divelab/Sys2Bench huggingface dataset:
Question: The rate of increase of the price of sugar is observed to be three percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 25 per kg. The inflation rate for the years 1994 and 1995 are expected to be 12% each. The expected price of sugar on January 1, 1996 would be
Options:
A)33.06
B)34.1
C)34.2
D)24.6
E)None of these
Rationale: Explanation :
Increase in the price of sugar = (12+3)= 15%
Hence, price of the sugar on Jan 1, 1996
=> (25 * 115 * 115)/( 100 * 100 ) = Rs 33.06.
Answer : A
Answer: A
Question: The ratio between the sale price and the cost price of an article is 6:4. What is the ratio between the profit and the cost price of that article?
Options:
A)23
B)1:2
C)2:5
D)3:5
E)25
Rationale: C.P. = Rs. 4x and S.P. = Rs. 6x.
Then, Gain = Rs. 2x
Required ratio = 2x : 4x = 1:2
B
Answer: B
Question: 40 men can catch 200 sharks in 20 days working 6 hours a day. In how many days 25 men can catch 300 sharks working 4 hours a day?
Options:
A)30
B)34
C)24
D)20
E)50
Rationale: We have, M1D1H1/W1 = M2D2H2/W2
40*20*6/200 = 25*D2*4/300
D2= 40*20*6*300/200*25*4 = 24
ANSWER:C
Answer: C
Question: What is the CP of Rs 100 stock at 7 discount, with 1/5% brokerage?
Options:
A)93.9
B)96.3
C)93.2
D)96.7
E)96.21
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-7+1/5
93.2
Thus the CP is Rs 93.2.
ANSWER: C
Answer: C
Question: For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Looking for (n + nC3) = 8
2 types of flower arrangements: some with 1 flower and some with 3 different flowers.
Therefore, total number of arrangements we could make from n different types of flowers = (n + nC3).
Since 4C3 = 4 (nC(n-1) always equals n combinations i.e. nC(n-1) = n),	(n + nC3) = (4 + 4C3) = (4 + 4) = 8
Aim to get 8 distinct floral arrangements, 4 different types of flowers is the answer.
Answer: A
Answer: A
Question: When N is divided by T, the quotient is A and the remainder is V. Which of the following expressions is equal to N?
Options:
A)ST
B)S + V
C)ST + A
D)T(S+V)
E)T(S – V)
Rationale: Using the rule dividend = Quotient * divisor + remainder =>ST + A C is correct
Answer: C
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?
Options:
A)27 grams
B)30 grams
C)29 grams
D)31 grams
E)35 grams
Rationale: Let original mass be 100
The final mass of that element will be 7
So whatever option we have it will be divisible by 7
Check for the options the one that doesn't produce non terminating decimal is our answer
A. 27 grams
27/7 = 3.857...
B. 30 grams
28/7 = 4.285...
C. 29 grams
29/7 = 4.142.......
D. 31 grams
31/7 = 4.428.....
E. 35 grams
35/7 = 5
Hence our answer will be (E)
Answer: E
Question: 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 20 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?
Options:
A)15 km/hr
B)16 km/hr
C)17 km/hr
D)18 km/hr
E)None of these
Rationale: Explanation :
Total distance covered by B=20*6=120kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=120/8=15 km/hr
Answer : A
Answer: A
Question: If X:Y is 1:2 and Y:Z is 2:5 then X:Z is equal to
Options:
A)2:5
B)3:5
C)1:5
D)4:5
E)1:3
Rationale: The two ratios given are having the same number 2 for Y in both the ratios.
Hence- X:Y = 1:2 Y:Z = 2:5
=> X:Z = 1:5
Answer C
Answer: C
Question: man buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is?
Options:
A)12
B)76
C)26
D)20
E)12
Rationale: Let the article be worth Rs. x.
C.P. 90% of Rs. x = Rs. 9x/10
S.P. = 110% of Rs. x = Rs. 11x/10
Gain = (11x/10 - 9x/10) = Rs. x/5
Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%
Answer: D
Answer: D
Question: When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 1/3 of the remaining balance, what will be the final balance in her bank account?
Options:
A)300
B)375
C)400
D)500
E)575
Rationale: As per the question 200=2a/5
thus- a which is the total amount =500
The amount thus left =300
She then deposited 1/3 of 300=100
total amount in her account =400
Answer C
Answer: C
Question: The sum of all consecutive odd integers from −27 to 37, inclusive, is
Options:
A)110
B)135
C)150
D)165
E)235
Rationale: The sum of the odd numbers from -27 to +27 is 0.
Let's add the remaining numbers.
29+31+33+35+37 = 5(33) = 165
The answer is D.
Answer: D
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Options:
A)480
B)289
C)279
D)276
E)911
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer:A
Answer: A
Question: In the quadrilateral PQRS d=7 cm, h1=4.2 cm and
h2=2.1 cm. Find the area
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)
so 1/2*7*(4.2+2.1)=22.05
ANSWER:B
Answer: 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, 50 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)70.
C)50.
D)40.
E)25.
Rationale: STREET-CAT DOMESTIC-Cat
70 130
(50gray+20other) 60gray+70other
Answer:B
Answer: B
Question: Bhaman travelled for 15 hours. He covered the first half of the distance at 40 kmph and remaining half of the distance at 10 kmph. Find the distance travelled by Bhaman?
Options:
A)240
B)230
C)260
D)220
E)340
Rationale: Let the distance travelled be x km.
Total time = (x/2)/40 + (x/2)/10 = 15 => x/80 + x/20 = 15 => (x + 4x)/80 = 15
=> x = 240 km
Answer:A
Answer: A
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 3025., the number of the member is the group is:
Options:
A)55
B)67
C)77
D)87
E)97
Rationale: Money collected = (30.25 x 100) paise = 3025 paise.
Number of members =Square root of 3025 = 55.
Answer: Option A
Answer: A
Question: What ratio must a shopkeeper mix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.21?
Options:
A)10 : 7
B)9 : 8
C)4 : 5
D)13 : 11
E)14 : 8
Rationale: Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 4 : 5
Answer: C
Question: A rectangular window is twice as long as it is wide. If its perimeter is 20 feet, then what are its dimensions in feet?
Options:
A)3/2 by 7/2
B)5/3 by 10/3
C)2 by 4
D)3 by 6
E)10/3 by 20/3
Rationale: Let x be the width of the window. Then the length is 2x.
x+2x+x+2x = 20
6x = 20
x = 20/6 = 10/3
The width is 10/3 and the length is 20/3.
The answer is E.
Answer: E
Question: Dick and Jane each saved $2,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $4,000. Approximately what percent less did Jane save in 1990 than in 1989?
Options:
A)10%
B)20%
C)25%
D)30%
E)35%
Rationale: 1990
Dick saved = $ 2200
Jane saved = $ 1800 (jane saved $200 less than she did the prior year)
Jane saved approximately $200/2000$ (10%) less in 1990
Answer: A
Answer: A
Question: A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train?
Options:
A)300 m
B)270 m
C)200 m
D)250 m
E)260 m
Rationale: speed = 72*5/18 = 20 m/sec
t = 26 sec
length => x
x+250 = 520
x= 270
ANSWER B
Answer: B
Question: X can lay railway track between two station in 16; Y can do the same work in 20 days,both are working together for 2 days after Y left the job then how many days X requires to complete the remaining work ? Total number of days taken to complete the whole work?
Options:
A)7 Days and 9 days
B)5.89 Days and 7.89 days
C)8.26 Days and 10.26 days
D)7.75 Days and 9.75 days
E)9 Days and 11 days
Rationale: First take LCM of (16,20) = 160; Total work = 160; X's one day work = 160/16 =10; Y's one day work =160/20 = 8; One day work of both X+Y= 10+8 = 18; Total work completed in 2 days = 18*2=36; remaining work is = 160 - 36 =124; remaining work completed by X in = 124/16= 7.75 days.Total number of days taken to complete the whole work = 2+7.75 = 9.75 days.
Answer =D
Answer: 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 $845,000 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)$4,225,000
Rationale: Portion invested in preferred stock = 3/5 * 1/3 = 1/5
1/5 of fund = 845---
Fund = 5 * 845---
Here, we can avoid the math and simply look at 5 * 5 -> 25. Only option E has 25 in it.
Answer (E).
Answer: E
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
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480.Answer:D
Answer: D
Question: If two sides of a triangle have lengths 4 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
Rationale: Let x be the length of the third side.
7-4 < x < 7+4
3 < x < 11
14 < perimeter < 22
The answer is D.
Answer: D
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)188m
B)278m
C)887m
D)100m
E)776m
Rationale: 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
Answer: D
Question: Two trains start simultaneously from opposite ends of a 140-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 140-km trip in 4 hours. Train Y, travelling at a constant rate, completes the 140-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y?
Options:
A)60
B)64
C)68
D)72
E)76
Rationale: If the two trains cover a total distance D, then Train X travels (3/7)*D while Train Y travels (4/7)*D. If the trains travel 140 km to the meeting point, then Train X travels (3/7)*140 = 60 km.
The answer is A.
Answer: A
Question: The area of a circle is subtracted from its diameter, and the circumference is then added to this total, the result is 0. What is the radius of the circle?
Options:
A)2*pi
B)pi
C)1
D)2
E)3
Rationale: The equation is; diameter - Area + Circumference = d - A + C = d - pi * r^2 + 2 * pi * r = 2r - pi * r(r + 2).
By plugging in the answers we can test the answers quickly; then, 2 is the only possible answer.
Answer: D
Answer: D
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 30,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
Options:
A)104,000
B)60,000
C)80,000
D)90,000
E)10,000
Rationale: The distance traveled by each tyre:
4/5 * 1, 30, 000km = 104,000 km. A
Answer: A
Question: On a certain day, mangrov farm harvested 4267 apples. If mangrov distributes his apples evenly across 7 different retail shops, how many apples would remain with him.
Options:
Options:
A)1 apple
B)2 apple
C)3 apple
D)4 apple
E)5 apple
Rationale: This is equivalent to finding the first number that is divisible by 7 that occurs before 4267.
In order to divide the sum in 7 parts, the amount must be divisible by 7
Divisibility rule of 7: The sum of the digits must be divisible by 7
Sum of digits of 4267 = 19 and 7 is divisible by 7.
Hence, we need to remove 5 to this number for it to be divisible by 7
Correct Option:E
Answer: E
Question: In a group of ducks and cows, the total number of legs are 34 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)11
B)12
C)14
D)17
E)18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 34
=> 2x = 34 => x = 17
D
Answer: D
Question: A shop owner sells 15mtr of cloth and gains SP of 10 mtrs. Find the gain %?
Options:
A)30%
B)40%
C)50%
D)100%
E)200%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 15 m cloth) – (C.P. of 15 m cloth)
Selling price of 5 m cloth = Selling Price of 15 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 5 m cloth = Rs. 500 and S.P. of 5 m cloth = Rs. Rs. 1500
Profit% = 1000/500 × 100 = 200%
Profit of 200% was made by the merchant.
E
Answer: E
Question: The positive number x is q percent greater than the positive number b, which is p percent less than x itself. If a is increased by p 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 > x
II. c = x
III. c < x
Options:
A)I only
B)II only
C)III only
D)I and II only
E)II and III only
Rationale: Let q = 10% then p = 100/11 %
let b = 100 then x = 110
after increasing x by p and decreasing by q we get c= 108
therefore c<x
C it is answer
Answer: C
Question: A certain company had a total annual expenditure of 2.55∗10^7 on employee salaries last year. If the company employed 425 people, what was the average employee salary?
Options:
A)$60,000
B)$25,000
C)$35,000
D)$40,000
E)$45,000
Rationale: Given: Total annual expenditure of 2.55∗10^7 on employee salaries
Total employees = 425
Observe that 425*6 = 2550
Therefore try to bring the numerator in terms of 2550
Average salary = (2550*10^4) /425 = 6*10^4 = 60,000
Option A
Answer: A
Question: In a class of students, the ratio of girls to boys is 1:2. If 3 more girls joined the class, the ratio would be 3:4. How many students are in the class?
Options:
A)16
B)18
C)20
D)22
E)24
Rationale: Let x be the number of students in the class.
(1/3)*x=(3/7)(x+3)-3
7x=9x+27-63
2x=36
x=18
The answer is B.
Answer: B
Question: A fair coin is tossed 3 times. What is the probability of getting at least 2 heads?
Options:
A)3/4
B)3/2
C)1/4
D)1/2
E)1/5
Rationale: Let's find the probability of 2 heads , 3 heads
P(HHH)=((1/2)^3=1/8.
P(HHT)=(3!/2!)*(1/2)^3=3/8
Total Probablity = 1/8 + 3/8
=1/2
Answer(D)
Answer: D
Question: Which one of the following is the sum of the numbers 1, 3, 5, 7, 9â€¦. up to nth number?
Options:
A)N2 + 1
B)N2 - 1
C)N(N + 1)/2
D)N2
E)N(N + 1)
Rationale: Explanation:
N2
Answer: D
Answer: D
Question: A car costs a dealer Rs.50,000.Dealer raised price by Rs.10,000 and then deducted 4% of new price.
What is the profit/loss %?
Options:
A)14
B)15
C)15.2%
D)16
E)17.2%
Rationale: Ans: Let P be the percentage of price raised=(10000/500000) * 100 =20%
Discount %=4%
profit %=(20-4- 20*4/100 ) =15.2%
Answer C
Answer: C
Question: If 'c' is a positive integer exactly divisible by 6 or 5 but not divisible by 12.What could possibly be the value of 'c' ?
Options:
A)30
B)60
C)120
D)24
E)72
Rationale: 60 and 120 are both divisible by 6 and 5 but also by 12. so they are not the right answer.
24 and 72 are both clearly not divisible by 5(not correct)
30 is both divisible by 6 and 5 but not by 12.
answer : (A) 30
Answer: A
Question: What number continues the sequence?
25, 50, 27, 46, 31, 38, 39, ?
Options:
A)11
B)33
C)52
D)22
E)66
Rationale: D
22
There are two alternate sequences, the first increases by 2, 4, 8 etc and the second decreases by 4, 8, 16 etc.
Answer: D
Question: Victor gets 92 % marks in examinations. If these are 368 marks, find the maximum marks.
Options:
A)334
B)500
C)400
D)288
E)271
Rationale: Let the maximum marks be m
Then 92 % of m = 368
⇒ 92/100 × m = 368
⇒ m = (368 × 100)/92
⇒ m = 36800/92
⇒ m = 400
Therefore, maximum marks in the examinations are 400.
Answer : C
Answer: C
Question: If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?
Options:
A)0
B)1
C)2
D)3
E)5
Rationale: There are several algebraic ways to solve this question, but the easiest way is as follows: since we cannot have two correct answers just pick a prime greater than 3, square it and see what would be the remainder upon division of it by 12.
n=5 --> n^2=25 --> remainder upon division 25 by 12 is 1.
Answer: B
Answer: B
Question: If a quality control check is made inspecting a sample of 2 light bulbs from a box of 10 lighbulbs, how many different samples can be chosen?
Options:
A)6
B)24
C)45
D)66
E)72
Rationale: Try using the formula for combinations:
n!/r!(n-r)!
10!/2!(10-2)!
10!/2!*8!
10*9/2*1
=45
C
Answer: C
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)27.8 km/hr
B)22.9 km/hr
C)26.6 km/hr
D)79.2 km/hr
E)12.9 km/hr
Rationale: 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: D
Answer: D
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 10 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)95
B)28
C)90
D)26
E)11
Rationale: Explanation:
SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 10 = Rs. 95.
Answer: A
Answer: A
Question: A fort had provision of food for 150 men for 45 days. After 20 days, 40 men left the fort. The number of days for which the remaining food will last, is:
Options:
A)29	1/5
B)37	1/4
C)42
D)34
E)45
Rationale: we have food for 150 men for 45 days.
After 20 days food left for 150 men for 25 days.
so
150 : 25
now we have 110 men and x days
110 : 150 :: 25 : x
x = (150*25)/110 = 34 days.
ANSWER:D
Answer: D
Question: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 7?
Options:
A)A)1
B)B)2
C)C)4
D)D)7
E)E)16
Rationale: Points to remember -
1. If oneAdd/Subtractthe same amont from every term in a set, SD doesn't change.
2. If oneMultiply/Divideevery term by the same number in a set, SD changes by same number.
Hence the answer to the above question is D
Answer: D
Question: A merchant purchased a jacket for $48 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
Options:
A) $0
B) $3
C) $4
D) $12
E) $16
Rationale: Actual Cost = $48
SP = Actual Cost + Mark up
= Actual Cost + 40% SP
= 48*100/60
on sale SP = 80/100(48*100/60) = 64
Gross profit = $16
Answer is E
Answer: E
Question: A certain machine produces 650 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 7 days?
Options:
A)7,000
B)24,000
C)40,000
D)109,200
E)168,000
Rationale: Since 7 days consist of 24*7 hours the total hours of a week is 168 hours.
Since every hour the machine produces 650 units of product P the total product during 168 hours is 650*168= 109,200
Correct Option : D
Answer: D
Question: How many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?
Options:
A)45
B)47
C)49
D)52
E)63
Rationale: Selling Price(SP) of 1 kg mixture= Rs. 9.24
Profit = 10%
Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP
=100(100+10)×9.24=100110×9.24=92.411= Rs.8.4
By rule of alligation,
CP of 1 kg sugar of 1st kind CP of 1 kg sugar of 2nd kind
Rs. 9 Rs. 7
Mean Price
Rs.8.4
8.4 - 7 = 1.4 9 - 8.4 = 0.6
i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3
Suppose x
kg of kind1 sugar is mixed with 27 kg of kind2 sugar.
then x : 27 = 7 : 3
⇒3x=27×7⇒x=9×7=63
E
Answer: E
Question: What is the place value of 5 in the numeral 5259
Options:
A)2500
B)3400
C)3500
D)5000
E)4000
Rationale: Option 'D'
5 * 1000 = 5000
Answer: D
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%
Rationale: 8 = (1*20*R)/100
R = 40%
Answer:D
Answer: D
Question: What is the probability that when a hand of 5 cards is drawn from a well shuffled deck of 52 cards, it contains all the Queens?
Options:
A)191/379015
B)171/379015
C)181/379015
D)379015/192
E)192/379015
Rationale: nCr = n!/(n-r)!r!
Total number of possible hands = 52C5
52C5 = 2274090
Number of hands with 4 Queens = 4C4 × 48C1
4C4 = 24
48C1 = 48
(other 1 card must be chosen from the rest 48 cards)
Hence P (a hand will have 4 Queens) = (4C4 × 48C1)/52C5 = 192/379015
E
Answer: E
Question: A cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm. Find the total area of the wet surface.
Options:
A)42 m sqaure
B)49 m sqaure
C)52 m sqaure
D)64 m sqaure
E)None of these
Rationale: Explanation:
Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(4*1.25+6*1.25)]+6*4 = 49 m square
Option B
Answer: B
Question: When positive integer p is divided by positive integer x, the remainder is 5 and when positive integer q is divided by positive integer y, the remainder is 8. Which of the following is a possible value for x + y?
I.16
II. 15
III. 14
Options:
A)I and II only
B)II only
C)III only
D)II and III only
E)None
Rationale: p/x -- remainder is 5 => x is anything greater than 5. Minimum value of x could be 6.
q/y -- remainder is 8 => y is anything greater than 8. Minimum value of y could be 9.
Hence, the minimum value of x+y = 15. So, I and II are correct.
ANSWER:A
Answer: A
Question: The average age of a group of 16 students was 20. 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)30 years
C)38 years
D)32 years
E)None of these
Rationale: Answer
The average age of a group of 16 students is 20.
Therefore, the sum of the ages of all 16 of them = 16 * 20 = 320
When two new students join the group, the average age increases by 2. New average = 22.
Now, there are 18 students.
Therefore, the sum of the ages of all 18 of them = 18 * 22 = 396
Therefore, the sum of the ages of the two new students who joined = 396 - 320 = 76
And the average age of each of the two new students = 76/2 = 38 years.
Answer C
Answer: C
Question: Which of the following is NOT prime?
Options:
A)1,556,551
B)2,442,113
C)3,893,257
D)3,999,991
E)9,999,991
Rationale: 3,999,991 = 4,000,000 - 9 = (2000)^2 - 3^2
So this number is a product of two numbers other than 1 and itself. This means it is not prime. This must be the answer.
Let's take a look at (E) too.
9,999,991 = 10,000,000 - 9
Here the difference is that 10,000,000 is not a perfect square. It has odd number of 0s. So this would be a prime number.
Answer (D)
Answer: D
Question: A, B and C can do a work in 4 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
Options:
A)2 2/3
B)2 2/8
C)2 2/0
D)2 2/2
E)2 2/11
Rationale: Work done by all three of them in one day = 1/4 + 1/8 + 1/12 = 11/24
The number of days required = 24/11 = 2 2/11 days.
Answer:E
Answer: E
Question: There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is
Options:
A)1/5
B)2
C)3
D)4
E)5
Rationale: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5
A
Answer: A