divelab/Sys2Bench huggingface dataset:
Question: A tradesman is marketing his goods 20% above the cost price of the goods. He gives 10% discount on cash payment, find his gain percent.
Options:
A)12%
B)8%
C)15%
D)18%
E)None of these
Rationale: Let the C.P. of the goods be 100
⇒ Marked price of the goods = 120
Discount = 10% ⇒ S.P. is 90% of 120 = 108
∴ Gain = (108 – 100) i.e. 8%.
Answer B
Answer: 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, 90, 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)79
Rationale: ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 90 + 77*5x) = 260x+540x+385x = 1185x
total number of students = 15x
average = 1185x/15x = 79
E is the answer
Answer: E
Question: The average weight of 10 students decreases by 6 kg when one of them weighing 120 kg is replaced by a new student. The weight of the student is
Options:
A)62 kg
B)60 kg
C)70 kg
D)72 kg
E)None of these
Rationale: Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 6 kg
=> (120-x)/10 = 6
=> x = 60
Answer : B
Answer: B
Question: At milk factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?
Options:
A)8/17
B)1/2
C)8/9
D)9/8
E)17/8
Rationale: At milk factory, Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;
Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;
The ratio of the second shift production to the total is 8/(9+8)=8/17.
Answer: A.
Answer: A
Question: The price of a jacket is reduced by 10%. During a special sale the price of the jacket is reduced another 30%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
Options:
A)32.5
B)58.7
C)48
D)65
E)67.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 10% , therefore bringing down the price to $90.
3) Again it is further discounted by 30%, therefore bringing down the price to $63.
4) Now 67.5 has to be added byX %in order to equal the original price.
63 + ( X% ) 63 = 100.
Solving this eq for X, we get X = 58.7
Ans is B
Answer: B
Question: An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.80 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?
Options:
A)130,000
B)300,000
C)325,000
D)400,000
E)420,000
Rationale: Total royalties for first 100.000 books = .8*100,000= 80,000
Total royalties for the rest of the books = 260,000-80,000 = 180,000
Remaining books = 180,000/0.8 = 225,000
Total books = 225,000+100,000 = 325,000 Answer C
Answer: C
Question: If P represents the product of the first 16 positive integers, then P is not a
multiple of:
Options:
A)a) 99
B)b) 84
C)c) 133
D)d) 65
E)e) 57
Rationale: a) 99 = 9*11
b) 84 = 4*7*3
c) 133 =19*7
d) 65 = 5*13
e) 57 =19*3
since 19 is not there in first 15 positive numbers it is the only possibility
C
Answer: C
Question: A person sold two cows each for Rs.9900. If he gained 10% on one and lost 20% on the other, then which of the following is true ?
Options:
A)He lost Rs. 200
B)He gained Rs. 200
C)Neither he gained nor lost
D)None of the above
E)He gained Rs. 300
Rationale: Explanation:
In first he got Rs. 990
But in second he lost Rs. 1980
So he lost Rs. 990.
ANSWER IS D
Answer: D
Question: What is the average of xx, 2x2x, and 66?
Options:
A)x+2x
B)x+2
C)x+2x+2
D)2x+2
E)2x
Rationale: By the definition of an average, we get:
x+2x+63=3x+63x+2x+63=3x+63
=3(x+2)3=x+2.=3(x+2)3=x+2.
Hence, the answer is x+2x+2 or Option C
Answer: C
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
Rationale: Two students can be selected from 6 in 6C2 =15 ways.
Therefore, the teacher goes to the zoo 15 times.
Option C is answer
Answer: C
Question: What percent of 60 is 90?
Options:
A)133 1⁄3
B)75
C)150
D)33 1⁄3
E)25
Rationale: To find out the % of 90 in 60
Do 90/60 = 150%
Answer C)
Answer: C
Question: In a bread recipe, the ratio of water to flour is 13 to 20. There is 168 g more flour than water. How much flour does the recipe call for?
Options:
A)400 g
B)440 g
C)480 g
D)510 g
E)525 g
Rationale: Let x equal the amount of water, and y equal the amount of flour.
We know that x = 13/20y.
We also know that x = y-168.
So we can simplify:
y-168 = 13/20y
So to isolate y, we get:
7/20y = 168
And to solve for y:
y = 480
Answer: C
Answer: C
Question: Five persons - A, B, C, D and E are being compared in weight and height. The second heaviest person. D is the shortest. A is the 2nd tallest and shorter than E, The heaviest person is the third tallest person. There is only one person shorter than B, who is lighter than E and A respectively. What is the position of A in height and weight respectively?
Options:
A)2nd,4th
B)4th,3rd
C)2nd,1st
D)5th,3rd
E)2nd,5th
Rationale: Explanation:
A is the second tallest person. There is only one person shorter than B. So, B is the fourth tallest person. D is the shortest and second heaviest.
A is shorter than E. So, the third tallest person is C. Who is the heaviest person. B is lighter than E and A respectively. So, the final arrangement is as follows.
A is the second tallest and the fourth heaviest person.
ANSWER IS A
Answer: A
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)Rs.28
B)Rs.280
C)Rs.140
D)Rs.70
E)Rs.15
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: B
Question: Evaluate combination
100C98=100!/(98)!(2)!
Options:
A)4950
B)1510
C)4170
D)3170
E)None of these
Rationale: Explanation:
nCr=n!/(r)!(n−r)!
100C98=100!/(98)!(2)!
=100∗99∗98!/(98)!(2)!
=100∗99/2∗1
=100∗99/2∗1=4950
Option A
Answer: A
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 300 shares of the company's stock?
Options:
A)$92
B)$96
C)$156
D)$120
E)$240
Rationale: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*300 --> $156
answer is C
Answer: C
Question: If (1 – 1.25)N = 2, then N =
Options:
A) −400
B) −140
C) −8
D) 4
E) 400
Rationale: (1 – 1.25)N = 2
Simplify to get: -0.25N = 2
Rewrite as (-1/4)N = 2
Multiply both sides by -4 to get: N = -8
Answer: C
Answer: C
Question: During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 18% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?
Options:
A)714,240
B)2,261,760
C)2,522,033
D)3,690,240
E)3,915,790
Rationale: Let number of cars sold in 1st quarter = x
Number of cars sold in 2nd quarter = 18% greater than the number sold during the first quarter = (1 + 18/100)x = 1.18 x
1.18 x = 2,976,000
=> x = 2,522,033
So, answer will be C
Answer: C
Question: John Traveled from point A to B in 4 merter per sec and from B to A in 6 meter per sec. What is his average speed?
Options:
A)4.6m/s
B)4.8m/s
C)5.2m/s
D)5.4m/s
E)5.8m/s
Rationale: Since the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2)
2X4X6/10= 4.8. 'B' is the answer.
Answer: B
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?
Options:
A)430
B)287
C)267
D)262
E)927
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate
= x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10
= 172 => 4x/10 = 172
=> 4x = 1720 => x
= 430.
Answer:A
Answer: A
Question: A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is
Options:
A)2.5 km/hr
B)4.2 km/hr
C)5 km/hr
D)10.5 km/hr
E)None
Rationale: Solution
Speed of stream	= 1 / 2 (13 - 8 )kmph
= 1/2 x 5
=5 /2
= 2.5
Answer A
Answer: A
Question: What is 120% of 13/24 of 840?
Options:
A)436
B)478
C)512
D)546
E)620
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 35 = 546
The answer is D.
Answer: D
Question: There are 81 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
Options:
A)4
B)7
C)27
D)21
E)37
Rationale: let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets. 81 = x + 2xx = 27In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.81 = 2xBut x cannot be a decimal so (x-1) could be the overlap (= Both) and there could be 1 in only the Golf club.81 = 2 x + x - (x - 1)x = 40In this case Both = 40 - 1 = 39 So Both lies between 0 and 39 Only option (E) satisfies this condition. ANSWER:E
Answer: E
Question: In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?
Options:
A)65 liters
B)68 liters
C)60 liters
D)26 liters
E)27 liters
Rationale: 2:1 --- 60
1:2
2:4
---------------
3
3 ----------- 60
3 ----------- ? => 60 liters
Answer: C
Answer: C
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.
Options:
A)240 km
B)225 km
C)452 km
D)300 km
E)290 km
Rationale: D
300 km
Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11 => x = 300 km
Answer: D
Question: The average of 11 numbers is 10.7. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
Options:
A)9
B)9.2
C)10
D)13.7
E)12
Rationale: Explanation:
1 to 11 = 11 * 10.7 = 117.7
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 117.7 = 13.7
6th number = 13.7
D)
Answer: D
Question: Two pipes A and B can fill a tank in 15 min and 21 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
Options:
A)14 min 19 sec
B)14 min 42 sec
C)14 min 20 sec
D)14 min 40 sec
E)15 min 12 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/21
1/21 : 8/15 :: 1 ; x
x = 8/15 * 1 * 21 = 11 1/5 min = 11 min 12 sec.
The tank will be full in (4 min. + 11 min. 12 sec) = 15 min 12 sec.Answer: E
Answer: E
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
Options:
A)15 days
B)12 days
C)10 days
D)9 days
E)8 days
Rationale: Explanation:
3/12 + (3 + x)/16 = 1
x = 9 days
Answer: D
Answer: D
Question: A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21 . What is the remainder left, when twice the number is divided by 3D?
Options:
A)13
B)12
C)3
D)2
E)42
Rationale: making eqn as per the question
a=Dx+8......1
a=3Dy+21....2
multiplying 3 in eqn 1 we get eqn 3
3a=3Dx+24....3
a=3Dy+21......2
now subtract 2 from 3 we get..
2a=3D(x-y)+3
so here's the remainder we got is 3
ANSWER:C
Answer: C
Question: A batsman makes a score of 90 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
Options:
A)39
B)35
C)42
D)40.5
E)42
Rationale: let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+90
then average run after 17th inning=(16x+90)/17
(16x+90)/17=x+3 => 16x+90 = 17x+51 => x=39
x=39;
average after 17th inning =39+3=42
ANSWER:E
Answer: E
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%
Rationale: 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
Answer: D
Question: A shopping cart contains only apples, oranges, and pears. If there are four times as many oranges as apples, and five times as many pears as oranges, then the apples are equivalent to what fraction of the pears?
Options:
A)1/8
B)1/9
C)1/12
D)1/16
E)1/20
Rationale: O = 4A
P = 5O = 20A
A = P/20
The answer is E.
Answer: E
Question: Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 2, 2, 2 3, 3, 2
II. 32, 32, 32, 30, 30, 32
III. 37, 38, 39, 40, 44, 42
Options:
A)I, II, III
B)I, III, II
C)II, I, III
D)II, III, I
E)III, II, I
Rationale: (D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.
sequence lowest to highest = I,II,III
A
Answer: A
Question: How many 3-letter words can be formed using the letters of the English alphabet that contain 1 different vowels and 2 different consonants?
Options:
A)4!*5c2 *21c2
B)4!*5c3 *21c2
C)3!*5c1 *21c2
D)5!*5c2 *21c2
E)6!*5c2 *21c2
Rationale: combination for 1 vowels out of 5 =5c1 ways
combination for 2 consonants of 21 = 21c2 ways
Additionally the arrangement can be = 3!
total arrangements =3!*5c1 *21c2
C
Answer: C
Question: If (x+4)2−−−−−−−√=3(x+4)2=3, which of the following could be the value of x−4x−4?
Options:
A)-11
B)-7
C)-4
D)-3
E)5
Rationale: X+4)2=9(X+4)2=9
(X−4+8)2=9(X−4+8)2=9
let X-4 = A
(A+8)2=9(A+8)2=9
Now, sub answer choices in A
A) (−11+8)2=(−3)2=9(−11+8)2=(−3)2=9
A is your answer
Answer: A
Question: what is the smallest number should be added to 5377 so that the sum is completely divisible by 7?
Options:
A)5
B)4
C)6
D)2
E)1
Rationale: Solution: Divide 5377 with 7 we get remainder as 1. so, add 6 to the given number so that it will divisible by 7.
Answer C
Answer: C
Question: Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
Options:
A)1
B)8
C)9
D)2
E)7
Rationale: Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise sh
Answer: B) 8
Answer: B
Question: if each of its sides of a rectangle is increased by 18%, what is the percentage increase in the area of the rectangle, ?
Options:
A)39.24%
B)38.24%
C)36.24%
D)37.24%
E)38.24%
Rationale: Assume original length = 100m by 50m
original area = 100*50= 5000
18% increase on each side
l = 100 + 18= 118
w = 50 + 9 = 59
new area = 118*59= 6962
increase in area = 6962 - 5000 = 1962
%increase =39.24%
Answer A
Answer: A
Question: If 4 : 6 :: x : 36, then find the value of x
Options:
A)24
B)22
C)28
D)30
E)18
Rationale: Explanation:Treat 4:6 as 4/6 and x:36 as x/36, treat :: as = So we get 4/6 = x/36=> 6x = 144=> x = 24 Option A
Answer: A
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. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 30,000
B)Rs. 50,000
C)Rs. 60,000
D)Rs. 90,000
E)Rs. 70,000
Rationale: N/3=P/2
N+P=150000
60000
ANSWER:C
Answer: C
Question: A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in?
Options:
A)22 1/2
B)22 1/3
C)23
D)23 1/2
E)23 1/3
Rationale: Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes 3	x 60 = 90 days.
2
So, A takes 30 days to do the work.
A's 1 day's work =	1
30
B's 1 day's work =	1
90
(A + B)'s 1 day's work = 1	+	1 =	4	=	2
30	90	90	45
A and B together can do the work in	45	= 22	1	days.
2	2
Answer is A
Answer: A
Question: Ten circular coins are thrown on the street so that no two of them
overlap or touch, and no three of them have a tangent line in common.
What is the total number of lines which are tangent to two of the coins?
Options:
A)60
B)100
C)180
D)240
E)360
Rationale: There are n(n-1)=2 different ways
of choosing 2 objects from a given collection
of n objects. Thus, there are 10*9/2 = 45
different ways of choosing 2 of the 10 coins.
For each selection of two coins, one can form 4
tangent lines as shown at the right. Therefore,
the answer is 4*45 = 180.
correct answer C
Answer: C
Question: The diameter of a wheel of cycle is 21 cm. It moves slowly along a road. How far will it go in 500 revolutions?
Options:
A)220
B)330
C)360
D)390
E)410
Rationale: In revolution, distance that wheel covers = circumference of wheel Diameter of wheel = 21 cm
Therefore, circumference of wheel = πd
= 22/7 × 21
= 66 cm
So, in 1 revolution distance covered = 66 cm
In 500 revolution distance covered = 66 × 500 cm
= 33000 cm
= 33000/100 m
= 330 m
ANSWER B
Answer: B
Question: A metallic sheet is of rectangular shape with dimensions 40m x 30 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is:
Options:
A)3220 m cube
B)4140 m cube
C)2688 m cube
D)4000 m cube
E)None of these
Rationale: Explanation:
l = (40 - 16)m = 24 m, [because 8+8 = 16]
b = (30 -16)m = 14 m,
h = 8 m.
Volume of the box = (24 x 14 x 8) m cube
= 2688 m cube.
Option C
Answer: C
Question: A work can be finished in 13 days by ten women. The same work can be finished in fifteen days by ten men. The ratio between the capacity of a man and a woman is
Options:
A)14:13
B)13:15
C)12:13
D)13:12
E)14:15
Rationale: Work done by 10 women in 1 day = 1/13
Work done by 1 woman in 1 day = 1/(13Ã—10)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15Ã—10)
Ratio of the capacity of a man and woman =1/(15Ã—10) : 1/(13Ã—10) = 1/15 : 1/13
= 1/15 :1/13 = 13 : 15
Answer is B.
Answer: B
Question: A 3% stock produces 10%. The market value of the stock is:
Options:
A)Rs. 15
B)Rs. 25
C)Rs. 20
D)Rs. 30
E)Rs. 40
Rationale: Let the face value of the product is Rs.100
It stock Rs.3
Market value of the stock=(3/10)*100=Rs.30
ANSWER:D
Answer: D
Question: In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
Options:
A)240
B)260
C)370
D)409
E)360
Rationale: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360
E
Answer: E
Question: There are 20 poles with a constant distance between each pole. A car takes 20 second to reach the 12th pole. How much will it take to reach the last pole.
Options:
A)34.4543
B)34.5455
C)34.45128
D)34.51288
E)34.41222
Rationale: Assuming the car starts at the first pole.
To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).
11 poles 20 seconds
1 pole (20/11) seconds
To reach the last (20th) pole, the car needs to travel 19 poles.
19 pole 19 x (20/11) seconds
= 34.5455 seconds
Answer:B
Answer: B
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 10 : 5?
Options:
A)16
B)45
C)277
D)92
E)11
Rationale: Let the distances between city A to B and B to C be 10x km and 5x km respectively.
Total time taken to cover from A to C
= (10x)/40 + (5x)/60 = (30x + 10x)/120 = 40x/120 = x/3 Average speed = (10x + 5x)/(x/3) = 45 kmph.
Answer:B
Answer: B
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
Options:
A)4/9
B)4/3
C)4/2
D)4/8
E)4/1
Rationale: 2/3 ---- 12
? ----- 8 ==> 4/9
Answer: A
Answer: 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
Rationale: Explanation:
Total number of cases = 52
Total face cards = 16 [favourable cases]
So probability = 16/52 = 4/13
Answer: A
Answer: A
Question: A sells a bicycle to B at a profit of 70% and B sells it to C at a loss of 40%. Find the resultant profit or loss.
Options:
A)-4%
B)2%
C)-5%
D)6%
E)-7%
Rationale: The resultant profit or loss = 70 - 40 - (70*40)/100 = +2%
Profit = 2%
Answer is B
Answer: B
Question: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 15 members of this sequence?
Options:
A)618
B)900
C)788
D)928
E)1022
Rationale: I would split them up like this.
23 28 33 and so on (8 terms)....the 8th term = 23+7*5 = 58
27 32 37 and so on (7 terms)......the 7th term = 27+6*5 = 57
Since the distance between any two numbers is the same we can use arithmetics
first+last/2 times no of numbers = the sum
(23+58)/2 * 8= 324
(27+57)/2 * 7 = 294
= 618
A
Answer: A
Question: An empty pool being filled with water at a constant rate takes 5 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
Options:
A)5 hr 30 min
B)5 hr 20 min
C)4 hr 48 min
D)3 hr 20 min
E)2 hr 40 min
Rationale: (3/5) of a pool/ 5 hours = 3/25 (the rate)
(3 pools/25 hours) = (2/5* pool)/ x hours
Cross multiply 3x = (2/5) 25
x = 3 1/3
1/3 of an hour = 20 minutes
D
Answer: D
Question: If 5x + y = 15, 5y + z = 25 and 2z + x = 2, what is the value of x ?
Options:
A)2
B)7
C)9
D)12
E)None of these
Rationale: Explanation:
5x + y = 15 –-------I * 5
5y + z = 25 –------ II
2z + x = 2 -------- III
Subtract (I) and (II)
25x + 5y + 0 = 75
- 0 + 5y + z = 25
-------------------------------
25x + 0 – z = 50 ….......... IV
Multiply (IV)*2, we get 50x – 2z = 100
Adding (III) and (IV) we get,
50x – 2z = 100
+ x + 2z = 2
------------------------
51 x = 102
x = 2
The value of x = 2
ANSWER A
Answer: A
Question: 7^8 is equal to which of the following?
Options:
A)5,764,787
B)5,764,788
C)5,764,799
D)5,764,800
E)5,764,801
Rationale: Units digit spotting can be fun
Cyclicity of 7 to the power of anything
7^1= 7
7^2= 9
7^3= 3
7^4= 1
7^5= 7
--- pattern formed --
So the cycle of this is 4. The fifth power will start the cycle again. Therefore, 7 to the power of 8 will give a units digit of 1. Answer E
Answer: E