mathewhe/aqua_rat huggingface dataset:
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 25 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:6
(B) 4:3
(C) 4:9
(D) 4:5
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš16 : âˆš25 = 4:5.Answer:D
Answer: (D) 4:5
Question: Set #1 = {A, B, G, F, E}
Set #2 = {K, L, M, N, O, Q}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/6
(E) 1/7
Rationale: At least questions are best solved by taking the opposite scenario and subtracting it from 1. Probability of choosing no vowel from set 1 is 3/5 and set 2 is 5/6. Multiply these to get 1/2. Therefore, probability of picking at least one vowel = 1-1/2=1/2.
Answer: (A) 1/2
Question: In a certain company, the formula for maximizing profits is P = -25x^2 + 7500x,, where P is profit and x is the number of machines the company operates in its factory. What value for x will maximize P?
This one is from IntegratedLearning.
Here's what I did:
The OA states: To find a maximum or minimum value of an equation with an exponent in it, you take the derivative of the equation, set it to zero, and solve. I dont really get what that means. So whoever solves it, could you plz post explanation of what the above sentence mean as well?
(A) 10
(B) 50
(C) 150
(D) 200
(E) 300
Rationale: Recognize that 25 is a factor of 7500. If we take this out, we have two parts to the equation:
-X^2300X
One part of the equation brings our value down, whereas the other part brings our value up. At this point, we can test the numbers in the answer choice. Notice that they are very straight forward to square, and multiplication by 300 is very easy.
A) 10 - 3000 - 100 = 2900
B) 50 - 15000 - 2500 = 12500
C) 150 - 45000 - 22500 = 22500
D) 200 - 60000 - 40000 = 20000
E) 300 - recognize that this is zero
Therefore, answer is 150.
Hope this helps those - like myself - who haven't thought about calculus for over half a decade.C
Answer: (C) 150
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:
(A) 850
(B) 525
(C) 550
(D) 750
(E) 950
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
ANSWER:D
Answer: (D) 750
Question: Ramu crosses a 1000 m long street in 10 minutes. What is his speed in km per hour?
(A) 5.6km/hr
(B) 7.2km/hr
(C) 3.6km/hr
(D) 5.9km/hr
(E) 10km/hr
Rationale: Speed =1000/10 *60 = 1.66m/sec
Converting m/sec to km/hr .
=1.66*18/5=5.9km/hr
Answer is D
Answer: (D) 5.9km/hr
Question: 3x+4y=10
x3 + y3=6
What is the minimum value of 3x+11y=?
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: By solving the two gvn eqns,we get x=-2 and y=4. so by substituting these values in 3rd eqn we get 3(-2)+11(4)=38. so ans is 38.
ANSWER:C
Answer: (C) 38
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 228
(B) 277
(C) 288
(D) 270
(E) 128
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m. Answer: D
Answer: (D) 270
Question: A train 150 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
(A) 5 sec
(B) 9 sec
(C) 12 sec
(D) 15 sec
(E) 18 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50 sec = 9sec
Answer : B.
Answer: (B) 9 sec
Question: Working alone, A can complete a certain kind of job in 12 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs?
(A)  1
(B)  3
(C)  4
(D)  6
(E)  9
Rationale: Let total time taken by S to complete the job = S
total time taken by A to complete the job = 12
Work done by A in an hour
1/A = 1/12
Working together A and D can complete the job in 4 hours
1/A + 1/D = 1/4
=>1/D = 1/4 - 1/12
= 1/4 - 1/12
= 1/6
=> D = 6 hours
Answer D
Answer: (D)  6
Question: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 9 ½ sec
(B) 5 ½ sec
(C) 6 ½ sec
(D) 8 ½ sec
(E) 2 ½ sec
Rationale: D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 ½ sec
Answer:D
Answer: (D) 8 ½ sec
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 4
Rationale: Explanation:
x – y = 5
4x – 6y = 6
x = 12 y = 7
Answer: Option C
Answer: (C) 7
Question: A coin is tossed 4 times. What is the probability x that the number of Heads is equal to the number of Tails?
(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 9/16
Rationale: We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.
Using the binary formula and defining a head as a success,
P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2
x= 6/16
= 3/8
The answer is therefore (C)
Answer: (C) 3/8
Question: How many two letter words are formed using the letters of the word MACHINE?
(A) 52
(B) 56
(C) 38
(D) 42
(E) 48
Rationale: The number of letters in the given word is seven.
The number of two letter words that can be formed using these seven letters is 7P2
= 7 * 6 = 42.
Answer: D
Answer: (D) 42
Question: If 9 persons can do 9 times of a particular work in 9 days, then, 7 persons can do 7 times of that work in?
(A) 2 days
(B) 3 days
(C) 5 days
(D) 7 days
(E) 9 days
Rationale: That is, 1 person can do one time of the work in 9 days.
Therefore, 7 persons can do 7 times work in the same 9 days itself.
E)
Answer: (E) 9 days
Question: A boat running up stram takes 6 hours to cover a certain distance, while it takes 9 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
(A) 2 : 3
(B) 5 : 1
(C) 4 : 5
(D) 7 : 1
(E) 8 : 1
Rationale: Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
6(x+y) = 9(x-y)
6x+6y = 9x-9y
15y = 3x
5y = x
x/y = 5/1
5 : 1
Answer: Option B
Answer: (B) 5 : 1
Question: The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?
(A) 1
(B) 20
(C) 0
(D) 19
(E) 18
Rationale: Explanation:
Average of 20 numbers = 0
=>Sum of 20 numbers/20=0
Hence at the most, there can be 19 positive numbers.
(Such that if the sum of these 19 positive numbers is x, 20th number will be -x)
ANSWER IS D
Answer: (D) 19
Question: At the end of the first quarter, the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 50 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?
(A) 20%
(B) 25%
(C) 30%
(D) 33%
(E) 40%
Rationale: Say price at the beginning of year = 100
End of 1st Quarter = 100+20 = 120
End of 2nd Quarter = 100+50 = 150
Percentage increase between 1st & 2nd Quarter=150−120/120∗100=25
Answer = B
Answer: (B) 25%
Question: Which of the following is a prime number ?
(A) 27
(B) 45
(C) 97
(D) 98
(E) 100
Rationale: Clearly, 97 is a prime number.
Answer: (C) 97
Question: A cistern can be filled by pipes A, X in 3 minutes 45 seconds. If the larger pipe takes 4 minutes less than the smaller pipe to fill the cistern, how much time will the smaller pipe take to fill the tank?
(A) 12min
(B) 6min
(C) 10min
(D) 8min
(E) 9min
Rationale: let A is larger pipe and X is smaller then,
let time taken to X = t
then time taken to A= t-4
so efficiency of X=t-4
and efficiency of A=t
using formula time= total work/total efficiency
total work =t(t-4)
total time= 3 + 45/60= 15/4
using formula
15/4=t(t-4)/(t+t-4)
by solving it
t=10 min
so smaller pipe take 10 mins.
ANSWER:C
Answer: (C) 10min
Question: How many even integers from 1 to 200 (both inclusive) have even number of factors?
(A) 13
(B) 14
(C) 5
(D) 6
(E) 7
Rationale: Integers having even number of factors will be perfect squares. even numbers will have even perfect squares. Thus, the possible values for the perfect squares are :
4,16,36,64,100,144,196 and the corresponding integers are 2,4,6,8,10,12,14 (more than 6). Thus E is the correct answer .
Answer: (E) 7
Question: What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?
(A) 551.28
(B) 551.25
(C) 551.2
(D) 551.23
(E) 551.21
Rationale: Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1025
820x + 1025 * 441
x = 551.25
So, value of each installment = Rs. 551.25.Answer: B
Answer: (B) 551.25
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
(A) 17 kmph
(B) 45 kmph
(C) 86 kmph
(D) 197 kmph
(E) 15 kmph
Rationale: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed
= 60/(4/3) = 45 kmph.
Answer:B
Answer: (B) 45 kmph
Question: An Indian company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
(A)  3,024
(B)  4,536
(C)  5,040
(D)  9,000
(E)  10,000
Rationale: An Indian company plans to assign identification numbers to its employees.The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.
Total = 9*9*8*7 = something with the units digit if 6.
Answer: B.
Answer: (B)  4,536
Question: A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35*7/17. What was the number erased?
(A) 7
(B) 8
(C) 6
(D) 5
(E) 4
Rationale: Explanation :
Let the higher number be n and x be the number erased.
Then((n(n+1)/2)+x)/(n+1) = 35*7/17 = 602/17
Hence, n = 69 and x =7 satisfy the above conditions.
Answer : A
Answer: (A) 7
Question: In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability R at least one of the shirts he draws will be blue?
(A) 25/153
(B) 28/153
(C) 5/17
(D) 4/9
(E) R=12/17
Rationale: P(at least one blue) = 1- P(0 blue) = 1 - 10/18*9/17 =R= 12/17.
Answer: E.
Answer: (E) R=12/17
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) 3377
(B) 3677
(C) 4200
(D) 2871
(E) 2123
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer: D
Answer: (D) 2871
Question: A man has Rs. 640 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) 110
(B) 115
(C) 120
(D) 125
(E) 130
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 640
16x = 640
x = 40.
Hence, total number of notes = 3x = 120
ANSWER :C
Answer: (C) 120
Question: A trader sells 92 meters of cloth for Rs. 9890 at the profit of Rs. 24 per metre of cloth. What is the cost price of one metre of cloth?
(A) 22
(B) 89.5
(C) 76.9
(D) 83.5
(E) 11
Rationale: SP of 1m of cloth = 9890/92 = Rs. 107.5
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 107.5 - Rs. 24 = Rs. 83.5
Answer: D
Answer: (D) 83.5
Question: In a 500 m race Dishu beats Abhishek by 100 m or 5 seconds. In another race on the same track at the same speeds. Abhishek and Prashant start at one end while Dishu starts at the opposite end. How many metres would Abhishek have covered, by the time Dishu meets Prashant given that Dishu's speed is 10 m/sec more than that of Prashant.
(A) 250 m
(B) 560 m
(C) 100 m
(D) 320 m
(E) 240 m
Rationale: Explanation :
Abhishek's speed = 100/5=20 m/s.
Time taken by Abhishek to cover 500 m =500/20=25 seconds.
Dishu's speed = 500/20 or 25 m/s
Prashant's speed = 15 m/s
Time taken by Dishu to meet Prashant in 500m race in opposite direction:
Distance covered by Abhishek:
=>500/(15+25).
=>12.5 sec.
=>12.5(20)= 250 m.
Answer : A
Answer: (A) 250 m
Question: Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?
(A) 10%
(B) 18%
(C) 19%
(D) 12%
(E) 13%
Rationale: Let the rate of interest during the second year be R%. Given,
4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544
R = 10%
Answer:A
Answer: (A) 10%
Question: The speed of a boat in upstream is 20 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph.
(B) 17 kmph.
(C) 18 kmph.
(D) 41 kmph.
(E) 30 kmph.
Rationale: Speed of the boat in still water = (20+80)/2 = 50 kmph. Speed of the stream = (80-20)/2
= 30 kmph.
Answer:E
Answer: (E) 30 kmph.
Question: in what proportion water to be mixed with spirit to gain 12.5% by selling it at cost price?
(A) 1:2
(B) 1:3
(C) 1:4
(D) 1:8
(E) 1:16
Rationale: If the total quantity=100
Actual quantity of spirit to be sold to get 12.5% gain=100*100/112.5=800/9
So the water =100-(800/9)=100/9
Proportion of water:spirit =100/9 : 800/9= 1:8
ANSWER:D
Answer: (D) 1:8
Question: The length of a rectangle is doubled while its width is doubled. What is the % change in area?
(A) 250%
(B) 300%
(C) 500%
(D) 650%
(E) 700%
Rationale: The original area is L*W
The new area is 2L*2W = 4*L*W = L*W + 3*L*W
The area increased by 300%.
The answer is B.
Answer: (B) 300%
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 60
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
(A) 51
(B) 98
(C) 90
(D) 125
(E) 162
Rationale: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 60 + (35-15) + (40-10-12) = 60+20+18 = 98
Hence, Answer will be B.
Answer: (B) 98
Question: Students of three different classes appeared in common examination. Pass average of 10 students of first class was 65%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
(A) 74%
(B) 75%
(C) 69%
(D) 71%
(E) None
Rationale: Solution:
Sum of pass students of first, second and third class,
= (65% of 10) + (60% of 15)+ (80% of 25)
= 6.5+9+20 = 35.5
Total students appeared,
= 10+15+25 = 50
Pass average,
= 35.5*100/50 = 71%.
Answer: Option D
Answer: (D) 71%
Question: Bhanu spends 30% of his income on petrol on scooter 30% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
(A) 2287
(B) 140
(C) 128
(D) 210
(E) 123
Rationale: Given 30% (Income ) = 300 ⇒⇒ Income = 1000
After having spent Rs.300 on petrol, he left with Rs.700.
His spending on house rent = 30% (700) = Rs.210
Answer:D
Answer: (D) 210
Question: A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 4 km/h that day, what was its approximate downstream speed?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Another way will be:
Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed
If 5D is the total distance, then distance covered in lake = D, distance covered upstream = 2D and distance covered downstream = 2D
=>5D/4 = D/4 + 2D/3 + 2D/x (where x is the downstream speed)
=> 5/4 = 1/4 + 2/3 +2/x (div. both sides by D)
=> 1.25 = .25+.66 +.33/x => x=5.99 ~6
option C
Answer: (C) 6
Question: A batsman makes a score of 80 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
(A) 40
(B) 50
(C) 62
(D) 30
(E) 56
Rationale: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+80 = 11x
x = 80-50 = 30
Answer is D
Answer: (D) 30
Question: For what values of k is the system of equations independent? The equations are as follows:
kx + 5y = 3; 3x + 4y = 9
(A) 15/9
(B) 15/2
(C) 15/1
(D) 15/4
(E) 15/7
Rationale: For the equations to be independent, conditions is a1a2≠b1b2a1a2≠b1b2
k3≠54k/3≠5/4 or k ≠15/4
Answer:D
Answer: (D) 15/4
Question: If it is 4:37 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.)
(A) 4:40
(B) 4:44
(C) 4:47
(D) 4:30
(E) 4:32
Rationale: 4:37minus 2,880,717in any way must end with 0, the only answer choice which ends with 0 is A.
Answer: A.
Answer: (A) 4:40
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 2
(B) 4
(C) 6
(D) 3
(E) 8
Rationale: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
ANSWER C
Answer: (C) 6
Question: A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 72
(B) 67
(C) 28
(D) 126
(E) 27
Rationale: Length = Speed * time
Speed = L/T
S = 700/20
S = 35 M/Sec
Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 126 Kmph
Answer:D
Answer: (D) 126
Question: What is the 28th digit to the right of the decimal point in the decimal form of 5/11?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 5/11 = 0.45454545...
The even numbered positions in the decimal expansion are all 5.
The answer is C.
Answer: (C) 5
Question: If E:F = 3:1 and F:G = 5:2 then E:F:G is
(A) 15:5:3
(B) 15:5:2
(C) 16:5:2
(D) 15:4:2
(E) 5:5:2
Rationale: Solution:
E/F = 3/1;
F/G = 5/2;
E:F:G = 3*5:1*5:1*2 = 15:5:2.
Answer: Option B
Answer: (B) 15:5:2
Question: If a trader sold two cars each at Rs. 325475 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is?
(A) 1.44%
(B) 1.74%
(C) 1.84%
(D) 1.97%
(E) 2.25%
Rationale: SP of each car is Rs. 325475, he gains 15% on first car and losses 15% on second car.
In this case, there will be loss and percentage of loss is given by
= [(profit%)(loss%)]/100
= (15)(15)/100 % = 1.44%
Answer:E
Answer: (E) 2.25%
Question: If the first day of a year (other than leap year) was Wednesday, then which was the last day of that year?
(A) Saturday
(B) Wednesday
(C) Tuesday
(D) Monday
(E) None of these
Rationale: Explanation :
Given that first day of a normal year was Wednesday
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Wednesday+ 1 Odd day) = Thursday
Therefore, last day of the mentioned year = Wednesday. Answer : Option B
Answer: (B) Wednesday
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is
(A) 2 km/hr
(B) 3 km/hr
(C) 4 km/hr
(D) 5 km/hr
(E) None of these
Rationale: Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr
So we know from question that it took 4(1/2)hrs to travel back to same point.
So,
30/15+x−30/15−x=4 1/2
=>900/225−x2=9/2
=>9x2=225
=>x=5km/hr
Option D
Answer: (D) 5 km/hr
Question: A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice?
(A) 1/16
(B) 5/16
(C) 2/5
(D) 13/16
(E) 27/32
Rationale: Fair coin is tossed 5 times . Hence total number of outcomes = 2^5 = 32.
Problem asks for probability of getting atleast heads twice. Hence if we calculate probability of getting Heads exactly once and probability of not getting Heads at all and subract it from the total probability of the event which is 1 (As total probability of certain event will be always 1) we can get the probability of getting atleast heads twice.
Probability of getting exactly one head and no heads= (Number of possible outcomes [ HTTTT , THTTT, TTHTT, TTTHT, TTTTH , TTTTT] = 6)/ (Total possible outcomes = 32)
=> 6/32 = 3/16
Hence probability of getting atleast heads twice = 1 - (3/16) = 13/16 => Choice [D]
Answer: (D) 13/16
Question: If 8a = 9b and ab ≠0, what is the ratio of a/9 to b/8?
(A) 64/81
(B) 8/9
(C) 1
(D) 9/8
(E) 81/64
Rationale: if ab ≠0
then a and b has two integer sets of pair
if a=9 then b=8
and if a=-9 then b=-8
also in fraction if a=1/8 then b=1/9
any of the pair we check the ratio 8a/9b=1
ANSWER:C
Answer: (C) 1
Question: The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A?
(A) 81
(B) 65
(C) 75
(D) 89
(E) 90
Rationale: A + B + C = 3 *70 = 210
A + B + C + D = 4 * 70 = 280 ---- (i)
So, D = 70& E = 70 + 3 = 73
B + C + D +E =68 * 4 = 272 --- (ii)
From Eq. (i) & (ii)
A-E = 280 –272 = 8
A = E +8 = 73 + 8 = 81
Answer : A
Answer: (A) 81
Question: How many legs are there if each sheep has 4 legs and there are total 250 of that kind?
(A) A)700
(B) B)800
(C) C)1000
(D) D)10000
(E) of the above
Rationale: Sol.
Total of 250 each has 4 legs
= 250 * 4
= 1000
Answer : C
Answer: (C) C)1000
Question: A, B and C rents a pasture for Rs.1073. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 289
(C) 267
(D) 255
(E) 333
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 1073 = 333
Answer: E
Answer: (E) 333
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 10 days
(B) 20 days
(C) 5 days
(D) 25 days
(E) 15 days
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
ANSWER A
Answer: (A) 10 days
Question: If 14 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
(A) 78 days.
(B) 154 days.
(C) 149 days.
(D) 148 days.
(E) 167 days.
Rationale: B
154 days.
From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (14*6*88/1) = (6*8*d/1)
on solving, d = 154 days.
Answer: (B) 154 days.
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
A. 3 4/9 days
(A) 9 3/7 days
(B) 9 7/8 days
(C) 9 3/8 days
(D) 9 3/8 days
(E) 2 3/8 days
Rationale: 1/15 + 1/25 = 8/75
75/8
= 9 3/8 days
Answer:C
Answer: (C) 9 3/8 days
Question: . Data sufficiency question:
What will be the percentage profit of selling one liter milk.?
1) 16 liter of milk is sold at cost price after adding 20% water to it.
2) the cost price of one liter milk is Rs.16.
(A) 23
(B) 29
(C) 27
(D) 1291
(E) 11
Rationale: Explanation:
Let us assume one liter costs Rs.1. So C.P = Rs.16
When 20% water is added, then total volume = 20 liters. So SP = 20. Profit can be calculated.
Statement 1 is sufficient.
Statement 2 is not required.
Answer:B
Answer: (B) 29