mathewhe/aqua_rat huggingface dataset:
Question: A fill pipe can fill 1/5 of tank in 25 minutes in how many minutes, it can fill 4/5 of the cistern?
(A) 48min
(B) 80 min
(C) 100 min
(D) 50 min
(E) 56 min
Rationale: 1/5 of the cistern can fill in 25 min
4/5 of the tank can fill in = 25*5*4/5 = 100 min
Answer is C
Answer: (C) 100 min
Question: At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number W of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: Circular arrangements= (n-1)!
Hence (4!) = 24=W
Answer is C
Answer: (C) 24
Question: The sale price of an article including the sales tax is616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is :
(A) 500
(B) 515
(C) 550
(D) 600
(E) None of these
Rationale: Sol.(a) Let the CP of the article be x
Then, SP = x × 1.12 × 1.1
Now, x × 1.12 × 1.1 = 616
=> x = 616⁄1.232 = 500 Answer A
Answer: (A) 500
Question: If both 5^2 and 3^3 are factors of n x (2^5) x (12^2) x (7^3) x (10), what is the smallest possible positive value of n?
(A) 15
(B) 45
(C) 75
(D) 125
(E) 150
Rationale: (2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and one appearance of 5 (in the 10).
Thus n must include at least 3 * 5 = 15
The answer is A.
Answer: (A) 15
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
(A) 2211
(B) 3000
(C) 2772
(D) 1211
(E) 1321
Rationale: 4 --- 2000
5 --- ? => 3000
Answer: B
Answer: (B) 3000
Question: If 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
(A) 198
(B) 288
(C) 360
(D) 396
(E) 484
Rationale: I will go with C (pending elements to match is 2^2*3^2*10^1 = 360
Answer: (C) 360
Question: A certain type of concrete mixture is to be made of cement, sand and graved (gravel?) in a ratio 1:3:5 by weight. What is the greatest number of kilograms of this mixture that can be made with 5 kilograms of cement ?
(A) 13 1/2
(B) 15
(C) 25
(D) 40
(E) 45
Rationale: We're given a ratio of cement, sand and gravel as 1:3:5 by weight. This means that for every 1 kg of cement, we'll mix in 3 kg of sand and 5kg of gravel....
1+3+5 = 9 kg of concrete
We're asked for the greatest number of kilograms of this mixture that can be made with 5 kilograms of cement...
From the prior work, we know that 1 kg of cement will get us 9 km of concrete. Since we're dealing with 5kg of cement, we'll end up with (5)(9) = 45 kg of concrete.
Final Answer:E
Answer: (E) 45
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 44 meters. How many times did the ball bounce?
(A) 5
(B) 6
(C) 7
(D) 3
(E) 9
Rationale: Going down = 16 m
Going Up = 8 --> Total = 24
Going down = 8 --> Total = 32
Going Up = 4 --> Total = 36
Going down = 4 --> Total = 40
Going up = 2 --> Total = 42
Going down = 2 --> Total = 44 (Caught)
No of bounce = 3 ..
Answer : D
Answer: (D) 3
Question: The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass?
(A) 73
(B) 35
(C) 83
(D) 63
(E) 83
Rationale: Explanation:
7/20 * 100 = 35
Answer: Option B
Answer: (B) 35
Question: The ratio of cost price to the marked price of an article is 4 : 5. If the ratio of the
profit percentage on selling the article to the discount allow ed on it is 5 : 4, w hat is the
profit percentage?
(A) 10%
(B) 12%
(C) 12.5%
(D) 15%
(E) 17%
Rationale: CP:MP=4:5
so assume cp=400 and MP=500.
PROFIT%:DISCOUNT=5:4. so let 5x and 4x.
now from the problem
After giving discount on marked price still he has a profit too.
500 - (4x% of 500) = 400 + (5x% of 400)
500 - 2x = 400 + 2x
solving we get x=5/2
profit percentage = 5x = 5(5/2) = 12.5%
ANSWER:C
Answer: (C) 12.5%
Question: A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.
(A) 4360
(B) 4460
(C) 4580
(D) 4690
(E) 5480
Rationale: Let the sum be Rs.P.thenP(1+R/100)^3=6690…(i) and P(1+R/100)^6=10035…(ii)On dividing,we get (1+R/100)^3=10025/6690=3/2.Substituting this value in (i),we get:P*(3/2)=6690 or P=(6690*2/3)=4460Hence,the sum is rs.4460. Answer : B
Answer: (B) 4460
Question: Sahil purchased a machine at Rs 9000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
(A) Rs. 22500
(B) Rs. 24500
(C) Rs. 26500
(D) Rs. 28500
(E) None of these
Rationale: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 9000 + 5000 + 1000 = 15000
150% of 15000 = 150/100 * 15000 = 22500
Option A
Answer: (A) Rs. 22500
Question: The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 800 per sq. metre.
(A) Rs. 15,550
(B) Rs. 15,600
(C) Rs. 16,500
(D) Rs. 17,600
(E) Rs. 17,900
Rationale: Area of the floor = (5.5 × 4) m2 = 22 m2.
Cost of paving = Rs. (800 × 22) = Rs. 17600.
Answer: Option D
Answer: (D) Rs. 17,600
Question: A is half good a work man as B and together they finish a job in 18 days. In how many days working alone B finish the job?
(A) 27 days
(B) 21 days
(C) 17 days
(D) 18 days
(E) 19 days
Rationale: WC = 1:2
2x + x = 1/18 => x = 1/54
2x = 1/54 => 27 days
Answer:A
Answer: (A) 27 days
Question: Find the average of the series : 312, 162, 132, 142 and 122?
(A) 174
(B) 178
(C) 119
(D) 110
(E) 171
Rationale: Average = (312 + 162 + 132 + 142 + 122)/5
= 870/5
= 174
Answer: A
Answer: (A) 174
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.2.0 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) s.1014
(B) s.1332
(C) s.999
(D) s.1085
(E) s.1020
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 2.0 = 1332
ANSWER:B
Answer: (B) s.1332
Question: How many bricks are needed to build a pillar of dimension .5x.5x25 m , if the dimension of the brick is 8x5x22 cm and the 15% of the total volume of the pillar is filled with concrete and steel.
(A) 3500
(B) 4100
(C) 4847
(D) 5310
(E) 5568
Rationale: Volume of the pillar that needed to be filled with bricks=.5x.5x25x0.85=5.31
Volume of the brick=0.08x0.05x0.25=.001
No. of bicks needed to build the pillar=5.31/0.001= 5310
Answer: D
Answer: (D) 5310
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a odd. You pick a card from a full playing-card deck, and success would be picking a red color card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
(A) 5/8
(B) 9/16
(C) 1/8
(D) 7/16
(E) 3/8
Rationale: Event(1): Probability of getting head in a flip of coin = 1/2
Event(2): Probability of getting odd in a roll of dice = 3/6 = 1/2
Event(3): Probability of getting red color in a pack of card = 26/52 = 1/2
Probability of winning is having exactly one successful event is:
P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)
= 1/2*1/2*1/2 +1/2*1/2*1/2 +1/2*1/2*1/2
=1/8 + 1/8 +1/8
=3/8
Answer :E
Answer: (E) 3/8
Question: Ross has 80 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
(A) 12 ; 20.
(B) 12 ; 19.
(C) 12 ; 18.
(D) 12 ; 17.
(E) 12 ; 16.
Rationale: Total shirts = 80
Green shirts = 3/4*80 = 60, Non green shirts = 20
Shirts without button = 1/10*80 = 8, shirts with button = 72
Required: Range of shirts with buttons that are not green.
Maximum non green shirts with buttons = number of non green shirts = 20
Minimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 20 - 8 = 12
Hence the range would be (12, 20)
Correct Option: A
Answer: (A) 12 ; 20.
Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?
(A) 175.5
(B) 182.5
(C) 170.0
(D) 180.0
(E) 190.0
Rationale: Tea worth Rs. 126
ratio 1 : 1
average price
= (126+135)/2=130.5
Mean price = (x-153):22.50
=>x-153=22.50
x=175.5
ANSWER A
Answer: (A) 175.5
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
(A) 620 ways
(B) 299 ways
(C) 167 ways
(D) 765 ways
(E) 600 ways
Rationale: The number of ways of selecting three men, two women and three children is:
= ⁴C₃ * ⁶C₂ * ⁵C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 4 * 15 * 10
= 600 ways.
Answer: E
Answer: (E) 600 ways
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.3267 in 3 years. Find the rate percent?
(A) 11
(B) 10
(C) 28
(D) 24
(E) 35
Rationale: Explanation:
2420 --- 847
100 --- ? => 35%
Answer: Option E
Answer: (E) 35
Question: The letters of the word 'SURATI' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SURITI'
(A) - 236
(B) - 245
(C) - 307
(D) - 415
(E) - 275
Rationale: Total Number of Words = 6! = 720 [(number of characters)/(repeating group )!]
After S, we have T and U.
Number of words starting with T = 5! = 120
Number of words starting with U = 5! = 120
So any word starting with S will have rank < 720 - 120(for Us) - 120(for Ts) = 480
Only option A < 480, so Answer is D
Answer: (D) - 415
Question: On a scale that measures the intensity of a certain phenomenon, a reading of d+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of d. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
(A)  5
(B)  50
(C)  10^5
(D)  5^10
(E)  8^10 - 3^10
Rationale: To solve this problem we need to examine the information in the first sentence. We are told that “a reading of d + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of d.”
Let’s practice this idea with some real numbers. Let’s say d is 2. This means that d + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.
Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.
Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.
We have found a pattern, which can be applied to the problem presented in the stem:
3 is “one” unit away from 2, and thus a reading of 3 is 10^1 times as great as the intensity of a reading of 2.
4 is “two” units away from 2, and thus a reading of 4 is 10^2 times as great as the intensity of a reading of 2.
5 is “three” units away from 2, and thus a reading of 5 is 10^3 times as great as the intensity of a measure of 2.
We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is 10^5 times as great as the intensity corresponding to a reading of 3.
Answer C.
Answer: (C)  10^5
Question: Which of the following points is closest to line y=x
(A) (2, -1)
(B) (2, 4)
(C) (-1, -2)
(D) (-2, 1)
(E) (-2, 0)
Rationale: Attachment:
m12-20.pngAs you can see point (-1, -2) is the closest to line y=x.
Answer: C.
Answer: (C) (-1, -2)
Question: The present worth of Rs.169 due in 2 years at 4% per annum compound interest is
(A) Rs.156.25
(B) Rs.156.22
(C) Rs.156.28
(D) Rs.156.19
(E) Rs.156.92
Rationale: Explanation:
Present Worth
=
=
= Rs.156.25
Answer: A
Answer: (A) Rs.156.25
Question: If 4XZ + YW = 6 and XW + YZ = 12, what is the value of the expression (2X + Y)(2Z + W)?
(A) 9.
(B) 30.
(C) 15.
(D) 16.
(E) 18.
Rationale: (2x+y)*(2z+w) = 6+2(12) =30
Answer : B
Answer: (B) 30.
Question: When x is divided by y, the quotient is q with remainder r. What is x in terms of r, y, and q?
(A) y + r + q
(B) yq + r
(C) x/y+r
(D) y/q+r
(E) rq + y
Rationale: (x/y) = q + r
solve for x
x=(q*y)+r
Ans B.
Answer: (B) yq + r
Question: A train 150 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 36
(B) 50
(C) 88
(D) 59
(E) 22
Rationale: Speed of the train relative to man
= (150/10) m/sec = 15 m/sec. [15 * (18/5)] km/hr
= 54 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5
= 54 ==> x
= 59 km/hr.
Answer:D
Answer: (D) 59
Question: The ratio of the present ages of Ramesh and mahesh is 2:5. 10 years hence, the ratio of their ages will be 10:15. Find the difference in their present ages?
(A) 7.5
(B) 6
(C) 5.5
(D) 6.5
(E) 5
Rationale: Let the present ages of Ramesh and Mahesh be 2x and 5x years respectively.
(2x + 10)/(5x + 10) = 10/15
6x + 30 = 10x + 20 => x = 2.5
Difference in their ages will be the same at all times.
This difference = Difference of their present ages
=> 5x - 2x = 3x => 7.5 years
Answer: A
Answer: (A) 7.5
Question: The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time Q will it take to fill the tank now?
(A)  50% less time
(B)  50% more time
(C)  75% less time
(D)  75% more time
(E)  100% more time
Rationale: (VC)Volume of the cylinderical vessal is directly proportional to R^2.
So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)
Now if with velocity V tank can be filled in T1 time of volume VC
So now Velocity is 50% less i..e V/2
So time taken to fill the capacity VC/4 by V/2 velocity is T2.
VT1 = VC
V/2*T2 = VC/4
So T1/T2 = 1/2
So Tank will be filled in less time. that is Q=50 % less.A
Answer: (A)  50% less time
Question: 2, 3, 6, 0, 10, -3, 14, (...)
(A) 6
(B) 2
(C) -2
(D) 0
(E) -6
Rationale: There are two series
2, 6, 10, 14, ... (Adding 4)
3, 0, -3, ... (Subtracting 3)
Hence, next term is -3 - 3 = -6
Answer is E.
Answer: (E) -6
Question: During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?
(A) 714,240
(B) 2,261,760
(C) 2,400,000 cars
(D) 3,690,240
(E) 3,915,790
Rationale: Let number of cars sold in 1st quarter = x
Number of cars sold in 2nd quarter = 24% greater than the number sold during the first quarter = (1 + 24/100)x = 1.24 x
1.24 x = 2,976,000
=> x = 2,400,000
So, answer will be C
Answer: (C) 2,400,000 cars
Question: During a certain week, a seal ate 60% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
(A) 32
(B) 40
(C) 55
(D) 64
(E) 96
Rationale: Total smelt = x.
Then, 0.6*80+0.3(x-80)=0.4*x --> x=240 --> 0.4*x=96.
Answer: E.
Answer: (E) 96
Question: A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was 115. Find the divisor?
(A) 370
(B) 365
(C) 380
(D) 367
(E) 460
Rationale: Easy solution:
N= Dq1+241
2N = 2Dq1 + 482 - (1)
2N = Dq2 + 115 - (2)
As (1) = (2) = 2N
D*(q2-2q1) = 367
D * Some integer = 367
Checking all options only (D) syncs with it.
ANswer D
Answer: (D) 367
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 13% per annum then the gain of B in a period of 3 years is?
(A) 320
(B) 300
(C) 310
(D) 315
(E) 330
Rationale: (3500*3*3)/100 => 315
Answer: D
Answer: (D) 315
Question: How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr?
(A) 1 1/5min
(B) 4 1/5min
(C) 3 1/5min
(D) 2 1/5min
(E) None of these
Rationale: Explanation :
We know that,Time=Distance/SpeedSpeed=20 km/hr=20 x 5/18m/sec=509m/secTime =(400 x 9/50) = 72sec=1 1/5min
Answer : A
Answer: (A) 1 1/5min
Question: If P represents the product of the first 13 positive integers, then P is not a
multiple of:
(A) a) 99
(B) b) 84
(C) c) 72
(D) d) 65
(E) e) 95
Rationale: a) 99 = 9*11
b) 84 = 4*7*3
c) 72 =9*11
d) 65 = 5*13
e) 95 =19*5
since 19 is not there in first 15 positive numbers it is the only possibility
E
Answer: (E) e) 95
Question: How many 8's are there preceded by 0 but not followed by 1?
5 0 8 1 2 7 4 2 6 9 7 4 6 1 3 0 8 7 4 1 0 8 3 2 5 6 7 4 3 9 5 8 2 0 8 2 7 4 6 3
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: 0 8 2
0 8 7
0 8 3
Only at these places 3 is preceded by 0 but not followed by 1
Answer: A
Answer: (A) 3
Question: Shawn is planning a bus trip across town that involves three buses. Bus 1 travels between Shawn’s house and downtown, and it leaves every half-hour starting at 7:20 AM. Shawn will need to be on bus 1 for 1.2 hours. Bus 2 travels between downtown and uptown every half-hour starting at 7:10 AM. Shawn will need to be on bus 2 for 2/3 hour. Lastly, bus 3 travels between uptown and Shawn’s destination every hour starting at 9 AM. Assuming all buses stay on schedule, what is the least amount of time Shawn must spend waiting for buses?
(A)  12 minutes
(B)  18 minutes
(C)  48 minutes
(D)  1 hour, 12 minutes
(E)  1 hour, 20 minutes
Rationale: Here's my solution. My first approach was to brute force the objective function in this optimization problem, minimize time spent waiting between buses
Givens:
1.2 hour=1 hour,12 minutes
2 2/3 hour=2 hour,40 minutes
Once you start filling out a table, you realize that there's only 2 solutions to this problem, leaving at the 20 minute mark of any hour versus leaving at the 50 minute mark of any hour.
[Reveal]Spoiler:
Answer, B
Answer: (B)  18 minutes
Question: What will be the product of (25-1)*(25-2)*(25-3)*..............*(25-99)*(25-100)?
(A) 0
(B) 1
(C) 625
(D) less than -100,000
(E) more than 100,000
Rationale: One of the terms is (25-25) so the product is 0.
The answer is A.
Answer: (A) 0
Question: A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: To fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible
so we will take the base as 12 feet by 8 feet
Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less.
Therefore the radius of the cylinder will become Diameter 2===>8/2=4 Diameter
ANSWER:D
Answer: (D) 8
Question: A family has two children. find the probability that both the children are boys given that at least
one of them is a boy?
(A) 1/3
(B) 3/7
(C) 3/11
(D) 4/5
(E) 5/11
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are boys’
F : ‘at least one of the child is a boy’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A)
Answer: (A) 1/3
Question: Last year a worker saved 4% of her annual salary. This year, she made 10% more money than last year and she saved 5% of her salary. The amount she saved this year was what percent of the amount she saved last year?
(A) 137.5%
(B) 142.5%
(C) 147.5%
(D) 152.5%
(E) 157.5%
Rationale: Let x be the worker's salary last year.
Last year, she saved 0.04x.
This year, she saved 0.05(1.1x)=0.055x
0.055x/0.04x=55/40=137.5%
The answer is A.
Answer: (A) 137.5%
Question: If a certain number of people can dig earth 100m deep, 25m long, and 30m broad in 12 days, then find the number of days the same number of people will require to dig earth 75m deep, 20m long and 50m broad.
(A) 18
(B) 16
(C) 12
(D) 99
(E) 13
Rationale: Explanation:
More number of days means – more length, more depth and more width. Hence, it’s a direct proportion.
(100*25*30):(75*20*50)::12:x
75000:75000::12:x
x = 12
ANSWER:C
Answer: (C) 12
Question: It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?
(A) 15 Minutes.
(B) 17 Minutes.
(C) 19 Minutes.
(D) 15 Minutes.
(E) 12 Minutes.
Rationale: D
15 Minutes.
After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.
Answer: (A) 15 Minutes.
Question: If a, b, c, d, and e are positive integers, which of the following could not become a terminating decimal?
(A) 33/2^(4b)
(B) 34/5^(2c)
(C) 35/100^e
(D) 36/4^w
(E) 37/3^(5v)
Rationale: Knowledge of Decimal equivalent Fractions will work wonders here , no need to consider the Numerator part
1/ 2 = 0.50 ( Terminating )
1/5 = 0.20 ( Terminating )
1/100 = 0.01 ( Terminating )
1/4 = 0.25 ( Terminating )
1/3 = 0.33 ( Non Terminating )
Check the above rule with any higher powers the result will be same.....
Among the given options only (E) has a non terminating denominator , so this will be our answer..
Answer: (E) 37/3^(5v)
Question: a man have 4 goat,2 sheep and 3 buffalo.he have to take three cattle out one each.with two available door.in how many ways he can out three cattle?
(A) 72
(B) 12
(C) 36
(D) 48
(E) 24
Rationale: from, fundamental principle of calculate
simple,4*2*3*2=48ways
answer D
Answer: (D) 48
Question: A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?
(A) 1/4
(B) 1/6
(C) 4/6
(D) 1/2
(E) 1/8
Rationale: Given that B alone can complete the same work in half the time taken by A
= 9days
A’s one day work = 1/18
B’s one day work = 1/9
(A+B)’s one day work = 1/18+1/9 = 1/6. Answer is B.
Answer: (B) 1/6
Question: Simplify (3^y + 3^y + 3^y + 3^y + 3^y) (5^y + 5^y + 5^y)
(A)  15^y+1
(B)  12^y+1
(C)  16^y + 9^y
(D)  12^y
(E)  4^y * 12^y
Rationale: A
(3^y + 3^y + 3^y + 3^y + 3^y) (5^y + 5^y + 5^y)
(5*3^y)(3*5^y)
15*15^y=15^(y+1)..
Answer: (A)  15^y+1
Question: if x and y are different integers and x^2=xy, which of the following must be true?
(A) x=0
(B) x=6
(C) x=3
(D) x=2
(E) x=1
Rationale: (1) when x is 0, above eqn is satisfied regardless of y - true
(2) when x is not zero, the eqn is not satified
eg whn x = 2, 2*2 is not equal to 2 * 0 - false
(3) when x = -y, clearly product xy is negative.
but x^2 is positive - doesnt satify eqn
Answer A
Answer: (A) x=0
Question: A is the average (arithmetic mean) of the first 7 positive multiples of 7 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?
(A) 4
(B) 12
(C) 14
(D) 21
(E) 28
Rationale: If A^2 - B^2 = 0, then let's assume that A = B.
A must equal the 4th positive multiple of 4, thus A = 28, which also equals B.
B is the second positive multiple of n, thus n = 28/2 = 14.
The answer is C.
Answer: (C) 14