mathewhe/aqua_rat huggingface dataset:
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 331/8%
(B) 331/3%
(C) 381/3%
(D) 351/3%
(E) 231/3%
Rationale: 100
150
------
150-------50
100-------? => 331/3%
Answer: B
Answer: (B) 331/3%
Question: Population of a city in 20004 was 1000000. If in 2005 there is an increment of 30% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
(A) 967532
(B) 977522
(C) 984424
(D) 997454
(E) 1225250
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 30/100)(1 - 35/100)(1 + 45/100)
= 1225250
E
Answer: (E) 1225250
Question: When a student Joe, weighing 42 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
(A) 5.5 kg
(B) 6 kg
(C) 30 kg
(D) 36.5 kg
(E) 71 kg
Rationale: After two persons leave the group the average remains the same. That means the weight of the two persons = 42+30 = 72
So, the average the two persons = 36
That gives the answer 42-36 = 6
Answer B
Answer: (B) 6 kg
Question: A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
(A) 6 days
(B) 7 days
(C) 8 days
(D) 5 days
(E) 2 days
Rationale: 4/10 + 9/x = 1 => x = 15
1/10 + 1/15 = 1/6 => 6 days
\Answer:A
Answer: (A) 6 days
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?
(A) 24
(B) 66
(C) 88
(D) 92
(E) 22
Rationale: 10/40 + 10/30 + 10/x = 1
x = 24 days
Answer:A
Answer: (A) 24
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5
(B) 6
(C) 7
(D) 1
(E) 2
Rationale: 160 = (180*4*R)/100
R = 5%
Answer: A
Answer: (A) 5
Question: 25 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?
(A) 8 days
(B) 6 days
(C) 7 days
(D) 9 days
(E) 10 days
Rationale: 1 women's 1 day work = 1/175
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/175 + 10/140) = 1/10
5 women and 10 children will complete the work in 10 days.
Answer: E
Answer: (E) 10 days
Question: The speed of a boat in still water is 30kmph and the speed of the current is 15kmph. Find the speed downstream and upstream?
(A) 76,20 kmph
(B) 40,10 kmph
(C) 29 ,10,kmph
(D) 26,20 kmph
(E) 45,15 kmph
Rationale: Speed downstream = 30 + 15
= 45 kmph
Speed upstream = 30 - 15
= 15 kmph
Answer: E
Answer: (E) 45,15 kmph
Question: The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches.
(A) 33.25
(B) 33.5
(C) 34.25
(D) 35
(E) None
Rationale: Solution:
Total sum of last 4 matches,
= (10 * 38.9) – (6 * 42)
= 389 – 252 = 137.
Average = 137 /4 = 34.25
Answer: Option C
Answer: (C) 34.25
Question: Find the value for m?
19(m + n) + 17 = 19(-m + n) - 135
(A) 0
(B) -1
(C) 1
(D) 2
(E) -4
Rationale: 19m + 19n + 17 = -19m + 19n - 135
38m= -152 => m = -4
E
Answer: (E) -4
Question: How many multiples of 8 are there between 100 and 200 (both are inclusive)?
(A) 27
(B) 4
(C) 6
(D) 13.5
(E) 8
Rationale: the answer is (200-100)/8+1=13.5
Answer is D
Answer: (D) 13.5
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?
(A) 338
(B) 240
(C) 287
(D) 400
(E) 191
Rationale: 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
Answer: (D) 400
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?
(A) Rs. 1550
(B) Rs. 1650
(C) Rs. 1750
(D) Rs. 2000
(E) Rs. 2500
Rationale: 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 IS C
Answer: (C) Rs. 1750
Question: If 50% of a number is equal to one-third of another number, what is the ratio of first number to the second number?
(A) 2:5
(B) 1:4
(C) 3:7
(D) 6:11
(E) 2:3
Rationale: Let 50% of A = 1/3 B
then 50A/100 = 1B/3
A/2 = B/3
A/B = 2/3
A:B = 2:3
Answer is E
Answer: (E) 2:3
Question: Two horses begin running on an oval course at the same time. One runs each lap in 9 minutes; the other takes 15 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?
(A) 36
(B) 12
(C) 9
(D) 45/2
(E) 3
Rationale: The rate of the faster horse is 1/9 lap/minute;
The rate of the slower horse is 1/15 lap/minute;
Their relative rate is 1/9-1/15=2/45 lap/minute;
The faster horse to gain one full lap will need time=distance/rate=1/(2/45)=45/2 minutes.
Answer: D.
Answer: (D) 45/2
Question: In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is eleven years older than Ellen, how old is Aaron?
(A) 1–5
(B) 3–5
(C) 11–15
(D) 16–20
(E) 21–25
Rationale: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'
In ten years, David will be four times as old as Aaron --> d+10 = 4(a+10)
Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)
David is seven years older than Ellen --> d = e + 11
e+11-20 = 2e-40
e-9 = 2e-40
e = 31
d = 42
52 = 4a + 40
a = 3
Answer: B
Answer: (B) 3–5
Question: A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the amount of money that the student earned per day for the 16th day?
Amounts earned per day : $96 $84 $80 $70 $48
Number of days : 4 7 4 3 2
(A) (1) $96
(B) (2) $84
(C) (3) $80
(D) (4) $70
(E) (5) $48
Rationale: 4+7+4+3+2 = 20
The series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount.
1st to 2nd term = 48 (2 days)
3rd to 5th term = 70 (3 days)
6th to 9th term = 80 (4 days)
10th to 16th term = 84 (7 days)
Pick B
Answer: (B) (2) $84
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/4 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
(A) 0
(B) 1/15
(C) 2/15
(D) 1/8
(E) 2/10
Rationale: Suppose the water in each jug is L liters
CX x (1/4) = L
CX = 4L liters
CX is capacity of X
CY x (2/3) = L
CY = 3L/2 liters
CY is capacity of Y
Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X
Jug X's remaining water = L - L/2 = L/2
Fraction of X which contains water = water / CX
= (L/2)/ 4L
= 1/8
Answer will be D
Answer: (D) 1/8
Question: Ten coins are tossed simultaneously. In how many of the outcomes will the first coin turn up a head?
(A) 2^7
(B) 2^10
(C) 3 * 2^8
(D) 2^9
(E) 3 * 2^10
Rationale: Fix the third coin as H. The remaining 9 coins have 2^9 outcomes.
Ans:D
Answer: (D) 2^9
Question: Bill and Jane play a simple game involving two fair dice, each of which has six sides numbered from 1 to 6 (with an equal chance of landing on any side). Bill rolls the dice and his score is the total of the two dice. Jane then rolls the dice and her score is the total of her two dice. If Jane’s score is higher than Bill’s, she wins the game. What is the probability the Jane will win the game?
(A) 15/36
(B) 175/432
(C) 575/1296
(D) 583/1296
(E) 1/2
Rationale: There are three possible outcomes in the game:
1. B Wins
2. J Wins
3. Draw
So, 1=P(J)+P(B)+P(Draw)1=P(J)+P(B)+P(Draw)
The probability of B winning or J winning the game is same.
so, 1=2∗P(J)+P(Draw)1=2∗P(J)+P(Draw)
So, we need to calculate the probability of a draw.
A draw can happen when both will have the same sum.
The possible sums are - 2,3,4,5,6,7,8,9,10,11,12
Prob. of each sum is -
2 - 1,1 - 1/36
3 - 1 2, 2 1 - 2/36
4 - 1 3, 2 2, 3 1 - 3/36
5 - 1 4, 2 3, 3 2, 41 - 4/36
6 - 1 5, 2 4, 3 3, 4 2, 5 1 - 5/36
7 - 1 6, 2 5, 3 4, 4 3, 5 2, 61 - 6/36
8 - 2 6, 3 5, 4 4, 5 3, 6 2, - 5/36
9 - 3 6, 4 5, 5 4, 63 - 4/36
10 - 4 6, 5 5, 6 4 - 3/36
11 - 5 6, 6 5 - 2/36
12 - 6 6 - 1/36
Now, since both have to get the same sum, the probability will be same for both and the combined probability will be the square of the probabilities
i.e. 2 - (1/36)^2
3 - (2/36)^2
etc.
Squaring the probabilities and adding them will give 146/1296
So, P(D) = 146/1296
1 = 2*P(J) + P(D)
2*P(J) = 1150/1296
P(J) = 575 / 1296
Ans. C
Answer: (C) 575/1296
Question: A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets?
(A) 5
(B) 6
(C) 8
(D) None of these
(E) Cannot determined
Rationale: 7 + 4 + 0 + 3 + 1 + 5 + 1 + x = 26
21 + x = 26
x = 5 patrons have none of these animals
A)
Answer: (A) 5
Question: Two trains of equal are running on parallel lines in the same direction at 18 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 21
Rationale: 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/18 = 25/9 => x = 25.
Answer: A
Answer: (A) 25
Question: The tax on a commodity is diminished by 10% and its consumption increased by 25%. The effect on revenue is?
(A) 12% decrease
(B) 18% decrease
(C) 19% decrease
(D) 13% decrease
(E) 12.5% increase
Rationale: 100 * 100 = 10000
90 * 125 = 11250
-----------
10000-----------1250
100-----------? => 12.5% decrease
Answer: E
Answer: (E) 12.5% increase
Question: Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 2 times before stopping?
(A) 11/180
(B) 125/216
(C) 25/216
(D) 91/216
(E) 1/6
Rationale: The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:
The probability that Molly will roll the die once: P=1/6 (she gets 1on the first roll)
P = 1/6
Answer: E
Answer: (E) 1/6
Question: Wendy begins sanding a kitchen floor by herself and works for 7 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?
(A) 9/80 hours
(B) 3/20 hours
(C) 20/3 hours
(D) 80/9 hours
(E) 10 hours
Rationale: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.
Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.
If wendy works for 7 hours and is then joined by Bruce to finish the work in 2 more hours,
7/W + 2/W+2/B = 1 (1 denotes the total amount of work)
9/W + 2/B =1 and given B =20 hours.
Thus W = 10 hours , E is the correct answer.
Answer: (E) 10 hours
Question: Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 7 hours. How long would it take Taimour to paint the fence alone?
(A) 6 hours
(B) 8 hours
(C) 14 hours
(D) 21 hours
(E) 32 hours
Rationale: I believe the answer is D. Please see below for explanation.
if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T
if working together they can do the job in 8 hours we can infer 1 = 2T+T * 7 => 1/21
Working alone Taimour can do the job in 1 = 1/21 * hours => 21
Answer D
Answer: (D) 21 hours
Question: A bat is bought for Rs.800 and sold at a gain of 20% find its selling price
(A) Rs.920/-
(B) Rs.950/-
(C) Rs.860/-
(D) Rs.960/-
(E) None of these
Rationale: Explanation:
100 % ------> 800 (100 * 8 = 800)
120 % ------> 960 (120 * 8 = 960)
Selling price = Rs. 960/-
Answer: Option D
Answer: (D) Rs.960/-
Question: A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?
(A) 7 km
(B) 3 km
(C) 6 km
(D) 9 km
(E) 2 km
Rationale: Average speed = (2 * 3 * 2) / (3 + 2)
= 12/5 km/hr.
Distance traveled = 12/5 * 5 = 12 km.
Distance between house and school
= 12/2
= 6 km.
Answer: C
Answer: (C) 6 km
Question: If the mode of Set F is equal to the median of Set F, Set F could be
(A) [0, 1, 2, 2, 3, 4, 5, 6]
(B) [2, 2, 5, 7, 9]
(C) [x, x+1, x+2, x+2, x+3, x+3]
(D) [10, 102, 105, 105]
(E) [4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]
Rationale: Correct Answer: (C)
Set F could be The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set C is equal to the median of set C.
Answer: (C) [x, x+1, x+2, x+2, x+3, x+3]
Question: Three numbers are in the ratio 3:4:5 and their L.C.M. is 2400. Their H.C.F is?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let the numbers be 3x,4x and 5x
their L.C.M. = 60x
60x = 2400
x = 40
The numbers are 3*40 , 4*40 , 5*40
Hence required H.C.F. = 40
Answer is C
Answer: (C) 40
Question: There are a total of 12 students in Mr. Sri's gym class. Over the course of a badminton unit, each of the 12 students will compete exactly once against every other student in the class. How many total games of badminton will be played?
(A) 68
(B) 67
(C) 69
(D) 60
(E) 66
Rationale: there are 19 students , if each play with all other members .
then total games can be calculated as 11+10....+1 = 66.
alternate approach is to choose 2 distinct out of 12 = 12c2 = 66
Answer is E.
Answer: (E) 66
Question: Which of the following is the sum of all the even numbers between 1 and 97, inclusive?
(A) 2550
(B) 2450
(C) 2600
(D) 2449
(E) 2652
Rationale: This question can be solved withbunching.
We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 4, 6, 8.....96.
If you take the next smallest and next biggest numbers, you have...
4+96 = 100
This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...
44+56 = 100
46+54 = 100
48+52 = 100
There IS a middle number: 50; this number does NOT get paired up.
Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50-1 = 2449
Final Answer:
D
Answer: (D) 2449
Question: An article is bought for Rs.900 and sold for Rs.1000, find the gain percent?
(A) 11 2/5%
(B) 11 2/9%
(C) 11 1/9%
(D) 11 2/3%
(E) 11 3/3%
Rationale: 900 ---- 100
100 ---- ? => 11 1/9%
Answer: C
Answer: (C) 11 1/9%
Question: In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling price was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $5,100. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?
(A) 1. $15,600
(B) 2. $15,750
(C) 3. $17,100
(D) 4. $18,100
(E) 5. $19,200
Rationale: Edited the question as there was a typo.
Range = Highest Value - Lowest Value.
Range in May was 15,000 and the lowest price in May was 4,500, thus the highest price in May was 15,000+4,500=19,500.
Range in June was 16,500 and the lowest price in June was 5,100, thus the highest price in June was 16,500+5,100=21,600.
Lowest price of a car in May-June was 4,500 (May) and the highest price of a car in May-June was 21,600, thus the range for May-June is 21,600-4,500=17,100.
Answer: C.
Answer: (C) 3. $17,100
Question: A tour group of 25 people paid a total of $945 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22
(B) $23.94
(C) $36
(D) $25.20
(E) $30
Rationale: Soln:-
945/25=x+0.05x
945/25=1.05x
x=36
ANSWER:C
Answer: (C) $36
Question: A parking garage rents parking spaces for $10 per week or $40 per month. How much does a person save in a year by renting by the month rather than by the week?
(A)  $140
(B)  $160
(C)  $220
(D)  $40
(E)  $260
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 40 = 480$
520 - 480 = 40
Ans D
Answer: (D)  $40
Question: Which of the following fractions W has a decimal equivalent that is a terminating decimal?
(A) 10/189
(B) 15/196
(C) 16/225
(D) 25/144
(E) 39/128
Rationale: The fraction W will terminate if and only if the denominator has prime divisors only 2 and 5 or both.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: (E) 39/128
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference?
(A) 9 feet
(B) 12 feet
(C) 13 feet
(D) 15 feet
(E) 18 feet
Rationale: total circuit=12/4=3
total feet squirrel travels=3*3=9 feet
ANSWER:A
Answer: (A) 9 feet
Question: James and David work at a grocery shop with 12 other workers. For an internal review, 2 of the 12 workers will be randomly chosen to be interviewed. What is the probability that James and David will both be chosen?
(A) 1/26
(B) 1/36
(C) 1/46
(D) 1/66
(E) 1/56
Rationale: Probability that James and David will both be chosen out of 12 workers
= (2/12)*(1/11)
= 1/66
Answer D
Answer: (D) 1/66
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140 sq.units
(B) 149
(C) 148
(D) 17
(E) 143
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: Option A
Answer: (A) 140 sq.units
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $7 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
(A) 8n + 2
(B) 8n + 4
(C) 9n + 2
(D) 9n + 3
(E) 9n + 6
Rationale: its C
n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [7+ (n-1)]
= $ n+6
total cost
8n+n+6 = 9n+6
E
Answer: (E) 9n + 6
Question: What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle.
(A) 1 : 2
(B) 2 : 1
(C) 3 : 1
(D) Data inadequate
(E) None of these
Rationale: Area of ΔEBC = 1⁄2 × BC × EF
= 1⁄2 × BC × AB[Since, EF = AB]
Area of ΔEBC = 1⁄2 × area of ΔABCD
\ Required ratio = 2 : 1.
Answer B
Answer: (B) 2 : 1
Question: Winners will be announced the following day at 12 AM Pacific/1 PM Eastern Time.
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ?
(A) 13
(B) 21
(C) 23
(D) 24
(E) 25
Rationale: The reasoning is as follows:-
B) can't be answer because Y<X
D) can't be answer because it XY x YX will give 4 digit number. Thus wrong
E) can't be answer because it XY x YX will give 4 digit number. Thus wrong
A) can't be answer because it XY x YX will give 3 digit number but the middle digit will not be equal to Y. Thus wrong
C) is the correct answer because Y>xwill give 5 digit numbermiddle digit is Y
E
Answer: (E) 25
Question: The cost price of a radio is Rs.2300 and it was sold for Rs.1800, find the loss %?
(A) 18
(B) 99
(C) 27
(D) 26
(E) 21
Rationale: 2300 ---- 500
100 ---- ? => 21%
Answer: E
Answer: (E) 21
Question: The mean of 20 observations was 36. It was found later that an observation 25 was wrongly taken as 40. The corrected new mean is
(A) 30
(B) 25.4
(C) 40
(D) 35.25
(E) 26.55
Rationale: Explanation:
Correct Sum = (36 * 20 + 25 - 40) = 705
Correct mean = = 705/20 = 35.25
Answer: D
Answer: (D) 35.25
Question: For integers x and y, if (x+2)(y+3) is even then 4xy must be divisible by:
(A) 4
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: Just looking at the question, (x+2)(y+3) could be even*even, odd*even, or even*odd in order for the whole expression to be even.
However, just looking at 4xy, since x*y will always be an integer, it will always be divisible by 4. 4 divided by 4 is 1, hence preserving x*y.
Answer: A. 4
Answer: (A) 4
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?
(A) 12 sec
(B) 30 sec
(C) 36 sec
(D) 16 sec
(E) 18 sec
Rationale: 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
Answer: (C) 36 sec
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?
(A) 142
(B) 144
(C) 3680
(D) 3280
(E) 3680
Rationale: 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
Answer: (B) 144
Question: Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores 1/4, what is the value of Y/X ?
(A) 3.
(B) 2.
(C) 1/5
(D) 1/3.
(E) There isn't enough data to answer the question.
Rationale: Answer is C : 1/5
X - Y = (X + Y)/4
Solving for Y/X = 1/5
Answer: (C) 1/5
Question: A bowl was filled with 10 ounces of water, and 0.010 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
(A) 0.004%
(B) 0.04%
(C) 0.40%
(D) 5%
(E) 40%
Rationale: Total amount of water evaporated each day during a 50-day period = .008 * 50
=.010 * 100/2
= 1.0/2
= .5
percent of the original amount of water evaporated during this period = (.5/10) * 100%
= 5 %
Answer D
Answer: (D) 5%
Question: The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: 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
Answer: (C) 9