mathewhe/aqua_rat huggingface dataset:
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) 5
(B) 6
(C) 2
(D) 3
(E) 1
Rationale: 6 * 22 = 132
7 * 19 = 133
--------------
1
ANSWER E
Answer: (E) 1
Question: Lakshmi has $100 in her piggy bank. How much will she have in her bank 15 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?
(A) 210
(B) 220
(C) 230
(D) 240
(E) 250
Rationale: The dollar deposits are in an A.P.
1,2,3,4...15with common difference 1
Sum of the terms is n(n+1) / 2
i.e 15* (15+1) /2
= 15* 16/2 = 120
Total deposit therefore with Chiu-Lihas is 100 + 120= 220$
Answer: (B) 220
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum C of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) C=4x
(C) C=5x/3
(D) C=3x/2
(E) 3x/5
Rationale: OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B)
But what about C,D,E? Any ideas why these could be wrong?
Note that we have 5 positive temperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits.
Answer: B.
Answer: (B) C=4x
Question: A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number of imported lamps stocked at the store?
(A) 3
(B) 10
(C) 13
(D) 20
(E) 23
Rationale: F + T = 410
Now, expression for the no. of imported items = 0.05F+0.3T
=> 0.05F+0.3(410-F)=123-0.25F
=>F has to be a multiple of 4
to minimize the expression, we have to maximize F
Max value of F can only be 400, as anything beyond this (404 or 408) will give a fractional value of the no. of imported Ts
Hence, minimum no. of imported stuff = 123-400/4 = 23
ANSWER:E
Answer: (E) 23
Question: I have a fruit basket with only apples, pears and oranges. I have as many apples in grams as pears in hectograms, and I have as many apples in hectograms and oranges in kilograms. I have a total of 60 kilograms of fruit. How many oranges in kilograms do I have?
(A) 5 kilograms
(B) 20 kilograms
(C) 10 kilograms
(D) 15 kilograms
(E) 50 kilograms
Rationale: Let o be the oranges’ weight in kilograms. If p is the weight of pears in kilograms, then pears are p10 hectograms. If a is apples’ weight in kilograms, then apples’ is a1000 grams. Thus,a1000 = p10Since apples is a10 hectograms,a10 = oSince apples, pears and oranges together are 60 kilograms,a + p + o = 60The above system of 3 equations in 3 unknowns (a, p and o) can be solved as follows:o / 10 +10o + o = 60 oro + 100o + 10o = 600 oro = 600 / 111 = 5 yearsAnswer = A
Answer: (A) 5 kilograms
Question: A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter made instead a sandbox which was twice as long, twice as wide and twice as high as the original, what would the capacity be of the new larger sandbox?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: Explanation:
When all the dimensions of a three dimensional object are in fact doubled, then the capacity increases by a factor of 2x2x2=2^3=8. Thus the capacity of the new sandbox is 8x10=80 cubic feet.
Answer: Option D
Answer: (D) 80
Question: A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 60% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
(A) $37.80
(B) $38.50
(C) $39.20
(D) $39.50
(E) $51
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14=$21 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.4=$14 --> x=$35.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 35+21=$51.
Answer: E.
Answer: (E) $51
Question: don and his wife each receive an 8 percent annual raise. if don receives a raise rs.800 and his wife receives a raise of rs. 840, what is the difference between their annual income after their raises?
(A) 40
(B) 460
(C) 500
(D) 540
(E) 150
Rationale: Don salary 8% = 800 ; Therefore, 100% = 10000
His wife salary 8% = 840; Therefore, 100% = 10500
After raise 8%,
Don salary = 10000 + 800 = 10800
And his wife salary = 10500+ 840 = 11340
Difference = 11340 - 10800 = 540
ANSWER:D
Answer: (D) 540
Question: A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
(A) 2 km/hr
(B) 3 km/hr
(C) 4 km/hr
(D) 7 km/hr
(E) 8 km/hr
Rationale: B
Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
x2 - 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, A is faster than B, so A's speed = 4 km/hr and B's speed = 3 km/hr.
Answer: (B) 3 km/hr
Question: Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 4 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
(A) 2
(B) 2.5
(C) 3
(D) 3.25
(E) 3.5
Rationale: Let the distance to the top be x, so the total distance traveled by Natasha is 2x.
The total time is 4 + 2 = 6 hours
The average speed = total distance/total time taken = 2x/6 = x/3
The average speed of the complete journey is 4 km/hour
x/3 = 4
x = 12 km
The average speed while climbing = distance/time = 12/4 = 3 km/h
The answer is C.
Answer: (C) 3
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 5400 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
(A) 9000
(B) 98000
(C) 30000
(D) 11000
(E) 12000
Rationale: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 5400 ( 18 × 300 = 5400)
100% -------> 30000 votes (100 × 300 = 30000)
C
Answer: (C) 30000
Question: John is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 10%. What is the approximate interest he pays annually?
(A) 4000
(B) 9500
(C) 2500
(D) 2000
(E) 4500
Rationale: An easy way too attempt this is by approximation:
For the first quarter, he pays 10% of 10,000 which is $1000.
So for the four quarters in the year, he will approximately play 1000*4=4000 over the entire year.
Because of compound interest it will be more than 4000. Approx. option E is correct.
Answer :E
Answer: (E) 4500
Question: If n = 3^8 – 2^6 which of the following is NOT a factor of n?
(A) 89
(B) 65
(C) 73
(D) 89
(E) 1
Rationale: 3^8 - 2^6
= (3^4)^2 - (2^3)^2
=(3^4 + 2^3)(3^4 - 2^3)
=(81+8)(81-8)
=89*73
Therefore, 65 is Not a factor of n.
B
Answer: (B) 65
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 40%, what should be the sale price of the mixed tea?
(A) 22.4
(B) 22
(C) 20
(D) 19.2
(E) None of these
Rationale: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+40)/100×16=22.4
Answer A
Answer: (A) 22.4
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
(A) 1/16
(B) 12/14
(C) 33/91
(D) 8/22
(E) 9/36
Rationale: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = Â¹Â²Câ‚„/Â¹âµCâ‚„
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91
Answer: C
Answer: (C) 33/91
Question: A rectangular floor that measures 24 meters by 64 meters is to be covered with carpet squares that each measure 8 meters by 8 meters. If the carpet squares cost $24 apiece, what is the total cost for the number of carpet squares needed to cover the floor?
(A)  $200
(B)  $576
(C)  $480
(D)  $960
(E)  $1,920
Rationale: The width of the rectangular floor(24 m) is a multiple of one side of the square(8 m), and the length of the floor(64 m) is also a multiple of the side of the square. So the number of carpets to cover the floor is (24/8)*(64/8)=24.
The total cost is 24*24=$576.
The answer is, therefore, B.
Answer: (B)  $576
Question: a dealer buys 4 varieties of wheat costing rs. 18,rs.20,rs.22 and rs.24 per kg in the ratio 2:1:3:4 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of wheat?
(A) 30.5
(B) 31.8
(C) 32.0
(D) 32.7
(E) 34.0
Rationale: CP = 18*2+20*1+22*3+24*4 = 218
SP = 1.5*218=327
Total no.of kgs=2+1+3+4=10
SP per kg=327/10=32.70
ANSWER:D
Answer: (D) 32.7
Question: . In digging a pond 17 m * 20 m * 4 m the volumes of the soil extracted will be?
(A) 3323
(B) 1360
(C) 2877
(D) 2992
(E) 7111
Rationale: 17 * 20 * 4 = 1360
Answer: B
Answer: (B) 1360
Question: Luke and Seth started out to visit Uncle Arnie. After driving 50 miles, they saw a restaurant, and
Luke wanted to stop for lunch. Seth wanted to look for something better, so they drove on for 8
miles before giving up and going back to the restaurant. After eating they traveled on for 26 more
miles from the restaurant. Seth saw a sign for a classic car museum, which they decided to visit.
The museum was 6 miles from their route. After returning to the main road, they drove for another 40
miles and arrived at Uncle Arnie’s house.How many miles did they drive on the way there?
(A) 444 miles
(B) 344 miles
(C) 244 miles
(D) 144 miles
(E) 644 miles
Rationale: Use a drawing to show their travels.
The distances don’t have to be to sc
50 + 26 + 40 = 116 miles from house to house
50 + 8 + 8 = 66 miles past restaurant and back
66 + 26 = 92 miles to museum turnoff
92 + 6 + 6 = 104 miles back to main route
104 + 40 = 144 miles total driven
correct answer D
Answer: (D) 144 miles
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 64 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 55
Rationale: there are 11 books less(75-64) which represents 20% of the loaned books (100-80)
So total loaned out books = 55
Answer E
Answer: (E) 55
Question: Dexter and Prexter are competing with each other in a friendly community competition in a pool of 50 m length and the race is for 1000 m. Dexter crosses 50 m in 2 min and Prexter in 3 min 15 sec. Each time they meet/cross each other, they do handshake's. How many such handshake's will happen if they start from the same end at the same time?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 22
Rationale: Explanation :
When Dexter completes second round, they do handshake once.
Now for every round which Dexter completes, there will be one hand shake as the ratio of speed is 13:8.
D and P will meet at the pool end only after D completes 26 rounds.
In the 20th round, D finish the race and the total handshake's will be:
20−1= 19.
Answer : C
Answer: (C) 19
Question: The speed of a train is 70 kmph excluding stoppages and including stoppages it is 63 kmph. Of how many minutes does the train stop per hour?
(A) 3
(B) 6
(C) 7
(D) 9
(E) 14
Rationale: Explanation:
T = 7/70 * 60 = 6
Answer: Option B
Answer: (B) 6
Question: A fort had provision of food for 150 men for 45 days. After 15 days, 25 men left the fort. The number of days for which the remaining food will last, is:
(A) 36
(B) 37 1/4
(C) 42
(D) 54
(E) 48
Rationale: After 15 days : 150 men had food for 30 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 125 : 150 :: 30 : x <=> 125 x x = 150 x 30
=> x =150 x 30/125
=> x = 36.
Correct answer is A
Answer: (A) 36
Question: 70,54,45,41 ?
(A) 42
(B) 43
(C) 44
(D) 40
(E) 39
Rationale: 70 - 54 = 16 = 4^2
54 - 45 = 09 = 3^2
45-41 = 04 =2^2
so we can write
41 - x = 01 = 1^1 , where x is the next number
x = 41 - 1 = 40
so the next number will be 40
ANSWER:D
Answer: (D) 40
Question: A man took some money for borrowed, for 3 years the total will be Rs.6000 and 5 years it will be Rs.7000/-. Then how much amount he borrowed?
(A) s.4000/-
(B) s.4500/-
(C) s.4770/-
(D) s.4800/-
(E) s.4820/-
Rationale: 3 years --------> Rs.6000/-
5 years --------> Rs.7000/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.6000/- - Rs.1500/- = Rs.4500/-
P = Rs.4500/-
B
Answer: (B) s.4500/-
Question: If 1/a + 3/a + 3/a is an integer, which of the following must also be an integer?
(A) 12/a
(B) 3/a
(C) 7/a
(D) 9/a
(E) 15/a
Rationale: 1/a + 3/a + 3/a
=7/a
Answer C
Answer: (C) 7/a
Question: The H.C.F. of two numbers is 63 and the other two factors of their L.C.M. are 11 and 17. The larger of the two numbers is:
(A) 3421
(B) 2132
(C) 1111
(D) 4323
(E) 1071
Rationale: :	Explanation:
Clearly, the numbers are (63 x 11) and (63 x 17).
{\color{Blue} \therefore } Larger number = (63 x 17) = 1071.
Answer: E)1071
Answer: (E) 1071
Question: At a local supermarket, a box of cereal usually costs 13 dollars. This week, the supermarket sells the box of cereal for 7 dollars. How much money will you save if you buy this cereal at this supermarket?
(A) 5 dollars
(B) 3 dollars
(C) 4 dollars
(D) 2 dollars
(E) 6 dollar
Rationale: Solution:
In this situation, there is a decrease in the price.
Saving = 13 - 7 = 6 dollars
Option E
Answer: (E) 6 dollar
Question: A is twice as good a workman as B and together they finish a piece in 18 days. In how many days will A alone finish the work?
(A) 25 days
(B) 26 days
(C) 23 days
(D) 45 days
(E) 27 days
Rationale: Sol. (A’s 1 day’s work):)(B’s 1 days work) = 2 : 1.
(A + B)'s 1 day's work = 1/18
Divide 1/18 in the ratio 2 : 1.
:. A’s 1 day's work =(1/18*2/3)=1/27
Hence, A alone can finish the work in 27 days.
Ans: E
Answer: (E) 27 days
Question: For four days of work, a clerk had daily earnings of $160, $150, $160, and $160 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?
(A) Between $10 and $50
(B) Between $0 and $10
(C) Between $20 and $25
(D) Between $50 and $100
(E) Between $50 and $65
Rationale: The standard deviation is between 0 and 10.
The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(150-(160*3+150)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.
Answer : B
Answer: (B) Between $0 and $10
Question: Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
(A) 270
(B) 260
(C) 250
(D) 230
(E) None
Rationale: Solution:
Let x be the total number of pages in the book, then she finished 2/3⋅x pages.
Then she has x−2/3⋅x=1/3.x pages left.
2/3⋅x - 1/3.x=90
1/3.x=90
x=270
So the book is 270 pages long.
Answer A
Answer: (A) 270
Question: The average score of a cricketer for six matches is 36 runs. If the average for first four matches is 32, then average for last 2 matches is
(A) 48
(B) 46
(C) 44
(D) 34.5
(E) 35.5
Rationale: Explanation:
=(36×6)−(32×4)/2
=(216−128)/2=44
Answer: Option C
Answer: (C) 44
Question: A group of 11 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?
(A)  E/(12 - n)
(B)  (12 - n)/E
(C)  E/[12(12-n)]
(D)  nE / [11(11-n)]
(E)  (12-n)E/(12n)
Rationale: total cost =E
no of people willing to participate initially =11
initial cost for each =E/11
when n people decided not to participate
Cost for each =E/11-n
D
Answer: (D)  nE / [11(11-n)]
Question: The cost price of 17 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 58 2/91%
(B) 54 6/11%
(C) 58 9/11%
(D) 58 2/91%
(E) 52 2/11%
Rationale: 17 CP = 11 SP
11 --- 2 CP
100 --- ? =>54 6/11%
Answer:B
Answer: (B) 54 6/11%
Question: 10 men, working 7 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
(A) 4 hours a day
(B) 5 hours a day
(C) 6 hours a day
(D) 7 hours a day
(E) 8 hours a day
Rationale: Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[men 15 10
days 12 18] ::7:x
=>xâˆ—15âˆ—12=10âˆ—18âˆ—7
=>x=10âˆ—18âˆ—7/ 15âˆ—12
=>x=7
Option D
Answer: (D) 7 hours a day
Question: Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 72. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?
(A) (a) 80
(B) (b) 81
(C) (c) 60
(D) (d) 83
(E) (e) 84
Rationale: T1: 1,2,3,4,5
T2: 2,3,4,5,6
T3: 3,4,5,6,7
etc.
means that every multiple of 6 will be involved in 5 sets. We have (72-6)/6+1=12 such multiples.
So, final number of sets is 12*5=60
Answer : C
Answer: (C) (c) 60
Question: Lloyd normally works 7.5 hours per day and earns $5.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?
(A) $33.75
(B) $47.25
(C) $51.75
(D) $54.00
(E) $66.00
Rationale: Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*5.5+ 3*5.5*1.5=66.00
Answer E
Answer: (E) $66.00
Question: The forth proportional to 100,200,300 is?
(A) 200
(B) 600
(C) 750
(D) 450
(E) 1000
Rationale: Let the fourth proportional to 100,200,300 be x
then 100:200::300:x
100x = 200*300
x = 600
Answer is B
Answer: (B) 600
Question: If the speed of X meters per second is equivalent to the speed of Y kilometers per minute, what is Y in terms of X? (1 kilometer=1000 meters)
(A) 0.06x
(B) 6x/5
(C) 18x/5
(D) 60x
(E) 3600000x
Rationale: x=1000y/60
y = 0.06x
Answer : A
Answer: (A) 0.06x
Question: Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins.
(A) 1
(B) 5
(C) 4
(D) 8
(E) 9
Rationale: C
Four
three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.
Answer: (C) 4
Question: If line L passes through point (m, n) and (– m, – n), where m and n are not 0, which of the following must be true?
I.	The slope of L is positive
II.	L exactly passes through origin
III.	The slope of L is negative
(A) III only
(B) II only
(C) I only
(D) I and II only
(E) II and III only
Rationale: Let (m,n) = (2,3)
(-m,-n) = (-2,-3)
Slope = (3+3)/(2+2) = 6/4 = 3/2
So III may not be true
Let (m,n) = (2,-3) then (-m,-n) = (-2,3)
So slope = (3 +3)/(-2-2) = -3/2
so I may not be true
So such a line would be -> (y - 3) = 3/2(x - 2)
=> 2y - 6 = 3x - 6
=> 2y - 3x = 0, hence no x or y intercept, so it passes through origin.
II is true.
Answer - B
Answer: (B) II only
Question: 85% of a number is added to 24, the result is the same number. Find the number?
(A) 28
(B) 288
(C) 279
(D) 160
(E) 232
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: (D) 160
Question: There are 5 boxes of different weights. They are weighed in pairs taken 2 at a time and the weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121. What is the sum of the weights of the 5 boxes ?
(A) 250
(B) 289
(C) 290
(D) 295
(E) 305
Rationale: Let the 5 boxes be a, b, c, d and e. The ten weights correspond to all the possible combinations of 2 weights out of 5.
On adding all the given weights, each boxes weight gets added 4 times:
a+b, a+c, a+d, a+e.
Similarly for b:
b+c, b+d, b+e and a+b (already included above)
Similarly for c, d and e.
Therefore, 110+112+113+114 .....+120+121 = 4* (a+b+c+d+e)
or, 4* (a+b+c+d+e) = 1156
or, (a+b+c+d+e) = 1156/4 = 289
ANSWER:B
Answer: (B) 289
Question: The average of 5 quantities is 10. The average of 3 of them is 4. What is the average of remaining 2 numbers?
(A) 19
(B) 14
(C) 8
(D) 9.5
(E) None of these
Rationale: ANSWER: A
(5x10-3x4)/2=19
Answer: (A) 19
Question: John needs 4 balls out of 10 balls.How many ways are possible?
(A) 1050
(B) 220
(C) 630
(D) 540
(E) 720
Rationale: The possible way is 10C4
10C4=10!/6!*4!=10*9*8*7*6!/6!*4*3*2*1
=630 ways
Ans:option C
Answer: (C) 630
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) 4800
(B) 4991
(C) 5004
(D) 5000
(E) 5002
Rationale: Explanation:
Let the sale in the sixth month =x=x
Then 6435+6927+6855+7230+6562+x/6=6500
=> 6435+6927+6855+7230+6562+ =6×6500
=> 34009+x=39000
=> x=39000−34009=4991
Answer: Option B
Answer: (B) 4991
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
(A) 2:3:5
(B) 3:4:7
(C) 4:5:9
(D) 6:5:9
(E) None of these
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7
ANSWER:B
Answer: (B) 3:4:7
Question: What is the greatest value of n such that 30!/6^n is an integer?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 30/2 + 30/(2^2)+30/(2^3)+30(2^4) = 15+7+3+1=26
How many 3's are there ? so that the division leads to be an integer
30/3 + 30/(3^2)+30/(3^3)= 10+3+1=14
How many 3's and 2's are there so that the division leads to be an integer
Minimum or common between 26 and 14.
Answer is 14.
ANSWER:D
Answer: (D) 14
Question: Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 26 have long fur, 30 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
(A) 26
(B) 19
(C) 11
(D) 8
(E) 6
Rationale: No of dogs=45
Long fur=26
Brown=30
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=26+30-Both
Both=19
Answer B
Answer: (B) 19
Question: If v persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
(A) z
(B) x
(C) x/y
(D) z/x
(E) y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
v person can do z jobs in y days..
so v person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: (E) y/z
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent F of the gasoline in the tank is brand Z?
(A) 50%
(B) 40%
(C) 37.5%
(D) 331⁄3%
(E) 25%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) F= 3/8 = 37.5%
Answer (C)
Answer: (C) 37.5%