUTION:According to the stem we should use the digits 0 through 9 to construct 2 four-digit integers, so that their sum is as big as possible.
To maximize the sum, maximize the thousands digits of a and c, so make them 9 and 8.
Next, maximize hundreds digits. Make them 7 and 6 .
Next maximize 10's digit place by 5 and 4
Use the remaining digits (3,and 2) for units digits.
So, a would be 9753,and c would be 8642.
9753 + 8642 = 18395
Answer: D. #### D
QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840
SOLUTION:11+6=17%, therefore 17/100*6000= 1020, now add 1020 + 580= 1600. (B) #### B
QUESTION:If ty > 0 and yz < 0, which of the following must be negative:
options: A)tyz B)ty(z^2) C)t(y^2)z D)t(y^2)(z^2) E)(x^2)(y^2)(z^2)
SOLUTION:ty > 0 means that ty is positive.
yz < 0 means that yz is negative.
t(y^2)z = (ty)(yz) = positive*negative = negative. Thus option C is always negative. #### C
QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
options: A)37 B)85 C)48 D)43 E)84
SOLUTION:Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer: Option C #### C
QUESTION:There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted?
options: A)6 B)7 C)8 D)2 E)9
SOLUTION:Let xx be the number of roses. Then the number of birches is 24−x24−x, and the number of boys is 3×(24−x)3×(24−x). If each girl planted 3 roses, there are x3x3 girls in the class.
We know that there are 24 students in the class. Therefore x3+3(24−x)=24x3+3(24−x)=24
x+9(24−x)=3⋅24x+9(24−x)=3⋅24
x+216−9x=72x+216−9x=72
216−72=8x216−72=8x
1448=x1448=x
x=18x=18
So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches.
Answer:A #### A
QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy
SOLUTION:Payment of a week for 2 days a week = $2x
Payment of 4 weeks for 2 days a week = $2x*4 = $8x
Payment of a week for y days overtime a week = $3x+$2xy
Payment of 3 weeks for y days overtime a week = ($3x+$2xy)*3
Total Earnings = $8x + ($3x+$2xy)*3 = 17x+6xy
Answer: option E #### E
QUESTION:On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1?
options: A) 8 B) 12 C) 24 D) 32 E) 36
SOLUTION:Jan 1 = C
Feb 1 = C - 3
March 1 = C - 6
April 1 = C - 9
May 1 = C - 12
June 1 = C - 15
July 1 = C - 18
Aug 1 = C - 21
Sept 1 = C - 24
Difference between stock on September 1 than were in stock on January 1 will be -
C - ( C - 24 )= 24
Hence answer will be (C) #### C
QUESTION:How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
options: A)1875 B)2000 C)2375 D)2500 E)3875
SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375
ANSWER:C #### C
QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
options: A)49% B)90% C)60% D)40% E)41%
SOLUTION:8 = (1*20*R)/100
R = 40%
Answer:D #### D
QUESTION:A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass?
options: A)6 B)8 C)10 D)12 E)16
SOLUTION:1)If the two sides are co-prime, SUM of sides -1..
2)and if not co-prime , Sum of sides - HCF of sides..
the difference is related to the diagonal passing through a vertex of squares at some place..
here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12
ANSWER:D #### D
QUESTION:A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:
options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these
SOLUTION:Explanation:
For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3
For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10.
Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15.
Answer: C #### C
QUESTION:Express a speed of 90 kmph in meters per second?
options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps
SOLUTION:90 * 5/18
= 25 mps
Answer:E #### E
QUESTION:if 8^25 divided by 7 then what is reminder
options: A)25 B)1 C)0 D)2 E)3
SOLUTION:8^25/7
8 can be written as 7*1+1
(7*1+1)^25/7
(ax+1)^n/a always gives the remainder 1
here a=7,x=1,n=25
Hence remainder is 1
ANSWER:B #### B
QUESTION:One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
options: A)180 min B)160 min C)280 min D)18 min E)190 min
SOLUTION:Let the slower pipe alone can fill the tank in x minutes
Then the faster pipe can fill the tank in x/4 minutes
Part filled by the slower pipe in 1 minute = 1/x
Part filled by the faster pipe in 1 minute = 4/x
Part filled by both the pipes in 1 minute = (1/x)+(4/x)
Answer is A
It is given that both the pipes together can fill the tank in 36 minutes
⇒ Part filled by both the pipes in 1 minute = 1/36
(1/x)+(4/x)=1/36
5/x=1/36
x=5×36=180
i.e.,the slower pipe alone fill the tank in 180 minutes #### A
QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2
SOLUTION:42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer: C #### C
QUESTION:Deepak can read x pages in 10 minutes. At this rate, how long will it take him to read y pages?
options: A)(12/x)*y B)(5/x)*y C)(10/x)*y D)(10x)*y E)(13/x)*y
SOLUTION:x page in 10 mins
i.e. 1 page in 10/x mins
i.e. y pages in (10/x)*y
Answer: option C #### C
QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1
SOLUTION:Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer:A #### A
QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 90 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?
options: A)46 B)42 C)56 D)32 E)40
SOLUTION:I'm going in on this one.
So let's say that we have the following
So we know that L1 = 90 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 90 = 110. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 60 = 40.
Thus E is the correct answer choice #### E
QUESTION:If 144/0.144 = 14.4/x, then the value of x is:
options: A)0.144 B)1.44 C)0.0144 D)0.014 E)0.00144
SOLUTION:=144/0.144 = 14.4/x
=144 x 1000/144
=14.4/x
=x = 14.4/1000
= 0.0144
Answer is C. #### C
QUESTION:Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 5, what is the probability that it is an even number?
options: A)1/2 B)2/5 C)3/5 D)2/7 E)3/10
SOLUTION:There are 5 numbers higher than 5 and 3 of them are even.
The probability is 3/5.
The answer is C. #### C
QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5
SOLUTION:We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.
# of different approximations are possible.
Approach #1:
2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);
2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107
Answer: C.
Approach #2:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107.
Answer: C. #### C
QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
options: A)4% B)8% C)4.2% D)4.8% E)5%
SOLUTION:Let's say there is a TOTAL of100students at this college.
60 percent of the total number of students are freshmen.
# of freshmen = 60% of 100 =60
40 percent of the fresh-men are enrolled in the school of liberal arts...
Number of liberal arts freshmen = 40% of 60 =24
...and, of these, 20 percent are psychology majors...
Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8
What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
4.8/100= 4.8%
Answer:D #### D
QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make?
options: A)30% B)75% C)40% D)70% E)None of these
SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150
Profit(%) = (31150 - 17800)/17800* 100 = 75%
ANSWER:B #### B
QUESTION:A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
options: A)270 B)360 C)480 D)600 E)400
SOLUTION:as given 3 out of every 4 bruised apple is not fit to sell
or, 75% of the bruised apples are not fit to sell.
as per the question 12 are not fit to sell
or,
0.75x=12
x=1200/75=16
thus total number of bruised apples =16
total number of apples =25*16=400
Answer: E #### E
QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire?
options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters
SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 120,000 m : C is the circumference
C = 5 meters
correct answer C #### C
QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
options: A)2:3:9 B)24:25:36 C)7:6:10 D)12 : 15 : 16 E)None of these
SOLUTION:Explanation:
Aman : Rakhi : Sagar =(70000×36)=(70000×36) :(105000×30):(105000×30) :(140000×24):(140000×24)
=12:15:16=12:15:16.
ANSWER IS D #### D
QUESTION:A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road?
options: A)576 metres B)589 metres C)600 metres D)700 metres E)None
SOLUTION:Solution
Let the length of the outer edges be x metres.
Then, length of the inner edge = ( x - 6)m.
∴ x2 - (x-6)2 = 1764
‹=› x2-(x2-12x+36)= 1764
‹=›12x = 1800
‹=›x = 150.
∴ Required perimeter = (4x)m
‹=› (4 x 150)m = 600m.
Answer C #### C
QUESTION:38 69 22 43 31 47 13 82
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?
options: A)56 B)69 C)70 D)71 E)73
SOLUTION:Arrange the numbers in ascending order:
13, 22, 31, 38, 43, 47, 69, 82 (Just cross check the count to ensure that you didn't miss anything)
How many numbers do we see?
8, alright.
What's (1/4)8?
2.
What's (3/4)8?
6.
We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.
13, 22, 31, 38, 43, 47, 69, 82
13, 22, 31, 38, 43, 47: Find a number greater than any of these numbers.
69, 82: Find a number smaller than any of these numbers.
Only 56 fits the description.
Ans:A #### A
QUESTION:A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
options: A)287 B)27 C)28 D)25 E)28
SOLUTION:[50/x + 50/(x/2)] – 100/x = 2
x = 25
Answer: D #### D
<<<Examples ends
QUESTION:The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n?
options: A)w– 2n B)w–n + 1 C)w– 2(n– 1) D)n– 6 + w E)w – n/2
SOLUTION:Another method would be to use the concept of Arithmetic Progressions. Consecutive even integers form an AP where the common difference is 2.
In an AP, Last term = First term + (n-1)*common difference
w = First term + (n-1)*2
First term = w - 2(n-1)
ANSWER:C #### C
|
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer.
Examples starts>>>
QUESTION:A single discount equivalent to the discount series of 20%, 15% and 8% is?
options: A)37.4 B)31.8 C)31.6 D)31.3 E)31.1
SOLUTION:100*(80/100)*(85/100)*(92/100)
= 62.6
100 - 62.6 = 37.4
Answer:A #### A
QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
options: A)16cm B)18cm C)24cm D)Data inadequate E)None of these
SOLUTION:Explanation:
2(l+b)/b=5/1
2l + 2b = 5b
3b = 2l
b = 2/3 l
Then, Area = 216 cm2
l x b = 216
l x (2/3)l = 216
l2 = 324.
l = 18 cm.
Answer: B #### B
QUESTION:5 - [5 - {5 - 5(5 + 5)}] = ?
options: A)5 B)-45 C)45 D)50 E)60
SOLUTION:Explanation:
=> ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)]
= 5 - (50) = - 45
Answer: Option B #### B
QUESTION:A man is 30 years older than his son. In four years, his age will be twice the age of his son. The present age of this son is
options: A)22 years B)23 years C)24 years D)25 years E)26 years
SOLUTION:Explanation:
Let's Son age is x, then Father age is x+30.
=> 2(x+4) = (x+30+4)
=> 2x+8 = x+34
=> x = 26 years
Answer: Option E #### E
QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
options: A)22 B)287 C)48 D)277 E)21
SOLUTION:Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C #### C
QUESTION:a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple?
options: A)225 B)228 C)230 D)231 E)235
SOLUTION:CP = 140*2+150*3+160*4+170*1=1540
SP = 1.5*1540=2310
Total no.of kgs=2+3+4+1=10
SP per kg=2310/10=231
ANSWER:D #### D
QUESTION:Find the greatest number which leaves the same remainder when it divides 25, 57 and 105.
options: A)18 B)8 C)12 D)16 E)None of these
SOLUTION:105 - 57 = 48
57 - 25 = 32
105 - 25 = 80
The H.C.F of 32, 48 and 80 is 16.
ANSWER:D #### D
QUESTION:There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
options: A)776 B)864 C)299 D)257 E)125
SOLUTION:W = 60% L = 40%
60% - 40% = 20%
20% -------- 288
60% -------- ? => 864
Answer:B #### B
QUESTION:Smitty Farm picks 9866 cherries a day. If Smitty distributes their apples evenly across 9 different retail shops, how many cherries would remain with him.
options: A)1 cherry B)7 cherry C)2 cherry D)4 cherry E)5 cherry
SOLUTION:This is equivalent to finding the first number that is divisible by 9 that occurs before 9,866.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 9+8+6+6 = 29. If we add 7, then it is divisible by 9.
Hence, we need to add 7 to this number for it to be divisible by 9
Correct Option : B #### B
QUESTION:Positive Integer A gives the remainder of 18 when divided by another positive Integer B. If A/B = 147.24, what is the value of B?
options: A)96 B)75 C)48 D)25 E)12
SOLUTION:.24 of B = Remainder
.24 of B = 18
B = (18*100) / 24 = 75.
B #### B
QUESTION:The greatest number by which the product of three consecutive multiples of 5 is always divisible is
options: A)54 B)750 C)152 D)162 E)None of these
SOLUTION:Solution
Required number = Product of first three multiplies of 3
= (5 × 10 × 15)= 750.
Answer B #### B
QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age 10 years back was:
options: A)10 years B)19 years C)33 years D)38 years E)39years
SOLUTION:Let the son's present age be x years. Then, (40 - x) = x
2x = 40.
x = 20
Son's age 5 years back (20 - 10) = 10 years.
Answer:A #### A
QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 10 inches tall. How tall are the sculpture andbase together?
options: A)3.1 feet B)3.66 feet C)3.3 feet D)3.4 feet E)3.5 feet
SOLUTION:we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+10=40
44/12=3.66 feet
ANSWER:B #### B
QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is:
options: A)3000 B)3200 C)3450 D)4000 E)3570
SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5
= 105 : 40 : 36.
Let the initial investments be 105x, 40x and 36x.
=> A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12)
= 1680x : 480x : 432x
= 35 : 10 : 9.
Hence, A2's share = Rs. 21600 x 10/54
= Rs. 4000. Answer : D #### D
QUESTION:The true discount on a bill of Rs.1080 is Rs.180.The banker's discount is
options: A)210 B)212 C)214 D)216 E)None of these
SOLUTION:Solution
P.W = Rs.(1080 - 180)
= Rs. 900
S.I on Rs. 1080 =Rs.(180/900 x 1080)
= Rs. 216.
Answer D #### D
QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity?
options: A)7/18 B)9/18 C)2 D)18/7 E)18/5
SOLUTION:Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D
QUESTION:J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to
options: A)22 B)14 C)6 D)8 E)16
SOLUTION:Given J > P
J + P = 7, only options are (6, 1), (5, 2), (4, 3)
From the given options, If J = 4 the P = 3. Times taken by them = 244+243=14
Answer:B #### B
QUESTION:In a bag there are a certain number of black balls and blue balls. The probability of picking up exactly 1 blue ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of black balls to blue balls in the bag
options: A)1:2 B)1:4 C)1:1 D)1:5 E)1:6
SOLUTION:since the probability of drawing a blue ball out of two picks is 1/2.
the ratio of the blue ball to black balls should be 1:1
Answer : C #### C
QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use?
options: A)14 B)47 C)54 D)180 E)64
SOLUTION:Area = Length x Breadth
480 = 40 x Breadth
So, Breadth = 12 Units
Fencing required is -
Breadth + Breadth + Length
12 + 12 + 40 => 64 feet
Answer must be (E) 64 #### E
QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian?
options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m
SOLUTION:relative speed=20kmph=50/9m/sec
length of the train=50/9*5=250/9=27 7/9m
ANSWER:D #### D
QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is
options: A)420 B)520 C)620 D)780 E)820
SOLUTION:Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 300
=> x = 60
Total students = 8x+5x = 13x = 13(60) = 780
Option D #### D
QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
options: A)34 B)97 C)37 D)80 E)22
SOLUTION:1/2 * d (10 + 6) = 640
d = 80
Answer: D #### D
QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
options: A)288 B)492 C)877 D)278 E)178
SOLUTION:1h ----- 5
? ------ 60
12 h
RS = 20 + 21 = 41
T = 12
D = 41 * 12 = 492
Answer: B #### B
QUESTION:The area of a triangle is with base 4m and height 6m?
options: A)11 m2 B)10 m2 C)18 m2 D)19 m2 E)12 m2
SOLUTION:1/2 * 4 * 6
= 12 m2
Answer: E #### E
QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
options: A)28880 B)31200 C)28770 D)29990 E)12770
SOLUTION:Let A be the amount received at the end of the three years.
A = 48000[1 + 10/100][1 + 20/100][1 + 25/100]
A = (48000 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.79200
So the interest = 79200 - 48000 = Rs.31200
Answer: B #### B
QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest.
options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23
SOLUTION:R = 100 I / PT
=> R = (100 * 7200)/ (15000 * 5) = 9.6%
CI = P{ [1 + R /100]n - 1}
= 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24
Answer:D #### D
QUESTION:#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6?
options: A)–108 B)–44 C)10 D)16 E)18.25
SOLUTION:#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer. #### E
QUESTION:A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
options: A) 16 B) 20 C) 32 D) 44 E) 48
SOLUTION:lets say x ounces of P is mixed with Q.
=> 67-x ounces of Q is present in the mixture (as the total = 67 ounces)
given total almond weight = 15 ounces
(20x/100)+(25/100)(67-x) = 15
=> x = 35
=> 67-35 = 32 ounces of Q is present in the mixture.
Answer is C. #### C
QUESTION:A train 150 m long pass a telegraph pole in 5 seconds. Find the speed of the train
options: A)66 km/hr B)108 km/hr C)72 km/hr D)79.2 km/hr E)None
SOLUTION:Sol.
Speed = [150/5] m/sec = [30 * 18/5] km/hr = 108 km/hr.
Answer B #### B
QUESTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops.
options: A)6 B)6.5 C)7 D)7.5 E)5
SOLUTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops.
I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)
Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
It takes a total of nine hours to cover the 210 mile distance.
ANSWER: A 6 #### A
QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 85, what is the value of c − a?
options: A)25 B)80 C)90 D)140 E)It cannot be determined from the information given
SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=170 --2
subtracting 1 from 2 we have
c-a=80;
ANSWER:B #### B
QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series?
options: A)26 B)29 C)35 D)40 E)48
SOLUTION:Ans: A
Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 24*5= 120 so number of 24 can't be more than 5
so D=24x +2y = 124
24*5 + 2y =124 then y=2
24*4 + 2y = 124 then y=14
24*3 +2y = 124 then y= 26
24*2 +2y =124 then y = 38
24 +2y = 124 then y= 50
26 is the ans.A #### A
QUESTION:The forth proportional to 2,4,6 is?
options: A)8 B)12 C)15 D)18 E)22
SOLUTION:Let the fourth proportional to 2,4,6 be x
then 2:4::6:x
2x = 4*6
x = 12
Answer is B #### B
QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea?
options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None
SOLUTION:Solution: 1st Method:
Let the original price of tea be Rs. x/kg.
After reduction the price becomes = x -10% of x = 9x/10 per kg.
Now,
(22500/(9x/10))-22500/x = 25
Or, 22500[10/9x- 1/x] = 25
Or, 25*9x = 22500;
Or, x = (22500/2589) = Rs. 100.
Hence, new price = 90 per kg.
Thought process Method:
Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg.
After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg.
So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea.
Answer: Option C #### C
QUESTION:In how many ways the letters in the word MANAGEMENT can be arranged such that A’s does not come together.
options: A)181440 B)191440 C)171440 D)182440 E)185440
SOLUTION:Methods to arrange all the letters leaving A = 8*7*6*5*4*3*2*1/(2*1)*(2*1)*(2*1)= 5040
Now between these 8 letters , there are 9 places so methods to place A and A in these positions = 9*8/2*1 = 36
thus total methods are 5040*36 = 181440
ANSWER:A #### A
QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
.
options: A)Rs. 650 B)Rs. 690 C)Rs. 698 D)Rs. 700 E)Rs. 720
SOLUTION:S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698. Answer: Option C #### C
QUESTION:A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B?
options: A)7 B)14 C)21 D)28 E)35
SOLUTION:In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice.
With 36 liters of milk, we need a total of 48 liters of juice to make drink B.
We need to add 21 liters of juice.
The answer is C. #### C
QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is?
options: A)39 B)28 C)27 D)69 E)71
SOLUTION:1/2 * d (12 + 8) = 690
d = 69
Answer: D #### D
QUESTION:If n is a positive integer, which of the following is a possible value of |36 - 5n|?
options: A)7 B)14 C)12 D)15 E)20
SOLUTION:When 36>5n, then |36- 5n| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1
When 36<=5n, then |36- 5n| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits.
Answer: B #### B
QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is :
options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None
SOLUTION:Explanation:
Ratio of rents
=(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3)
=72:50:140:63
Let total rent = Rs.x
Then, A's share = Rs.(x×72/325)= Rs.(72x/325)
72x/325=360 or x = 325×360/72=1625
Correct Option: C #### C
QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 82 unique alphanumeric case sensitive characters.
options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6)
SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password
= 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways )
=82^4(1+ 82)
=82^4 * 83
Answer B #### B
QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only?
options: A)24 B)27 C)30 D)33 E)36
SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only.
Since 10% of students are in both, then 70% of students are in the band which is 84 students.
The number of students in the orchestra is (30/70)*84 = 36.
The answer is E. #### E
QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15
options: A)8600 B)8610 C)8620 D)8630 E)8640
SOLUTION:Explanation:
LCM of 27-18-16-15 is 2160.
After dividing 9999 by 2160 we get 1359 remainder.
So answer will be 9999-1359 = 8640
Option E #### E
QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3?
options: A)1 B)2 C)3 D)5 E)0
SOLUTION:As per question => N=3P+2 for some integer p
hence 2N => 6Q + 4 => remainder => 1 for some integer Q
hence A #### A
QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr
SOLUTION:Work done by the tank in 1 hour
= (1/2 - 1/3)
= 1/14 Leak will empty the tank in 14 hrs.
Answer:D #### D
QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers?
options: A)28 B)56 C)76 D)84 E)85
SOLUTION:Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 48
=> 12x = 48
=> x = 48/12 = 4
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 4 = 28
Answer: Option A #### A
QUESTION:The C.P of 10 pens is equal to the S.P of 15 pens. Find his gain % or loss%?
options: A)loss 16 2/8% B)loss 16 6/3% C)loss 16 2/3% D)loss 18 2/3% E)loss 33.33%
SOLUTION:10 CP = 15 SP
15 --- 5
100 --- ? => 33.33% (Loss)
Answer:E #### E
QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages.
options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these
SOLUTION:Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 136
20x = 160 => x = 8
Their present ages are 32, 56 and 72 years respectively.
ANSWER:D #### D
QUESTION:The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
options: A)180.27 cm B)180.29 cm C)978.29 cm D)178.89 cm E)176.29 cm
SOLUTION:Calculated average height of 35 boys = 182 cm.
Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182cm - (166 cm - 106 cm)/35
= 182 cm - 60 /35 cm
= 182 cm - 1.71 cm = 180.29 cm.
Answer: B #### B
QUESTION:If E is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of E?
options: A)10 B)12 C)14 D)16 E)18
SOLUTION:E = 30!
8
E = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3
3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3
So we have a total of 14 three's ...
Therefore the maximum value of K can be 14 (C) #### C
QUESTION:A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 5500. What is the share of B ?
options: A)1000 B)800 C)1400 D)1200 E)None of them
SOLUTION:Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 5500 x (2/11))= Rs. 1000.
Answer is A #### A
QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result?
options: A)132 B)127 C)125 D)152 E)112
SOLUTION:C
125
96 passes out of 125 give an average of 76.8% #### C
QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house?
options: A)25 B)49 C)3 D)87 E)36
SOLUTION:Aravind can select one or more than one of his 8 gang.
=> Required number of ways = 2^2 – 1= 3.
C #### C
QUESTION:A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width?
options: A)12 by 2 B)11 by 3 C)20 by 5 D)10 by 4 E)9 by 3
SOLUTION:2x+2y=50
x+y=25
x+4x=25
5x=25
x=5
Answer C #### C
QUESTION:An arithemetic sequence of numbers begins p, 2p + 1, 4p + 2... What is the 14th member of this sequence?
options: A)A)37 B)B)40 C)+ 13 D)D)53 E)+ 13
SOLUTION:Common difference of an arithmetic series is constant.
2p+2-p=4p+3-2p-2
p=1
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
Ans:B #### B
QUESTION:REDO’s manufacturing costs for sets of horseshoes include a $10,500 initial outlay, and $15per set. They can sell the sets $40. If profit is revenue from sales minus manufacturing costs, and the company producessells 500 sets of horseshoes, what was their profit?
options: A)$2100 B)$2000 C)$2050 D)$2070 E)$2500
SOLUTION:Total Manufacturing cost = 10500+500*15 = 18000
Total Selling cost = 500*40= 20000
Profit = 20000-18000 = 2000
Answer : B #### B
QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
options: A)1.7 B)1.4 C)1.1 D)1.5 E)1.2
SOLUTION:M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D #### D
QUESTION:At a meeting of the 8 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 8 Chiefs of Staff be seated around a circular table?
options: A)120 B)480 C)960 D)2520 E)5080
SOLUTION:Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E #### E
QUESTION:A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h?
options: A)42 km/h B)46 km/h C)50 km/h D)54 km/h E)58 km/h
SOLUTION:speed = distance / time = (130 + 320)/30 = 450/30 (m/s) * 3600/1000 = 54 km/h
The answer is D. #### D
QUESTION:In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
options: A)c/e B)e/c C)e/(c-e) D)c/(c-e) E)1- (e/c)
SOLUTION:We're given a couple of facts to work with:
1) There were a total of c earthquakes
2) Of those earthquakes, e of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Let's TEST VALUES
c = 5 total earthquakes
e = 2 occurred in Asia
Thus, there were 3 earthquakes that DID NOT occur in Asia....
The answer to the question is 2:3
We just need to plug in the values for c and e and find the match...
Answer A: c/e = 5/2 NOT a match
Answer B: e/c = 2/5 NOT a match
Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match
Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match
Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match
C #### C
QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice?
options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7
SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2*(1/2)^2 = 2/4 =0.5.
The answer is, therefore, (A). #### A
QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years. The age of the 15th student is
options: A)9 years B)11 years C)17 years D)21 years E)25 years
SOLUTION:Solution
Age of the 15th student =[15x15-(14x8+16x6)]
= (225 - 208)
= 17 years.
Answer C #### C
QUESTION:Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once?
options: A)9/100 B)1/10 C)11/100 D)19/100 E)1/5
SOLUTION:Probability = No of balls with exactly one 1 / total number of balls
= {1,10,12 to 19, 21,31,41,51,61,71,81,91,100}/100
= 19/100
Answer is D #### D
QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
options: A)23 days B)16 days C)11 days D)24 days E)35 days
SOLUTION:D
24 days
2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days #### D
<<<Examples ends
QUESTION:A shop owner has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 years. How much sale must she have in the 6th year so that she gets an average sale of Rs. 6500?
options: A)5000 B)5500 C)4991 D)5600 E)5700
SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991
C #### C
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