mathewhe/aqua_rat huggingface dataset:
Question: Suppose we have six marbles: 3 blue marbles, 2 yellow marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
(A) 190
(B) 180
(C) 200
(D) 240
(E) 160
Rationale: # ways to distribute Blue marbels(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute yellow marbels(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbels(1) is :
3 ways
total number of ways = 10*6 *3 = 180
B
Answer: (B) 180
Question: If s is the product of the integers from 10 to 20 inclusive, and if t is the product of the integers from 10 to 21 inclusive, what is 1/s + 1/t in terms of t?
(A) 22/t
(B) 24/t
(C) 26/t
(D) 28/t
(E) 30/t
Rationale: Similarly in the actual problem
s =t/21. 1/s = 1/(t/21) or 1/s = 21/t
1/s + 1/t = 21/t + 1/t = 22/t
A
Answer: (A) 22/t
Question: Sam purchased 20 dozens of shirts at the rate of $ 375 per dozen. He sold each one of them at the rate of $ 33. What was his percentage profit?
(A) 5%
(B) 4.8%
(C) 5.6%
(D) 8.2%
(E) 6%
Rationale: C
5.6%
C.P. of 1 shirt = 375/12 = $ 31.25
S.P of 1 shirt = $ 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6%
Answer: (C) 5.6%
Question: If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: t=4p
since t = 4p thenevendivisors are:
4p/4p= 1
4p/2p= 2
4p/4= p
4p/2= 2p
so the answer is (C)
Answer: (C)  Four
Question: A bag contains 50 tickets numbered 1,2,3,4......50 of which five are drawn at random and arranged in ascending order of magnitude.Find the probability that third drawn ticket is equal to 30.
(A) 551/15134
(B) 551/15139
(C) 551/15132
(D) 551/15196
(E) 551/15766
Rationale: Explanation:
Total number of elementary events = \inline {\color{Black}50C_{5}}
Given,third ticket =30
=> first and second should come from tickets numbered 1 to 29 = \inline {\color{Black}29C_{2}} ways and remaining two in \inline {\color{Black}20C_{2}} ways.
Therfore,favourable number of events = \inline {\color{Black}29C_{2}\times 20C_{2}}
Hence,required probability = \inline {\color{Blue}(29C_{2}\times 20C_{2})/50C_{5}} =551 / 15134
Answer: A) 551/15134
Answer: (A) 551/15134
Question: R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A) None
(B) Two
(C) Four
(D) Five
(E) Seven
Rationale: squares < 50 {1,4,9,16,25,36,49 }
S = {1,9,25,49}
R = {1,3,.....49}
Hence C.
Answer: (C) Four
Question: A certain essay consists of 16 paragraphs. Each paragraph contains at least 120 words but not more than 130 words. Which of the following could be the total number of words in the essay?
(A) 1440
(B) 1540
(C) 1640
(D) 1740
(E) 1940
Rationale: lets consider minimum no of words ... 16 * 120 = 1920
Lets consider maximum no of words .... 16*130= 2080
answer should be one of these two values or should lie between these two values ...
only 1 option E - 1940
Answer: (E) 1940
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
(A) 50028
(B) 50035
(C) 50400
(D) 50723
(E) 33030
Rationale: This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters =	7!/2!	= 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in	5!/3!	= 20 ways.
Required number of ways = (2520 x 20) = 50400.
Answer:D
Answer: (D) 50723
Question: A boy has 5 pens out of which a pair is to be selected for an examination. At most, how many different pairs are possible?
(A) 20
(B) 10
(C) 5
(D) 40
(E) 10
Rationale: N=5C2=5!/(3!2!)=5*2=10
Correct Option: E
Answer: (E) 10
Question: 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 24 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?
(A) 15 km/hr
(B) 16 km/hr
(C) 17 km/hr
(D) 18 km/hr
(E) None of these
Rationale: Explanation :
Total distance covered by B=24*6=144kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=144/8=18 km/hr
Answer : D
Answer: (D) 18 km/hr
Question: Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
(A) 1 year
(B) 3 year
(C) 6 year
(D) 8 year
(E) 2 year
Rationale: 6 * 22 = 132
7 * 19 = 133
--------------
1
Answer:A
Answer: (A) 1 year
Question: A certain psychologist charges $30 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $400, what is the total charge to a patient who receives only 3 hours of therapy ?
(A)  $120
(B)  $135
(C)  $150
(D)  $165
(E)  $252
Rationale: Let the charge for first hour = x+30
then charge for each additional hour = x
x+30 + 4x = 400
=> 5x = 370
=> x = 74
Total charge for patient for 3 hours of therapy = x+30 + 2x = 3x+30
= 252 $
Answer E
Answer: (E)  $252
Question: C is a working partner and B and A is a sleeping partner in a business. A puts in 50,000 and B 60,000 and C puts in 40000. C gets 25% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of A in profit of 20000.
(A) 4800
(B) 4500
(C) 5400
(D) 5000
(E) None of these
Rationale: The amount C gets for managing
= 25% of Rs. 20000 = 5000
Remaining profit = 20000 – 5000 = 15000
This is to be divided in the ratio 5 : 6 : 4
Share of A = 5/15 of 15000 = 5000
Answer D
Answer: (D) 5000
Question: By selling 24 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 9
(C) 16
(D) 6
(E) 4
Rationale: 80% --- 24
120% --- ?
80/120 * 24 = 16
Answer: C
Answer: (C) 16
Question: A sum of money is distributed among A,B,C,D in the proportion of 5:2:4:3. If C gets $1000 more than D, what is the B's share?
(A) $1000
(B) $2000
(C) $2500
(D) $2850
(E) $2950
Rationale: Let the shares of A,B,C,D are 5x,2x,4x,3x
4x-3x = 1000
x = 1000
B's share = 2x = $2000
Answer is B
Answer: (B) $2000
Question: If Renee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased?
(A) 1/4
(B) 1/5
(C) 1/10
(D) 2/25
(E) 1/20
Rationale: 5% is 5/100 = 1/20
10% is 10/100 = 1/10
The increase must be greater than 1/20 and less than 1/10.
1/4, 1/5, and 1/10 are not less than 1/10.
1/20 is not greater than 1/20.
The only option left is 2/25, which is in the specified range.
ANSWER:D
Answer: (D) 2/25
Question: Number of prime numbers between 20 and 60 is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: total 9=23, 29, 31, 37, 41, 43, 47, 53, 59
ANSWER:E
Answer: (E) 9
Question: In a box, there are 4 blue, 6 white and 5 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?
(A) 3/16
(B) 5/15
(C) 8/32
(D) 2/32
(E) 9/32
Rationale: Total number of bulbs = (4 + 6 + 5) = 15.
Let E = event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.
Therefore, P(E)=5/15
ANSWER:B
Answer: (B) 5/15
Question: A man bought 10 crates of bananas for $100 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 100 percent of the total cost?
(A) $35
(B) $45
(C) $50
(D) $25
(E) $40
Rationale: As given, after lost, the remaining 8 crates total cost = $100
So, 1 crate cost = 100/8 = 12.5
To get 100% profit, 1 crate cost should be =12.5+12.5*100/100 =$25
Answer : D
Answer: (D) $25
Question: How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 11, without any of the digits repeating?
(A) 216
(B) 96
(C) 81
(D) 72
(E) 100
Rationale: 0,1,2,3,4,5
One digit will have to remain out for all 5 digit numbers;
if 0 is out; Leftover digits will be 1,2,3,4,5 = Sum(1,2,3,4,5)=15. ignore
if 1 is out; Leftover digits will be 0,2,3,4,5 = Sum(0,2,3,4,5)=14. Ignore
if 3 is out; Leftover digits will be 0,1,2,4,5 = Sum(0,1,2,4,5)=12. ignore
if 4 is out; Leftover digits will be 0,1,2,3,5 = Sum(0,1,2,3,5)=11. =96
if 5 is out; Leftover digits will be 0,1,2,3,4 = Sum(0,1,2,3,4)=10. Ignore
Total count of numbers divisible by 11 = 96 = 96
Ans:B
Answer: (B) 96
Question: If n = 2.0423 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n?
(A)  -0.0053
(B)  -0.0023
(C)  0.0007
(D)  0.0047
(E)  0.0153
Rationale: n*=2.04
n*-n=2.04-2.0423
-0.0023
Answer: B
Answer: (B)  -0.0023
Question: A seven-digit number comprises of only 2's and 3's. How many of these are multiples of 12?
(A) 11
(B) 12
(C) 10
(D) 22
(E) 44
Rationale: DETAILED SOLUTION
Number should be a multiple of 3 and 4. So, the sum of the digits should be a multiple of 3. WE can either have all seven digits as 3, or have three 2's and four 3's, or six 2's and a 3. (The number of 2's should be a multiple of 3).
For the number to be a multiple of 4, the last 2 digits should be 32. Now, let us combine these two.
All seven 3's - No possibility.
Three 2's and four 3's - The first 5 digits should have two 2's and three 3's in some order. No of possibilities = 5!3!2! = 10
Six 2's and one 3 - The first 5 digits should all be 2's. So, there is only one number 2222232.
So, there are a total of 10 + 1 = 11 solutions.
CORRECT ANSWER : A.
Answer: (A) 11
Question: Which of the following fractions is the largest ?
(A) 7/8
(B) 13/16
(C) 31/40
(D) 63/80
(E) 72/80
Rationale: LCM of 8, 16, 40 , 80 is 80
7/8 * 10/10 = 70/80
16/16 * 5/5 = 65/80
31/40 * 2/2 = 62/80
63/80
Clearly 70/80 > 65/80 >63/80 >62/80
hence 7/8 is largest ANSWER : A
Answer: (A) 7/8
Question: A searchlight on top of the watch-tower makes 6 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 1
Rationale: 6 revolutions per minute = 1 revolution every 10 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 10 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 10 seconds) = 1 - P (man in dark for max of 10 seconds) = 1 - 10/10 = 1 - 1 = 0
or the other way would be:
P(man in dark for at least 10 seconds) is like saying he can be in dark for 5,6,7...all the way to 10 seconds because that is the max. In this approach it would be 10/10 seconds = 1.
Answer is E
Answer: (E) 1
Question: Suppose that fresh fruit contains 32% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100kg of fresh fruit?
(A) A)32kg
(B) B)40kg
(C) C)52kg
(D) D)80kg
(E) E)85kg
Rationale: Quantity of pulp in 100kg of fresh fruits = (100-32)% of 100kg = 68 kg
Let the quantity of dry fruit obtained be x kg
then, (100-20)% of x = 68
(80/100)*x = 68
x = 85
correct option is E
Answer: (E) E)85kg
Question: A woman is 18 years older than her son. In two years, her age will be twice the age of her son. The present age of her son is:
(A) 20
(B) 16
(C) 22
(D) 23
(E) 24
Rationale: Let the son's present age be x years. Then, woman's present age = (x + 18) years.
(x + 18) + 2 = 2(x + 2)
x + 20 = 2x + 4
x = 16.
Answer:B
Answer: (B) 16
Question: Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 4, what is the probability that one of the two cards drawn is numbered 2 ?
(A) 1/3
(B) 1/2
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: (2,2) (3,1) (1,3) – only 3 possible scenarios for sum to be 4.
From this three cases, only one we have 2. So, the probability is 1 chances out of 3 that the one that occurred had 2: P=1/3.
Answer: A.
Answer: (A) 1/3
Question: A room contains 160 people, 25 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 10
(B) 20
(C) 40
(D) 60
(E) 120
Rationale: Say group of x people left the room.
# of women in the room was 0.25*160=40;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(160-x);
So, 40-0.3x= 0.1(160-x) --> x=120.
Answer: E.
Answer: (E) 120
Question: A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price V per t-shirt that the vendor paid for these purchases?
(A) $12.20
(B) $12.50
(C) $12.55
(D) $12.70
(E) $13.00
Rationale: Correct Answer: A
Explanation: The relevant formula for this problem is Average V= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.
NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice A is a possibility.
Answer: (A) $12.20
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 3
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
A)
Answer: (A) 3
Question: A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour?
(A) 15 kmph
(B) 5 kmph
(C) 10 kmph
(D) Data inadequate
(E) None of these
Rationale: Here downstream speed = 15 km/hr and upstream speed = 5 km/hr
∴ Speed of the boat = 15+5/2=10km/h
Answer C
Answer: (C) 10 kmph
Question: A boat can move upstream at 50 kmph and downstream at 30 kmph, then the speed of the current is?
(A) 10
(B) 9
(C) 5
(D) 9
(E) 5
Rationale: US = 50
DS = 30
M = (50 - 30)/2 = 10
Answer is A
Answer: (A) 10
Question: The area of a parallelogram is 288sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 7
(D) 62
(E) 12
Rationale: 2x * x = 288 => x= 12
Answer: E
Answer: (E) 12
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 14
(B) 61
(C) 25
(D) 72
(E) 62
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer:C
Answer: (C) 25
Question: A picture is copied onto a sheet of paper 8.5 inches by 10 inches. A 1.5 inch margin is left all around. What area in square inches does the picture cover?
(A) 76
(B) 65
(C) 59.5
(D) 49
(E) 38.5
Rationale: Area covered by picture = (8.5-3)*(10-3)
=5.5*7
=38.5
Answer E
Answer: (E) 38.5
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, the three numbers in order are?
(A) 48,96,24
(B) 48,24,96
(C) 96,24,48
(D) 96,48,24
(E) 98,48,24
Rationale: Let the numbers be 2X, X and 4X
Average = (2X + X + 4X)/3
=> 7X/3 = 56
=> X = (3 x 56)/7 = 24
Hence, the numbers in order are 48, 24 and 96
ANSWER:B
Answer: (B) 48,24,96
Question: What percent of 15 kg is 30 gms ?
(A) 25
(B) 66
(C) 20
(D) 19
(E) 17
Rationale: Explanation:
Required percentage = (30/15000 * 100)% = 1/5% = 0.2%
Answer: C) .20%
Answer: (C) 20
Question: Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?
(A) 11
(B) 12
(C) 22
(D) 24
(E) 44
Rationale: 22 times in a day.
12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes)
ANSWER:C
Answer: (C) 22
Question: A jogger running at 9 km/hr along side a railway track is 290 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 67 sec
(B) 89 sec
(C) 36 sec
(D) 87 sec
(E) 41 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 290 + 120 =410 m.
Time taken = 410/10
=41 sec.
Answer: E
Answer: (E) 41 sec
Question: The probability of a team winning a match given Matt is playing the match is 0.70. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) 0.8321
(B) 0.8484
(C) 0.8571
(D) 0.7531
(E) 0.8213
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.70*80 = 56
Out of 20 matches Matt does not play in, team wins 0.5*20 = 10.
So, out of 100 matches 56 + 10 = 66 are won.
It is known that the team has won the last match. Out of 66 matches won, Matt is in 56: 56/66 = 0.8484...
Answer: B.
Answer: (B) 0.8484
Question: A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 15
matches are totally played, how many teams participated?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 2 ways to solve this problem..
summation(x)=n(n-1)/2
n(n-1)/2=15;
n^2-n-30=0
Ans : 6
ANSWER:C
Answer: (C) 6
Question: A man has Rs. 464 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 87
(B) 90
(C) 95
(D) 98
(E) 100
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 464
16x = 464
x = 29.
Hence, total number of notes = 3x = 87.
A
Answer: (A) 87
Question: A jar was full with honey. A person used to draw out 20% of the honey from the jar and replaced it with sugar solution. He has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was filled with the sugar solution. The initial amount of honey in the jar was filled with the sugar solution. The initial amount of honey in the jar was:
(A) 1.25 kg
(B) 1.29 kg
(C) 1.85 kg
(D) 3.25 kg
(E) 1.23 kg
Rationale: Answer: A) 1.25 kg
Answer: (A) 1.25 kg
Question: An automobile parts supplier charges $25 per package of gaskets. When a customer orders more than 10 packages of gaskets, the supplier charges 4/5 the price for each package in excess of 10. During a certain week, the supplier sold 60 packages of gaskets. If 15 percent of the gaskets went to Company X, 15 percent to Company Y, and the rest to Company Z, what was the total amount, in dollars, that the parts supplier received in payment for the gaskets?
(A) 1340
(B) 1445
(C) 1375
(D) 1415
(E) 1455
Rationale: $25 per packet of gasket in case a customer orders less than 10
in case a customer orders > 10 price per gasket = 25*4/5=20
a certain week the supplier sold 60 gasket
1.he sold 15 % of the gaskets to X = 9 gaskets = 25*9= 225
2.he sold 15 % of the gaskets to Y = 9 gaskets = 25*9= 225
3.he sold remaining 70% to z =42 gaskets = 25*10 =250 + 20*32=890
thus ,total money earned
225+225+890 = 1340
Answer is A
Answer: (A) 1340
Question: Tom drives from town E to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between E and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
(A) 12
(B) 20
(C) 24
(D) 30
(E) 36
Rationale: Let's assume that it takes 4 hours to go from point E to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B.
Answer: (B) 20
Question: if w,x,y,z represents the respective results obtained from rounding off the figure 8623.293 to the nearest thousand, hundred, ten and one, which of the following statements is accurate?
(A) x<y<z<w
(B) x<z<y<w
(C) x<w<z<y
(D) z<y<x<w
(E) d<c<b<a
Rationale: 8623.293..
Nearest thousand 9000..w
Nearest hundred 8600..x
Nearest ten 8620..y
Nearest one 8623...z
x<y<z<w
The correct option is A
Answer: (A) x<y<z<w
Question: In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a blank?
(A) 2/3
(B) 6/7
(C) 5/7
(D) 8/7
(E) 4/3
Rationale: total draws = prizes+blanks= 10+25=35
probability of getting a blank = 25/35 = 5/7
correct option is C
Answer: (C) 5/7
Question: A train 150 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 7
(D) 9
(E) 8
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 150 * 3/55 = 8 sec.Answer: E
Answer: (E) 8
Question: If m and n are positive integers and m^2 + n^2 = 137, what is the value of m^3 + n^3?
(A) 72
(B) 224
(C) 320
(D) 512
(E) 1,395
Rationale: You need to integers which squared are equal 40.
Which could it be ? Let's start with the first integer:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
11^2 = 121
Stop. The integers can't be greater than 6 or we will score above 137.
The second integer need to be picked up the same way.
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
11^2 = 121
The only pair that matches is 11^2 + 4^2 = 137.
So 11^3 + 4^3 = 1395.
Answer E.)
Answer: (E) 1,395
Question: A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 75 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: answer is E ...5 dozens ....
half sold by noon --> 20 dozens (20 *12 =240)
remaining --> 20 dozens i.e 240 eggs...
75% sold --> 75*240/100 =180 eggs
remaining 25 % --> 60 eggs (5 dozens ) --> answer
Answer: (E)  5
Question: A factory produces 6500 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
(A) 1375 toys
(B) 2375 toys
(C) 1300 toys
(D) 1375 toys
(E) 2375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.
6500 / 5 = 1300 toys
correct answer C
Answer: (C) 1300 toys
Question: If x/2 = y/4 = z/6, then find the value of (x + y + z)/z
(A) 1/3
(B) 1/4
(C) 1/6
(D) 1/8
(E) None of these
Rationale: Explanation:
x/2 = y/4 = z/6 = k, Then x = 2k, y = 4k and z = 6k.
Now, (x + y + z)/z = (2k + 4k + 6k)/6k = 12k/6k = 2
Answer: Option E
Answer: (E) None of these