mathewhe/aqua_rat huggingface dataset:
Question: 49 Ã— 49 Ã— 49 Ã— 49 x 49 = 7?
(A) 4
(B) 7
(C) 8
(D) 10
(E) None of these
Rationale: 49 Ã— 49 Ã— 49 Ã— 49 x 49= 7?
or, 7(2) Ã— 7(2) Ã— 7(2) Ã— 7(2) x 7(2)= 7?
or 7(10) = 7? or, ? = 10
Answer D
Answer: (D) 10
Question: Ajith can do a work in 12 days while Anand can do the same work in 18days. Both of them finish the work together and get $500. What is the share of Ajith?
(A) $150
(B) $200
(C) $350
(D) $250
(E) $300
Rationale: Ajith's wages: Anand's wages = 1/12 : 1/18 = 18:12 = 3:2
Ajith's share = 500*3/5 = $300
Answer is E
Answer: (E) $300
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years?
(A) 14300
(B) 14350
(C) 14400
(D) 14500
(E) 14600
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 × 120/100 = 14400
C
Answer: (C) 14400
Question: A rainstorm increased the amount of water stored in State J reservoirs from 130 billion gallons to 160 billion gallons. If the storm increased the amount of water in the reservoirs to 60 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 92
(B) 85
(C) 136.67
(D) 140.67
(E) 150
Rationale: Let total capacity be x
we know 160 = 0.60x
x = 160/0.60 = 266.67
Prior to storm, we had 130 bn gallons
266.67-130 = 136.67
Answer : C
Answer: (C) 136.67
Question: A farmer has 12 plots of land, arranged in a row. To ensure viability of the soil, the farmer
never uses two adjacent plots at the same time. This season, the farmer wishes to plant one
plot of each of the following: corn, wheat, soybeans, and rice. Each crop is assigned its own
plot of land. How many ways can the farmer allocate plots of land for these crops?
(A) 1680
(B) 3024
(C) 5040
(D) 7920
(E) 11880
Rationale: There is a natural one-to-one correspondence between all choices from a row of 9
plots, and all “legal” choices for the 12 plots in the problem: given a choice of four plots in 9,
insert a fallow plot after each of the first three plots. The number of ways to pick 4 plots of
land from 9 is
􀀀9
4. After the locations of plots have been selected, there are 4! ways to assign
the crops to the plots. The total number of ways is therefore 4!
􀀀9
4
or 3024.
correct answer B
Answer: (B) 3024
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5
(A) 136
(B) 148
(C) 150
(D) 158
(E) 160
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: (D) 158
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 22
(B) 20
(C) 99
(D) 88
(E) 11
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer:B
Answer: (B) 20
Question: The sides of a rectangular region measured to the nearest centimeter are 8 cm and 5 cm. Out of the following which is the largest possible value of actual area of rectangle ?
(A) 48
(B) 55.25
(C) 52.29
(D) 44
(E) 41.25
Rationale: acan be anywhere between 7.5 and 8.4 andbcan be anywhere between 4.5 and 5.4.
Hence max area can be 8.4*5.4 eq 45.36.
largest value which is near to 45.36 is 44.
Hence D.
Answer: (D) 44
Question: The product of all positive even numbers less than or equal to 20 is closest to which of the following?
(A) 10^6
(B) 10^7
(C) 10^8
(D) 10^9
(E) 10^10
Rationale: 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20
Replacing closest digits to 10 (6,8,12,14) with 10 and closest to 20 (16,18) with 20.
==>(2 * 4) * (10 * 10 * 10 * 10 * 10) * (20 * 20 * 20)
==>8 * (10^5) * (8 * 10^3)
==>64 * 10^8
==>64 is closest to 50
==>50 * 10^ 8
==>5 * 10^9
Answer D
Answer: (D) 10^9
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
(A) 2% decrease
(B) 8% decrease
(C) 9% decrease
(D) 3% decrease
(E) 2% decrease
Rationale: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B
Answer: (B) 8% decrease
Question: A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
(A) 1/50
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
Rationale: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 40/100 = 2/5
Three are independent;probability of rich and fair complexioned girl is:
(1/4) ×(1/5) × (2/5) = 1/50
Answer: A
Answer: (A) 1/50
Question: Speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph. A man rows to a place at a distance of 4864 km and comes back to the starting point. The total time taken by him is
(A) 700 hours
(B) 350 hours
(C) 1400 hours
(D) 1010 hours
(E) None of these
Rationale: Explanation :
Speed downstream = (14 + 1.2) = 15.2 kmph
Speed upstream = (14 - 1.2) = 12.8 kmph
Total time taken = (4864/15.2) + (4864/12.8) = 320 + 380 = 700 hours. Answer : Option A
Answer: (A) 700 hours
Question: (xn - an) is completely divisible by (x - a), if
(A) n is any natural number
(B) n is an even natural number
(C) n is and odd natural number
(D) n is prime
(E) n is not any natural number
Rationale: (xn - an) is completely divisible by (x - a) for every natural number n
Answer is A
Answer: (A) n is any natural number
Question: In Country A, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
(A)  50% decrease
(B)  30% decrease
(C)  15% decrease
(D)  30% increase
(E)  55% increase
Rationale: Country A 1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11
% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B
Answer: (B)  30% decrease
Question: Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many S hours does it currently take Anne to clean the house on her own?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14
Rationale: Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in S= 3 hours)
Solving these 2 equations we can find B as 12
So, D
Answer: (D) 12
Question: if 15% of X is added to X and 5% of the result is subtracted from the result, then the value of X
(A) increased
(B) decreased
(C) no change
(D) depend on x
(E) None of these
Rationale: Let assume X =100
15% of 100 = 15
Now, new value X = 100+15 = 115
5% of 115(new result) = 5.75
So, 115-5.75 = 109.25
So, X is increased. (100 increased to 109.25)
ANSWER:A
Answer: (A) increased
Question: x =1 2 2.5
y= 27 4 5 then what is the relation between x and y
(A) 3*X)^4
(B) 3*X)^1
(C) 3*X)^2
(D) 3*X)^3
(E) 3*X)^5
Rationale: Y=(3*X)^3
27=(3*1)^3
27=27
ANSWER:D
Answer: (D) 3*X)^3
Question: Alex age after 13years will be 10 times his age 10years back. What is the present age of Alex?
(A) 15
(B) 13
(C) 20
(D) 21
(E) 26
Rationale: Let Alex's present age be x
Alex's age after 17 years = x+17
Alex's age 10 years back = x-10
x+17= 10(x-10)
x = 13
Rajeev's present age = 13 years
Answer is B
Answer: (B) 13
Question: If A lends Rs.4000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
(A) 112.5
(B) 122.5
(C) 132.5
(D) 114.5
(E) 180
Rationale: (4000*1.5*3)/100 => 180
ANSWER:E
Answer: (E) 180
Question: Sonika deposited Rs.12000 which amounted to Rs.19500 after 4 years at simple interest. Had the interest been 3% more. She would get how much?
(A) 20940
(B) 21009
(C) 23000
(D) 23450
(E) 30000
Rationale: (12000*4*3)/100 = 1440
19500
--------
20940
Answer: A
Answer: (A) 20940
Question: A train 250 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
(A) 150m
(B) 200m
(C) 250m
(D) 270m
(E) 300 m
Rationale: D = 72 * 5/18 = 25 = 500 – 250 = 250m
ANSWER:C
Answer: (C) 250m
Question: You have two jars, 50 red marbles and 50 blue marbles. A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?
(A) 73/99
(B) 74/99
(C) 75/99
(D) 74/97
(E) 74/95
Rationale: one red ball in one jar. 49 red + 50 blue in second jar.
probability to get red ball is 1/2(1+49/99) = 74/99
ANSWER:B
Answer: (B) 74/99
Question: There are 408 boys and 288 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
(A) 31
(B) 32
(C) 35
(D) 30
(E) 29
Rationale: Explanation:
HCF (408, 288) = 24
The number of boys or girls that can be placed in a section = 24.
Thus the total number of sections is given by
408/24+288/24 =17+12 = 29
Answer: E
Answer: (E) 29
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 72 kmph
(B) 75 kmph
(C) 30 kmph
(D) 80 kmph
(E) 82 kmph
Rationale: S = (90 + 60)/2
= 75 kmph
ANSWER:B
Answer: (B) 75 kmph
Question: a piece of ribbon 4 yard long is used to make bows requiring 15 inches of ribbon for each.What is the maximum number of bows that can be made.
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: 1 yard = 36 Inch
4 yard = 36*4 = 144 inch
15 inch req. for 1 bow
Max. no. of bows possible = 144/15 = 9 bows and 9 inch ribbon left.
ANSWER:A
Answer: (A) 9
Question: 1. Internet: $80, with no sales tax, plus $10 shipping fee
2. Store X: $80, a 10% discount, plus 10% tax on discounted price
3. Store Y: $90, no tax
4. Store Z: $90, a 10% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
(A) 79.2
(B) 89.0
(C) 89.1
(D) 89.5
(E) 90.0
Rationale: Option 2 = (80 - 8) + 0.1 * 72=79.2
Option 4 = 90 + 0.1 * 90 - 10
= 89
So the OA is correct - A
Answer: (A) 79.2
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives
(A) Rs. 8400
(B) Rs. 11,900
(C) Rs. 13,600
(D) Rs. 14,700
(E) NONE
Rationale: Solution: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000.
=> 3x = 36000.
=> x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
So A's share = Rs. (35000 x 21/50) = Rs. 14,700.
Answer: Option D
Answer: (D) Rs. 14,700
Question: The value of 99^(91/99) x 99 is:
(A) 9989
(B) 9896
(C) 9892
(D) 9809
(E) 9810
Rationale: (100 â€“ 8/99) x 99 = 9900 â€“ 8
= 9892.
ANSWER:C
Answer: (C) 9892
Question: The tax on a commodity is diminished by 22% and its consumption increased by 11%. The effect on revenue is?
(A) 8
(B) 6
(C) 5
(D) 4
(E) 2
Rationale: 100 * 100 = 10000
88 * 111 = 9768
-----------
10000-----------232
100-----------? => 2% decrease
Answer:E
Answer: (E) 2
Question: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
(A) 21/46
(B) 25/117
(C) 1/50
(D) 3/25
(E) 6/25
Rationale: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S)	= Number ways of selecting 3 students out of 25
= 25C3 `
=	(25 x 24 x 23)
(3 x 2 x 1)
= 2300.
n(E)	= (10C1 x 15C2)
= 10 x	(15 x 14)
(2 x 1)
= 1050.
P(E) =	n(E)/n(S)	=	1050	/2300=	21/46	.
Answer : A.
Answer: (A) 21/46
Question: A container contains 40lit of milk. From this container
4 lit of milk was taken out and replaced by water.
This process was repeated further two times.
How much milk is now contained by the container?
(A) 29.16
(B) 29.19
(C) 30.0
(D) 25.3
(E) 25.0
Rationale: Amount of milk left after 3 operations = 40(1-4/40)3lit
=(40*9/10*9/10*9/10)
= 29.16 lit
ANSWER A
Answer: (A) 29.16
Question: The length of the bridge, which a train 180 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 388
(B) 167
(C) 195
(D) 288
(E) 261
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (180 + X)/30 = 25/2 ==> 2(180 + X) = 750 ==> X = 195 m.
Answer: C
Answer: (C) 195
Question: A sofa and a love seat together costs S444. The sofa costs double the love seat.
How much do they each cost?
(A) love seat costs $148-sofa costs $296.
(B) love seat costs $158-sofa costs $496.
(C) love seat costs $170-sofa costs $500.
(D) love seat costs $499-sofa costs $655.
(E) love seat costs $110-sofa costs $696.
Rationale: Love Seat x With no information about the love seat, this is our x
Sofa 2x Sofa is double the love seat, sowemultiply by 2
S +L=444 Together they cost 444, sowe add.
(x)+(2x)=444 Replace S and Lwith labled values
3x=444 Parenthesis are not needed, combine like terms x+2x
3 3 Divide both sides by 3
x=148 Our solution for x
Love Seat 148 Replace xwith 148 in the origional list
Sofa 2(148)=296 The love seat costs $148 and the sofa costs $296.
correct answer A
Answer: (A) love seat costs $148-sofa costs $296.
Question: Evaluate: 6402.5 + 640.25 + 64.025 + 6.4025 + 0.64025
(A) 6819.59775
(B) 6981.59775
(C) 6918.59775
(D) 7113.81775
(E) 6891.59775
Rationale: 6402.5
640.25
64.025
6.4025
+ 0.64025
---------------
7113.81775
Answer is D.
Answer: (D) 7113.81775
Question: What least number should be added to 1056,So that the sum is completely divisible by 23?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: =>1056/23=45
Remainder=21=21+2
=23
Hence 2 should be added to 1056 so that the number divisible by 23
Option :B
Answer: (B) 2
Question: How many prime numbers between 0 to 50?
(A)  11
(B)  13
(C)  14
(D)  15
(E)  16
Rationale: primes are of the form 6n+1 or 6n-1
Put n=0
6n+1=6*0+1=1 where 1 is not prime
for n=1
6n+1=6*1+1=7 and 6n-1= 6*1-1=5
for n=2
6n-1= 11 and 6n+1=13
for n=3 , ==> 19 and 17
for n = 4 ==> 23
for n =5 ==> 29 and 31
for n = 6 ==> 37
for n=7 ==> 41 and 43
for n = 8 ==> 47
therefore total number of prime numbers = 13 + 2(since 2 and 3 are prime numbers) =15
Ans - D
Answer: (D)  15
Question: If e and y are positive integer and e/y is an even integer, which of the following can be an odd integer?
(A) x
(B) xy
(C) x−y
(D) x+2y
(E) e/3
Rationale: C e-Y
Let says e =12 Y=3 iT BECOMES e-Y =9 This is odd True
e = 12 Y = 6 THEN e-Y = 2, Which is even hence this is False.
so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
Answer: (E) e/3
Question: The sum of ages of 4 children born at the intervals of 3 years each is 43 years. Find out the age of the youngest child?
(A) 8 1/4 years
(B) 6 1/4 years
(C) 6 2/4 years
(D) 6 3/4 years
(E) 7 1/4 years
Rationale: Let the age of the youngest child =a
Then, the ages of 4 children can be written as a,a+3,a+6 and a+9
a+a+3+a+6+a+9=43
4a+18=43
4a=25
a=6 1/4 years
ANSWER:B
Answer: (B) 6 1/4 years
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 5x km.
(A) 16
(B) 18
(C) 24
(D) 40
(E) 12
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 5x/(x/8) = 40 kmph
Answer: D
Answer: (D) 40
Question: The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 60 minutes after it was poured was how many degrees Fahrenheit?
(A) 125
(B) 95
(C) 80
(D) 61.8
(E) 50
Rationale: Answer: B
The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”.
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 60 minutes after it was poured is:
F = 120 ( 2 ^ -60/10) + 60
F = 120 * 1/ 64 + 60
F = 15/8 + 60
F = 495/8=61.8
D
Answer: (D) 61.8
Question: 7589-?=3434
(A) 4242
(B) 4155
(C) 1123
(D) 11023
(E) None of them
Rationale: Let 7589-x=3434
then x=7589-3434
=4155
Answer is B
Answer: (B) 4155
Question: Look at this series: 74, 71, 69, 66, 64, ... What number should come next?
(A) 60
(B) 61
(C) 59
(D) 58
(E) 56
Rationale: Explanation:
This is an alternating number subtraction series. First, 3 is subtracted, then 2, then 3, and so on.
Answer: Option B
Answer: (B) 61
Question: During a certain two-week period, 70 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 4 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
(A) 16A
(B) 13A
(C) 14A
(D) 11 2/3A
(E) 12A
Rationale: Total movies = 100.
Comedies = 70.
Action + Drama = 30. Since there were 5 times as many dramas as action movies, then Action + 4*Action = 30 --> Action = A = 6.
Comedies = 70 = 14A.
Answer: D.
Answer: (D) 11 2/3A
Question: hree persons A, B and C divide a certain amount of money such that A's share is Rs. 4 less than half of the total amount, B's share is Rs. 8 more than half of what is left and finally C takes the rest which is Rs. 14. Find the total amount they initially had with them?
A. Rs. 61 B. Rs. 85
(A) 20
(B) 20
(C) 30
(D) 80
(E) 33
Rationale: Let the total amount be Rs. p.
Let shares of A and B be Rs. x and Rs. y respectively.
C's share was Rs. 14
we have, x + y + 14 = p ----- (1)
From the given data, x = (p/2) - 4 ----- (2)
Remaining amount = p - (p/2 - 4) => p/2 + 4.
y = 1/2(p/2 + 4) + 8 => p/4 + 10 ----- (3)
From (1), (2) and (3)
p/2 - 4 + p/4 + 10 + 14 = p
3p/4 + 20 = p
p/4 = 20 => p = Rs. 80.
Answer: D
Answer: (D) 80
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
(A) 40
(B) 35
(C) 45
(D) 55
(E) 65
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) years = 90 years.
Sum of the present ages of wife and child = (20 * 2 + 5 * 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years
Option A
Answer: (A) 40
Question: If the probability of rain on any given day in City X is 60%, what is probability that it rains on exactly 3 days in a 4 day period?
(A) 16/25
(B) 86/125
(C) 96/125
(D) 216/625
(E) 336/625
Rationale: One possible way is rain-rain-rain-no rain.
The probability of this is 3/5*3/5*3/5*2/5 = 54/625
The number of possible ways is 4C3 = 4, so we multiply this by 4.
P(rain on exactly 3 days) = 4*54/625 = 216/625
The answer is D.
Answer: (D) 216/625
Question: A certain pair of used shoes can be repaired for $14.50 and will last for 1 year. A pair of the same kind of shoes can be purchased new for $32.00 and will last for 2 years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?
(A) 16
(B) 10.34
(C) 12.46
(D) 11.2
(E) 14
Rationale: 1) Cost of repairing = 14.5 ( for one year ), Therefore for 2 years it would be$ 29.
2) Cost of new pair which will last for 2 years is$ 32.
Percentage change formula =( Final value - Initial value ) / ( Initial Value ) * 100. In this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe.
I.e ( 32 - 29 ) / ( 29 ) * 100 = 10.34 %.
Ans is B
Answer: (B) 10.34
Question: Due to construction, the speed limit along an 9-mile section of highway is reduced from 45 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 5.61
(B) B) 3.42
(C) C) 10
(D) D) 15
(E) E) 24
Rationale: Old time in minutes to cross 9 miles stretch = 9*60/45 = 9*4/3 = 12
New time in minutes to cross 9 miles stretch = 9*60/35 = 9*12/7 = 15.42
Time difference = 3.42
Ans:B
Answer: (B) B) 3.42
Question: Tough and Tricky questions: Geometry.
A cylindrical tank, with radius and height both of 10 feet, is to be redesigned as a cone, capable of holding twice the volume of the cylindrical tank. There are two proposed scenarios for the new cone: in scenario (1) the radius will remain the same as that of the original cylindrical tank, in scenario (2) the height will remain the same as that of the original cylindrical tank. What is the approximate difference in feet between the new height of the cone in scenario (1) and the new radius of the cone in scenario (2)?
(A)  13
(B)  25
(C)  30
(D)  35
(E)  40
Rationale: volume of a cylinder = pi*r^2 *h
r=10
h=10
volume = 1000pi
volume of the cone: 2000pi
volume of the cone = pi*r^2 * h/3
2000=r^2 * h/3
1st case: r=10 -> h/3=20 => h=60
2nd case: h=10 -> r^2 = sqrt(600)
sqrt(600) = 10*sqrt(6)
sqrt(6)>sqrt(4)
sqrt(6)<sqrt(9)
so radius must be between 20 and 30. this approximation is enough.
60-30=30
60-20=40
so we are looking for smth between 30 and 40.
only D fits in here.
Answer: (D)  35
Question: In a chicken farm, due to certain disease 15% of chickens die every month. How many months it will take to the reduce the count of chicken by 50%?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 1 year: 100*15/100= 15: Total: 85
2nd year: 85*15/100= 13: Total: 85-13= 72
3rd year: 72*15/100 = 11: Total: 72-11= 61
4th year: 61*15/100 = 9: Total: 61-9 = 52
5th month : 52*15/100 = 8 : Total: 52-8= 44
;4 months;
ANSWER:B
Answer: (B) 5
Question: P is three times as old as Q. In 7 years, P will be twice as old as Q. How old was P three years ago?
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: P = 3Q so Q = P/3
P+7 = 2(Q+7) = 2(P/3+7)
P/3 = 7
P = 21
Three years ago, P was 18.
The answer is B.
Answer: (B) 18
Question: Which of the following cannot be the sum of 4 different prime numbers?
(A) 21
(B) 17
(C) 19
(D) 32
(E) 19
Rationale: Option A: 21 = 2+3+5+11. Sum of 4 different prime numbers
Option B: 17 = 2+3+5+7. Sum of 4 different prime numbers
Option C: 19 = 2+3+5+9. This cannot be expressed as a sum of 4 different prime numbers
Option D: 32 = 5+3+11+13. Sum of 4 different prime numbers
Option E: 31 = 5+2+11+13. Sum of 4 different prime numbers
Correct Option:C
Answer: (C) 19
Question: 9 people will pick a number between 1 and 9. What is the probability that exactly one person will pick a different number?
(A) 1/9
(B) 1/9*9
(C) 1/9!
(D) 9!/9
(E) 9!/9^9
Rationale: Each person out of 9 has 9 options, hence total # of outcomes is 9^9;
Favorable outcomes will be 9!, which is # of ways to assign 9 different number to 9 people.
P=favorable/total=9!/9^9
Answer: E.
Answer: (E) 9!/9^9
Question: For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
(A) 12%
(B) 26%
(C) 29%
(D) 32%
(E) 60%
Rationale: In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated.
In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.
Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%.
Answer: D.
Answer: (D) 32%
Question: 50 percent of the members of a study group are women, and 30 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?
(A) 0.16
(B) 0.25
(C) 0.45
(D) 0.35
(E) 0.15
Rationale: Say there are 100 people in that group, then there would be 0.5*0.30*100=15 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=15/100.
Answer: E
Answer: (E) 0.15