mathewhe/aqua_rat huggingface dataset:
Question: Three investors, M, N, and O, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor M earned $ 3,500, how much money did investors N and O earn in total?
(A) $4,000
(B) $4,900
(C) $5,600
(D) $9,500
(E) $10,500
Rationale: Let profit for M = 5x
profit for N = 7x
profit for O = 8x
Investor A earned = 3500
5x = 3500
Total profit for N and O = 7x+ 8x = 15x
Therefore , 15x = 5x * 3 = 3500 * 3 = 10,500
Answer E
Answer: (E) $10,500
Question: The ages of two person differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
(A) 30, 10
(B) 25, 5
(C) 29, 9
(D) 50, 30
(E) 20,10
Rationale: Let their ages be x and (x + 20) years.
Then, 5(x - 5) = (x + 20 - 5)
=> 4x = 40
=>x =10
Their present ages are 30 years and 10 year.
ANSWER:A
Answer: (A) 30, 10
Question: How many different positive integers are factors of 125 ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 125=5*25
Answer : B
Answer: (B) 2
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs.150
(B) Rs.200
(C) Rs.250
(D) Rs.350
(E) Rs.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C)
Answer: (C) Rs.250
Question: A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red
(A) 23/42
(B) 19/42
(C) 7/32
(D) 16/39
(E) 17/39
Rationale: A red ball can be drawn in two mutually exclusive ways
(i) Selecting bag I and then drawing a red ball from it.
(ii) Selecting bag II and then drawing a red ball from it.
Let E1, E2 and A denote the events defined as follows:
E1 = selecting bag I,
E2 = selecting bag II
A = drawing a red ball
Since one of the two bags is selected randomly, therefore
P(E1) = 1/2 and P(E2) = 1/2
Now, P[A/E1] =Probability of drawing a red ball when the first bag has been selected = 4/7
P[A/E2] = Probability of drawing a red ball when the second bag has been selected = 2/6
Using the law of total probability, we have
P(red ball) = P(A) = P(E1)P(A/E1)+ P(E2)P(A/E2)
= 1/2x4/7x + 1/2x2/6 = 19/42
Answer is B
Answer: (B) 19/42
Question: In a contest, a bowl contains 5 keys, one of which will open a treasure chest and Four of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If priya is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
(A) 2/7
(B) 2/5
(C) 2/9
(D) 2/11
(E) 2/13
Rationale: The total possibilities existing while withdrawing two keys are: 5C2 = 10
For priya to win, 4 combinations exist assuming Key 1 to unlock the treasure E.g(1,2), (1,3)....(1,4)
P = 4/10= 2/5
Option B
Answer: (B) 2/5
Question: A person has uncovered a secret that was a mystery for ages. He transfers the data into his hard drive and encrypts the drive with a password. Then, he writes a line on a paper to remember the password.
The line says 'You force heaven to be empty'.
Can you decrypt the line to reveal the password if you know that the password is seven characters long that comprise of just letters and numbers?
(A) M472BMT
(B) U472BMT
(C) S472BMT
(D) D472BMT
(E) V472BMT
Rationale: B
The password is U472BMT.
Read aloud the line and you will sound something like "U Four Seven 2 B M T".
Answer: (B) U472BMT
Question: Bill has d animals, 24 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 36
Rationale: Total d animals, suppose each has price of x - total price = dx
now 24 were sold at profit of 10%, making equation - - 24*1.1x
now d-24 were sold at loss of 20%, making eqn --- (d-24)*0.8x
Now he made no profit or loss so,
dx = 24*1.1x + (d-24)*0.8x
solving for d, we get d=36
Ans E
Answer: (E) 36
Question: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
(A) -4 and -1
(B) -1 and 4
(C) -4 and 1
(D) -2 and 5
(E) 2 and 5
Rationale: 2x + 7 > 5
i.e 2x >5-7
i.e. 2x > -2
i.e. x > -1
Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4
i.e. -1 < x < 4
Answer: Option B
Answer: (B) -1 and 4
Question: A Man is on the escalator moving down wards and in a hurry he also steps down 10 steps manually and by the time he has 10 steps he is on the ground floor.Then by hearing some noise in the escalator he ran back in the same escalator with 10 times speed than the 1st time and he has 25 steps to reach the 1st floor. Then the question is how many steps will be visible if escalator is switched off?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: When man is moving downwards =10+n (n and x=steps taken by escalator)
When man is running upwards =25 - x
according to question,
when man walks 10 step in down then he should take 100 steps in up,
so,
10+n = 25-(n/4)
n=12
So, no. of steps will be 12.
ANSWER:C
Answer: (C) 12
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 55% average total marks, it is necessary for him in third yearly examination to secure marks :
(A) 300
(B) 325
(C) 400
(D) 450
(E) 500
Rationale: total marks:1500 for three exams
55% of 1500=825
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =825
X=325
ANSWER:B
Answer: (B) 325
Question: Two persons starting from the same place walk at a rate of 12kmph and 18kmph respectively. What time will they take to be 18km apart, if they walk in the same direction?
(A) 17 hrs
(B) 3 hrs
(C) 5 hrs
(D) 2 hrs
(E) 16 hrs
Rationale: The relative speed of the boys = 18kmph – 12kmph
= 6 kmph
Distance between them is 18 km
Time= 18km / 6 kmph = 3 hrs
Answer : B
Answer: (B) 3 hrs
Question: If 9a - b = 10b + 80 = -12b - 2a, what is the value of 9a - 11b?
(A) -4
(B) -2
(C) 0
(D) 2
(E) 80
Rationale: This implies 9a - b = 10b + 80, 9a -b = -12b -2a, 10b + 80 = -12b -2a
Manipulating the second equation gives us 9a - b = 10b +80 ==> 9a - 11b = 80
Answer is E
Answer: (E) 80
Question: A train running at 50 km/hr, passes a man walking on the platform at 7 km/hr in same direction as that of train in 15 sec. If this train takes 30 seconds to cross the platform then find the length of train (L1) and length of platform (L2)?
(A) L1 =179.1 m, L2 = 237.3 m
(B) L1 = 150.5 m, L2 = 300 m
(C) L1 = 237.3 m, L2 = 179.1 m
(D) L1 = 300 m, L2 = 150.5 m
(E) None of these
Rationale: EXPLANATION:
Given: Speed of train = 50 km/hr, time required to cross the platform = 30 sec, time required to cross man standing on platform = 15 sec.
1) Convert km/hr into m/s
- 50 km/hr = 50 x	5/18= 13.88 m/s
- 7 km/hr = 7 x	5/18=1.94 m/s
2) The speed of train relative to man = ( 13.88 – 1.94) = 11.94 m/s ---- (The values are subtracted because the train and man move in same direction)
3) Length of train = (Relative speed x Time)
= (11.94) x (15) = 179.1 m
We know,
Speed =	(L1 + L2)/Time
13.88 =	(L1 + L2)/30 ---- consider L1 as length of train and L2 as length of platform
(L1 + L2) = 416. 4
L2 = 416.4 – 179.1 = 237.3 m
ANSWER IS A
Answer: (A) L1 =179.1 m, L2 = 237.3 m
Question: When a positive integer A is divided by 5 and 3, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 5 and 3, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 18
Rationale: A = 5k+1 = 3j+2
B = 5m+1 = 3n+2
A-B = 5(k-m) = 3(j-n)
A-B is a multiple of both 5 and 3, so it is a multiple of 15.
The answer is D.
Answer: (D) 15
Question: Find the unit's digit in 264^102+264^103
(A) 0
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102+264103264102+264103
= unit's digit in (6+4)=0
A
Answer: (A) 0
Question: If Q:R = 6:7 and R:S = 8:9 then Q:R:S is
(A) 48:56:68
(B) 48:56:66
(C) 48:56:63
(D) 44:52:63
(E) 48:50:63
Rationale: Solution:
Q/R = 6/7;
R/S = 8/9;
Q:R:S = 6*8:7*8:7*9 = 48:56:63.
Answer: Option C
Answer: (C) 48:56:63
Question: What is the difference between the place value and the face value of 8 in the numeral 296827?
(A) None of these
(B) 792
(C) 794
(D) 7994
(E) 795
Rationale: Explanation:
Place value of 8 = 800
Face value of 8 = 8
Difference = 800 - 8 = 792
Answer: B
Answer: (B) 792
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
(A) 21000
(B) 22888
(C) 26662
(D) 2992
(E) 8212
Rationale: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs. 21000.Answer:A
Answer: (A) 21000
Question: Three beauty pageant finalists-Cindy, Amy and Linda-The winner was musician. The one who was not last or first was a math major. The one who came in third had black hair. Linda had red hair. Amy had no musical abilities. Who was first?
(A) Cindy
(B) Amy
(C) Linda
(D) Sandy
(E) none
Rationale: she cant b 3rd bcoz she have red hair
mean she (Linda)
is 1 n 2.
now 1 have musician
but Amby cant first bcoz he have not such abilities.
so 1 n 2 may be
Linda or Cindy.
or 2 n 3 may be Amby or Cindy
Common is 2. so
so
cindy is second
then 1 is Linda
3 is Amby
ANSWER:C
Answer: (C) Linda
Question: In an examination 35% of the students passed and 520 failed. How many students appeared for the examination?
(A) A)540
(B) B)400
(C) C)800
(D) D)650
(E) E)840
Rationale: Let the number of students appeared be x
then, 65% of x = 520
65x/100 = 520
x = 520*100/65 = 800
Answer is C
Answer: (C) C)800
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 4 seconds.What is the length of the fast train?
(A) 23 m
(B) 22 2/9 m
(C) 27m
(D) 27 7/9m
(E) 29 7/9m
Rationale: relative speed=20kmph=50/9m/sec
length of the train=50/9*4= 22 2/9m
ANSWER:B
Answer: (B) 22 2/9 m
Question: In a single throw of a die, what is the probability of getting a number greater than 4?
(A) 1/3
(B) 1/4
(C) 2/3
(D) 2/5
(E) 3/7
Rationale: S = {1,2,3,4,5,6}
E = {5,6}
Probability = 2/6 = 1/3
Answer is A
Answer: (A) 1/3
Question: The avearge 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
Required average	=(38.9 x 10)-(42 x 6)/ 4
= 137 / 4.
= 34.25
Answer C
Answer: (C) 34.25
Question: An air conditioner can coo the hall in 10 minutes while another takes 15 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
(A) 5 minutes
(B) 6 minutes
(C) 3 minutes
(D) 8 minutes
(E) 10 minutes
Rationale: Take LCM of 10 and 15 = 30
10*3=30/ 15*2=30.
So if both are switched on together , room cooled in 30/(3+2)=30/5=6 minutes
ANSWER: B
Answer: (B) 6 minutes
Question: Find the annual income derived by investing $ 6800 in 10% stock at 136.
(A) 550
(B) 500
(C) 250
(D) 300
(E) 400
Rationale: By investing $ 136, income obtained = $ 10.
By investing $ 6800, income obtained = $ [(10/136)*6800] = $ 500.
Answer B.
Answer: (B) 500
Question: A certain farmer pays $60 per acre per month to rent farmland. How much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet? (43,560 square feet = 1 acre)
(A) $5,330
(B) $3,360
(C) $1,350
(D) $600
(E) $150
Rationale: Basically the question an error. 1 acre = 43,560 square feet and if it is then the answer is 600 (D)
Answer: (D) $600
Question: Which of the following fractions can be written as the difference of reciprocals of two consecutive integers
(A) 1/24
(B) 7/30
(C) 12/45
(D) 1/56
(E) 1/72
Rationale: Difference of reciprocals means 1 has to be in the numerator;
So option BD can be ignored
For option A, BE, we require to search two consecutive numbers whose product is the denominator
24 = 4 * 6 ......... Ignore
56= 7 * 8 ........ Answer
72 = 8 * 9 ................ Ignore
Answer = D
Answer: (D) 1/56
Question: A reduction of 25% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) 2.8
(B) 2.3
(C) 2.5
(D) 3.3
(E) 2.9
Rationale: 100*(25/100) = 25 --- 10
? --- 1 => Rs.2.5
100 --- 75
? --- 2.5 => Rs.3.3
Answer: D
Answer: (D) 3.3
Question: The ages of 2 persons differ by 21 years. If 15 years ago the elder one be 8 times as old as the younger one, find the present age of elder person.
(A) 30
(B) 48.5
(C) 50.4
(D) 62.6
(E) 47.9
Rationale: age of the younger person = x
age of the elder person = x+21
8(x-15) = x+21-15
x= 18
age of elder person = 18+21=39
Answer is E
Answer: (E) 47.9
Question: A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability D that the sum of the three numbers on the balls selected from the box will be odd?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);
P(OOO)=(1/2)^3;
P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);
So finally D=1/8+3/8=1/2.
Answer: C.
Answer: (C) 1/2
Question: Tough and Tricky questions: Work/Rate Problems.
A group of 4 junior lawyers require 6 hours to complete a legal research assignment. How many hours would it take a group of two legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?
Source: Chili Hot GMAT
(A) 8
(B) 10
(C) 9
(D) 6
(E) 5
Rationale: # of people times the # of hours:
4*6 = 24 --> 6 lawyers do 24worksin 5 hours.
2*12/3 = 8 --> 3 assistants do 8 worksin 4 hours
So, since the amount of work the assistants do is half the work the lawyers do, the time will be double, soANS A
Answer: (A) 8
Question: A block of wood has dimensions 10cm x 10cm x 100cm. The block is painted red and then cut evenly at the 50 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?
(A) 4.5%
(B) 8.3%
(C) 10.2%
(D) 12.5%
(E) 15.3%
Rationale: The area of each half is 100+4(500)+100 = 2200
The area that is not painted is 100.
The fraction that is not painted is 100/2200 = 1/22 = 4.5%
The answer is A.
Answer: (A) 4.5%
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?
(A) 665
(B) 625
(C) 630
(D) 645
(E) 628
Rationale: 8 * 84 = 672 â€“ 7 = 665
ANSWER A
Answer: (A) 665
Question: A man purchased 3 blankets @ Rs.200 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?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: 10 * 150 = 1500
3 * 200 + 5 * 150 = 1350
1350 – 1050 = 300
ANSWER:C
Answer: (C) 300
Question: At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.80. What is the price of 2 doughnuts?
(A) $ 0.55
(B) $ 1.00
(C) $ 1.10
(D) $ 0.90
(E) $ 1.80
Rationale: 3D + C = 2.25......(1)
2D + C = 1.8........(2)
(1) - (2) --> D = 0.45 --> 2D = 0.9
Answer: D
Answer: (D) $ 0.90
Question: Johnny makes $8.25 per hour at his work. If he works 2 hours, how much money will he earn?
(A) $30.50
(B) $16.50
(C) $28.50
(D) $12
(E) $9.60
Rationale: 8.25*2=16.50. Answer is B.
Answer: (B) $16.50
Question: Find large number from below question The difference of two numbers is 1345. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1235
(B) 1345
(C) 1678
(D) 1767
(E) 1611
Rationale: Let the smaller number be x. Then larger number = (x + 1345).
x + 1345 = 6x + 15
5x = 1330
x = 266
Large number = 266+1345 = 1611
E
Answer: (E) 1611
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,840,397 minutes earlier? (Assume standard time in one location.)
(A) 6:35
(B) 6:33
(C) 6:30
(D) 6:28
(E) 6:24
Rationale: 6:27 minus 2,840,397 in any way must end with 0.
The only answer choice which ends with 0 is C.
The answer is C.
Answer: (C) 6:30
Question: Find the odd man out
3, 5, 12, 39, 154, 772, 4634
(A) 39
(B) 154
(C) 5
(D) 3
(E) 12
Rationale: 3x1+2=5
5x2+2=12
12x3+2=38
38x4+2=154 .. and so on.
ANSWER:A
Answer: (A) 39
Question: Find the missing figures : ?% of 25 = 20125
(A) 4.5
(B) 6.5
(C) 2.5
(D) 7.5
(E) 8.5
Rationale: Let x% of 25 = 2.125. Then , (x/100)*25 = 2.125
X = (2.125 * 4) = 8.5.
Answer is E.
Answer: (E) 8.5
Question: If a and b are integers and (a*b)^5 = 64y, y could be:
(A) 16
(B) 32
(C) 64
(D) 128
(E) 256
Rationale: Distribute the exponent.
a^5 * b^5 = 64 y
Find the prime factorization of 64. This is 2^5 *2^1
We need 2^4 (or some other power of 2 that will give us a multiple of 2^5 as our second term).
2^4 = 16
The answer is A.
Answer: (A) 16
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?
(A) 80
(B) 86
(C) 92
(D) 98
(E) 104
Rationale: 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.
Answer: (C) 92
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 140 pages?
(A) 10 hours 30 mins
(B) 8 hours
(C) 9 hours
(D) 7 hours
(E) 6 hours
Rationale: Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 140 pages when Anil and Suresh work together = 140 × 3 /40 = 21/2
= 10 1/2 hours = 10 hour 30 minutes
Answer is A.
Answer: (A) 10 hours 30 mins
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
(A) 140
(B) 146
(C) 152
(D) 162
(E) 170
Rationale: Number of newborns that can die in first month = 1/10 * 200 = 20
Survived = 180
Number of newborns that can die in second month = 1/10 * 180 = 18
Survived = 162
Number of newborns that can die in third month = 1/10 * 162 = 16
Survived = 146
Answer:B
Answer: (B) 146
Question: 54671 - 18456 - 33466 = ?
(A) 2749
(B) 5449
(C) 6749
(D) 6449
(E) 6468
Rationale: A
If we calculate we will get 2749
Answer: (A) 2749
Question: TOM traveled the entire 20 miles trip. If he did the first 10miles of at a constant rate 12 miles per hour and the remaining trip of at a constant rate 10 miles per hour, what is the his average speed, in miles per hour?
(A) 12.45 mph
(B) 11.25 mph
(C) 10.95 mph
(D) 10.91 mph
(E) 10.56 mph
Rationale: avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (10+10) / ((10/12)+(10/10) =120/11 = 10.91 mph D
Answer: (D) 10.91 mph
Question: If x^2 – x = 2, then one possible value of x – 4 =
(A) -9
(B) -5
(C) -3
(D) -1
(E) 5
Rationale: x^2 –x = 2
i.e. x^2 – x - 2 = 0
i.e. x^2 +x -2x -2 = 0
i.e. (x-2)(x+1) = 0
i.e. x = 2 or -1
i.e. x-4 = 2-4 or -1-4
i.e. x-4 = -2 or -5
Answer: Option B
Answer: (B) -5
Question: Train X and train Y pass one another traveling in opposite directions. Thirty minutes later they are 100 miles apart. If train X’s constant speed is 40 miles per hour greater than train Y’s, how far does train X travel during that time?
(A) 28
(B) 40
(C) 60
(D) 72
(E) 80
Rationale: Let the rate of the Train Y be R
Then the rate of the Train X will be R+40 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+40) [add the rates] i.e. 2R+40
d=100 and t = 30 min i.e 30/60 hr
using RTD table, (2R+40) * 30/60 = 100 ==> R= 80 miles/hr
So the rate of train X is 120 miles/hr (since R+40)
The distance traveled by Train X in 30 min is R*T = 120 * 30/60 = 60 miles (C)
Answer: (C) 60
Question: 7 points are marked on a straight line and another 4 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
(A) 91
(B) 126
(C) 196
(D) 21
(E) 14
Rationale: getting the answer 126 which is not in the choices, what is the source of the problem?
7C2* 4C1 + 4C2* 7C1 = 126
B
Answer: (B) 126
Question: Which of the following is not the square of an integer?
(A) 275625
(B) 385641
(C) 426437
(D) 532900
(E) 318096
Rationale: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is C.
Answer: (C) 426437
Question: Two marathoners begin their training run on the river bank at the same time. Sally Slow runs due south at 5 miles/hour, while Freddy Fast runs due North at 10 miles/hour. At this pace, how long before they have run 26.2 miles away from each other?
(A) 1.75 hours
(B) 1.634 hours
(C) 1.5 hours
(D) 3 hours
(E) 2.92 hours
Rationale: The runners run a combined pace of 15 miles per hour (10+5).
26.2 miles/ 15 miles/hour= 1.75 hours
Answer is A
Answer: (A) 1.75 hours
Question: A portion of the 95% solution of dye was replaced with an equal amount of 20% solution of dye. As a result, 40% solution of dye resulted. What part of the original dye was replaced?
(A) 2/5
(B) 3/7
(C) 5/17
(D) 11/15
(E) 10/11
Rationale: This is a weighted average question. Say x% of the dye was replaced --> equate the amount of dye in the solution: 0.95(1-x)+0.2*x=0.4 --> x=11/15.
Answer: D.
Answer: (D) 11/15
Question: Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 8 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?
(A) 37.5 kilometers per hour
(B) 48 kilometers per hour
(C) 51.7 kilometers per hour
(D) 75 kilometers per hour
(E) 100 kilometers per hour
Rationale: Time taken to reach first 40 km is 40/60 = 2/3 hr
Time taken to reach next 40 km is 40/60 = 2/3 hr
Time taken to reach next 20 km is 20/60 = 1/3 hr
Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...
Each stop was of 8 min , so two 8min break = 2*2/15 => 4/15 hr
Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+4/15)= 29/15 hrs
So, Average speed is 100/(29/15) = 51.7 km/hour
Answer will be (C)
Answer: (C) 51.7 kilometers per hour