divelab/Sys2Bench huggingface dataset:
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
Options:
A)$900
B)$800
C)$1000
D)$700
E)$1500
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $200. So 1 / 4 of her savings is $200. So her original savings are 4 times $200 = $800
correct answer B
Answer: B
Question: I bought a book for Rs 60 , I sold off to a friend for Rs 70 but after a while i felt sorry , that i sold it and bought it back for Rs 80, how much loss did I incur?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: profit 70-60 = 10
b p =80-60 =20
20-10=10 loss.
ANSWER:A
Answer: A
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number T?
Options:
A)126
B)1386
C)3108
D)308
E)13986
Rationale: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.
So,Total possible numbers with these digits=3 X 3 X 3 =27.
First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D
Second, If you imagine numbers T with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.
You are left withanswer E.
Answer: E
Question: Due to 10% decrease in the price of sugar and John can buy 6kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)s. 1(23/27)
B)s. 2(2/9)
C)s. 2(1/9)
D)s. 3(2/7)
E)s. 4(2/9)
Rationale: Here r = 10 % ,x = 100 and A = 6 kg
Actual price of sugar = 10*100/((100-10 )*6) = Rs. 1(23/27)
A
Answer: A
Question: If a copier makes 20 copies every 6 seconds, then continues at this rate, how many minutes will it take to make 2,000 copies?
Options:
A)13
B)15
C)12
D)11
E)10
Rationale: 20 copies 6 seconds
2000 copies = (2000*6)/20 seconds
= 600/60 minutes
= 10 minutes
Answer : E
Answer: E
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?
Options:
A)Rs.200
B)Rs.250
C)Rs.290
D)Rs.300
E)Rs.310
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
B)
Answer: B
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)2007
B)2008
C)2002
D)2000
E)2001
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: D
Answer: D
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
Options:
A)233
B)37
C)25
D)27
E)11
Rationale: Explanation:
Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: C
Answer: C
Question: If a book is sold at 6% profit instead of 6% loss, it would have brought Rs 15 more. Find out the cost price of the book
Options:
A)75
B)72
C)60
D)70
E)125
Rationale: Let C.P. of the book be Rs. ’X’
Given, 1.06 X - 0.94X = 15
=> 0.12 X = 15 = 15/0.12 = Rs 125
ANSWER:E
Answer: E
Question: A man walking at 3/4th of the speed, reaches his office late by 2 hours. What is the usual time?
Options:
A)5 hours
B)3 hours
C)6 hours
D)12 hours
E)15 hours
Rationale: at 3/4th of speed he is late by' 2hrs'
x-3/4(x)=2
x=8
so 8-2=6hrs(since 2 hrs late)
ANSWER:C
Answer: C
Question: The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 660 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)
Options:
A)150π
B)240π
C)300π
D)480π
E)1,200π
Rationale: Distance traveled in 1 revolution = 2πr= 2π10/5280
Revolutions in one second= 660
Revolutions in 60 seconds (one minute)= 660*60
Total distance traveled= total revolutions *distance traveled in one revolution
660*60 *2π10/5280= 150π
A is the answer
Answer: A
Question: A man sells two flats at the rate of Rs.1.995 lakhs each. On one he gains 5% and on the other, he loses 5%. His gain or loss percent in the whole transaction is
Options:
A)0.25% loss
B)0.25% gain
C)2.5% loss
D)25% loss
E)None
Rationale: Solution
Loss %	= (5/ 10) ²%
=(0.5) ²%
= 0.25%.
Answer A
Answer: A
Question: Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 40 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?
Options:
A) 3
B) 5
C) 6
D) 8
E) 24
Rationale: Total work = 4*40 machine hrs
Time taken = 4* 40 /5 => 32 hours...
Thus all five machines, operating simultaneously will take ( 40 - 32 ) 8 hours..
Answer will be (D) 8
Answer: D
Question: Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Options:
A)15 min
B)20 min
C)25 min
D)30 min
E)12 min
Rationale: A in 1 min = 1/20
B in 1 min = 1/30
(A+B) in 1 min = 1/12
both pipes fill in =>12 min
ANSWER E
Answer: E
Question: add 20% of 40 and 25% of 60.
Options:
A)9.5
B)23
C)25
D)22
E)15
Rationale: 20% of 40 + 25% of 60
40*20/100+60*25/100
8+15=23
answer B
Answer: B
Question: If (2^x)(3^y) = 576, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
Options:
A)16
B)24
C)32
D)96
E)144
Rationale: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=6, y=2. now quickly 2^5(3^0)=32. Than answer should be number 3.
C
Answer: C
Question: find cp when sp=rs51.70:loss=12%
Options:
A)Rs 58.75
B)Rs 88.75
C)Rs 68.75
D)Rs 98.75
E)Rs 78.75
Rationale: cp=Rs{(100/88)*51.87}=Rs58.75
Answer is A.
Answer: A
Question: If 72 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?
Options:
A)120 hours
B)110 hours
C)100 hours
D)90 hours
E)80 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
15 : 72 : : 25 : x<=>(15 x x) =(72 x 25)<=>(72 x 25)/15 = 120
Hence, 15 men can do it in 60 hours
Answer is A.
Answer: A
Question: The sum of the even numbers between 1 and n is 85*86, where n is an odd number, then n=?
Options:
A)163
B)171
C)179
D)185
E)191
Rationale: Let n-1 = 2a.
2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 85*86
Then a = 85 and n = 171.
The answer is B.
Answer: B
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
Options:
A)2277
B)2987
C)4400
D)2678
E)2681
Rationale: X * (95/100) * (85/100) = 3553
X = 4400
Answer:C
Answer: C
Question: The difference between simple and compound interest on Rs. 1200 for one year at 10% per annum reckoned half-yearly is?
Options:
A)7
B)3
C)4
D)5
E)1
Rationale: S.I. = (1200 * 10 * 1)/100 = Rs. 120
C.I. = [1200 * (1 + 5/100)2 - 1200] = Rs. 123 Difference = (123 - 120) = Rs. 3.
Answer: B
Answer: B
Question: The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time T all five colored lights will all flash together at the exact same time?
Options:
A)0:03 AM
B)0:04 AM
C)0:06 AM
D)0:12 AM
E)0:24 AM
Rationale: Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
Answer: D
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?
Options:
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
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
Options:
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
Question: How many different positive integers are factors of 125 ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 125=5*25
Answer : B
Answer: B
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?
Options:
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
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
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
Options:
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
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?
Options:
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
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 :
Options:
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
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?
Options:
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
Question: If 9a - b = 10b + 80 = -12b - 2a, what is the value of 9a - 11b?
Options:
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
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)?
Options:
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
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)?
Options:
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
Question: Find the unit's digit in 264^102+264^103
Options:
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
Question: If Q:R = 6:7 and R:S = 8:9 then Q:R:S is
Options:
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
Question: What is the difference between the place value and the face value of 8 in the numeral 296827?
Options:
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
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%?
Options:
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
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?
Options:
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
Question: In an examination 35% of the students passed and 520 failed. How many students appeared for the examination?
Options:
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
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?
Options:
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
Question: In a single throw of a die, what is the probability of getting a number greater than 4?
Options:
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
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?
Options:
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
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?
Options:
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
Question: Find the annual income derived by investing $ 6800 in 10% stock at 136.
Options:
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
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)
Options:
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
Question: Which of the following fractions can be written as the difference of reciprocals of two consecutive integers
Options:
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
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?
Options:
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
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.
Options:
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
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?
Options:
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
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
Options:
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
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?
Options:
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
Question: A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
Options:
A)665
B)625
C)630
D)645
E)628
Rationale: 8 * 84 = 672 â€“ 7 = 665
ANSWER A
Answer: A
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?
Options:
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