mathewhe/aqua_rat huggingface dataset:
Question: A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river. They met at 500 yards away from A and after that they met 300 yards away from shore B without halting at shores. Find the distance between the shore A & B.
(A) 1100 yards
(B) 1200 yards
(C) 1300 yards
(D) 1400 yards
(E) 1000 yards
Rationale: If X is the distance, a is speed of A and b is speed of B, then ;
500/a= (x-500)/b and (x+300)/a = (2x-300)/b , solving it, we get x=1200 yards
ANSWER:B
Answer: (B) 1200 yards
Question: Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is?
(A) 40
(B) 99
(C) 88
(D) 44
(E) 11
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M = 60x. So, 60x = 2400 or x = 40.
The numbers are (3 * 40), (4 * 40) and (5 * 40).
Hence, required H.C.F = 40.
Answer: A
Answer: (A) 40
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 50% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 15%
(D) 22%
(E) 20%
Rationale: 0.1 M = 0.50 E
=> E/M = 1/5* 100 = 20%
So answer is E.
M - # of Motorists
E - # of Motorists exceeding speed
Answer: (E) 20%
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is
(A) 5200
(B) 5226
(C) 5286
(D) 5330
(E) 5336
Rationale: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336.
E
Answer: (E) 5336
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
(A) 22 days
(B) 77 days
(C) 88 days
(D) 11 days
(E) 18 days
Rationale: x/24 + x/30 + x/40 = 1
x = 11 days
Answer:D
Answer: (D) 11 days
Question: A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
(A) 73.9
(B) 72.9
(C) 73.0
(D) 73.5
(E) 92.2
Rationale: Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(90 - 9)/90]2 (90) = 72.9 litres.
Answer: Option B
Answer: (B) 72.9
Question: It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: The bacteria doubles each day, so after 29 days, the dish was half full.
After 28 days, the dish was one quarter full.
After 27 days, the dish was one eighth full.
After 26 days, the dish was one sixteenth full.
After 25 days, the dish was 1/32 full.
After 24 days, the dish was 1/64 full.
The answer is C.
Answer: (C) 24
Question: If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
(A) 6z
(B) 4z
(C) 5z/3
(D) 3z/2
(E) 3z/5
Rationale: The sum of three greatest should be more than sum of two lowest.
The total sum is; 5z
A. 6z; 6z is more than 5z. Not possible.
B. 4z; 5z-4z=z(Possible)
C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible
D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible
E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible.
Ans:B
Answer: (B) 4z
Question: Find number which is 60% less than 120.
(A) 18
(B) 22
(C) 28
(D) 48
(E) 98
Rationale: Explanation:
60% less is 40% of the given number
Therefore, 40% of 120 is 48.
ANSWER: D
Answer: (D) 48
Question: A shopkeeper marks the price of his goods at 25% higher than the original price. After that, he allows a discount of 12%. What profit or loss does he get?
(A) 10% profit
(B) 15% profit
(C) 10% loss
(D) 15% loss
(E) 25% loss
Rationale: Here, x = 25 and y = - 12
Therefore, the net % change in value
= ( x + y + xy/100) %
= [25 - 12 + ( -12 x 25)/100]% or 10%
Since the sign is positive , there is a profit of 10%
ANSWER:A
Answer: (A) 10% profit
Question: Sandy buys an old scooter for $800 and spends $200 on its repairs. If Sandy sells the scooter for $1400, what is the gain percent?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: selling price / total cost = 1400/1000 = 1.4
The gain percent is 40%.
The answer is C.
Answer: (C) 40%
Question: Sam bought a container of cashew for Rs.2200000 weighing 14 tons. Packed it in a package of 1 kg and sold the package for Rs. 200. What is the % of profit Sam has made?
(A) 20.3%
(B) 24.2%
(C) 29.5%
(D) 27.2%
(E) 30.1%
Rationale: Cost of buying= Rs. 2200000
Cost of selling= Rs(14000x200)=Rs.2800000
Profit made by Sam=Rs.600000
Percentage of profit made by Sam=(600000/2200000)x100=27.2%
Answer:D
Answer: (D) 27.2%
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 249 marks in the second test and failed by 66 marks in that test. Find the pass mark in the first test?
(A) 768
(B) 243
(C) 246
(D) 280
(E) 224
Rationale: Let the maximum mark in each test be M.
The candidate failed by 66 marks in the second test.
pass mark in the second test = 249 + 66 = 315
45/100 M = 315
Pass mark in the first test = 40/100 M = 40/45 * 315 = 280.
Answer:D
Answer: (D) 280
Question: The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 70 percent, then the value of T decreases by what percent?
(A) 16 1/3%
(B) 33 ¹/₃%
(C) 50%
(D) 66 ²/₃%
(E) 75%
Rationale: We can assign numbers:
lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T)
Now increasing S by 50% gives S=6, K remains constant, so T = 2 (6/2=3)
decrease in T= 1, percent decrease in T = (1/6)*100 = 16.33%
Answer A
Answer: (A) 16 1/3%
Question: John was 19 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/8 of John's. How old is Betty?
(A) 21
(B) 26
(C) 28
(D) 30
(E) 32
Rationale: Assume Betty's age on marriage = x years.
John's age on marriage = 19
John's age after 5 years = 24 years.
Betty's age after 5 years = x + 5
Given: x + 5 = 7/8 (24) = 21
Therefore Betty's current age = 21
Option A
Answer: (A) 21
Question: Find the area of a parallelogram with base 25 cm and height 15 cm?
(A) 295 cm2
(B) 385 cm2
(C) 275 cm2
(D) 375 cm2
(E) 285 cm2
Rationale: Area of a parallelogram = base * height = 25 * 15
= 375 cm2
Answer:D
Answer: (D) 375 cm2
Question: If x, y and r are positive integers greater than 1, and x and y are factors of r, which of the following must be the factor of r^(xy)?
I. x+y
II. y^x
III. x^2 * y^2
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: given that p and q are factors of r.
so we can picture it this way r=x*y*n (n-some another factor of r)
so, r^xy= (x*y*n)^xy
I. x+y .since the question is MUST BE TRUE, we eleminate this option
II. (x*y*n)^xy / y^x= integer YES!
III.(x*y*n)^xy/ x^2 * y^2 YEs, since we are said that integer x>1 and integer y>1
Answer: (E) II and III
Question: If the number 5 * 2 is divisible by 6, then * = ?
(A) 2
(B) 7
(C) 3
(D) 6
(E) 5
Rationale: Explanation :
Replacing * by x
5 x 2 is divisible by 2 (Reference : Divisibility by 2 rule)
For 5 x 2 to be divisible by 3, 5 + x + 2 shall be divisible by 3 (Reference : Divisibility by 3 rule)
=> 7 + x shall be divisible by 3
=> x can be 2 or 5 or 8
From the given choices, answer = 2. Answer : Option A
Answer: (A) 2
Question: What is the next number in the series?
2,4,7,10,15,18,....
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: Adding (0,1,2,3,4,5,6,7) to the prime numbers.
2+0=2
3+1=4
5+2=7
7+3=10
11+4=15
13+5=18
17+6=23
ANSWER:A
Answer: (A) 23
Question: The tax on a commodity is diminished by 25% and its consumption increased by 15%. The effect on revenue is?
(A) 12% decrease
(B) 18% decrease
(C) 19% decrease
(D) 13.75% decrease
(E) 12.5% decrease
Rationale: 100 * 100 = 10000
75 * 115 = 9200
-----------
10000-----------1375
100-----------? => 13.75% decrease
Answer: C
Answer: (C) 19% decrease
Question: In a certain pond, 60 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A) 400
(B) 1,500
(C) 1,250
(D) 2,500
(E) 10,000
Rationale: This is a rather straight forward ratio problem.
1. 60 fish tagged
2. 2 out of the 50 fish caught were tagged thus 2/50
2/50=60/x
thus, x=1500
Think of the analogy: 2 fish is to 50 Fish as 50 fish is to ...?
You've tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch.
B
Answer: (B) 1,500
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5620. What is the average monthly balance maintained by John in his
account during the year?
(A)  2840
(B)  5680
(C)  6840
(D)  7540
(E)  28100
Rationale: bank balance is doubled with accumulation of interest tp 5620..
this means INTEREST is 5620/2=2810 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 28100..
Answer: (E)  28100
Question: What sum of money will produce Rs.80 as simple interest in 4 years at 3 1/2 percent?
(A) 263
(B) 571.4
(C) 367
(D) 368
(E) 339
Rationale: 80 = (P*4*7/2)/100
P = 571.4
Answer: B
Answer: (B) 571.4
Question: If 0.75 of a number is equal to 0.025 of another number, the ratio of the numbers is :
(A) 2 :3
(B) 3 :4
(C) 1:30
(D) 20 : 3
(E) 30:7
Rationale: 0.75A = 0.025B
-> A/B = 0.025/0.75 = 25/750 = 1/30
:. A : B = 1 : 30
ANSWER:C
Answer: (C) 1:30
Question: The length of a rectangle is halved, while its breadth is tripled. Wat isthe % change in area?
(A) 40%
(B) 45%
(C) 50%
(D) 60%
(E) 67%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: (C) 50%
Question: If a pair of opposite sides of a square is increased by 5cm each, then the ratio of the sides of the new figure is 3 : 2. What is the original area of the square?
(A) 125 cm2
(B) 225 cm2
(C) 81 cm2
(D) 100 cm2
(E) None of these
Rationale: Let the original side of the square = x cm
x+5/x=3/2 or 2x + 10 = 3x
\ x = 10 cm
\ original area = (10)2 = 100 cm2
Answer D
Answer: (D) 100 cm2
Question: There are 150 'zeroes' and 151 'ones' written on a black board. A step involves choosing three digits and replacing them with a single digit. If all the three digits are identical, they are replaced with the same digit. Otherwise, the digit that appears twice replaces the three chosen digits. What is the minimum number of steps after which there will be no zero written on the blackboard?
(A) 11
(B) 37
(C) 36
(D) 76
(E) 33
Rationale: If we strike out 3 zeros, we are in effect reducing two zeroes. So we need 74 steps to reduce 148 zeroes. There are 2 zeroes and 151 ones left now. The remaining zeroes can be reduced in 2 steps. Hence the answer is 76.
Answer:D
Answer: (D) 76
Question: A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 6,000 meters of fabric?
(A) $9,300
(B) $10,400
(C) $11,500
(D) $12,600
(E) $13,700
Rationale: For first 2000 meters he does not get any discount.
The price is 2*2000 = $4000
For next 1500 meters, he gets a 5% discount.
The price is 1.9*1500 = $2850
For the next 1500 meters, he gets a 7% discount.
The price is 1.86*2500 = $4650
The total price is $4000 + $2850 + $4650 = $11,500
The answer is C.
Answer: (C) $11,500
Question: A man can hit a target once in 3 shots. If he fires 4 shots in succession, how many ways that he will hit his target?
(A) 71/234
(B) 81/133
(C) 81/343
(D) 16/81
(E) 91/324
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 - 1/3 = 2/3
Therefore, the probability that he will not hit the target in any of the four shots = 2/3 ^4 = 16/81
D
Answer: (D) 16/81
Question: Identify the next two numbers in this Sequence ?
101, 112, 131, 415, 161, 718, ???, ???
(A) 123005
(B) 456804
(C) 545788
(D) 342678
(E) 192021
Rationale: E
192 021
If you look at it as two-digit numbers you'll see:10 11 12 13 14 15 16 17 18 19 20 21
Answer: (E) 192021
Question: How many diagonals does a 59-sided convex polygon have?
(A) 1168
(B) 1652
(C) 2452
(D) 3304
(E) 4256
Rationale: A 59-sided convex polygon has 59 vertices.
If we examine a single vertex, we can see that we can connect it with 56 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be (59)(56) = 3304
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3304 by 2 to get 1652.
The answer is B.
Answer: (B) 1652
Question: An inspector rejects 0.04% of the meters as defective. How many will he examine to reject 2?
(A) A)1500
(B) B)2000
(C) C)2500
(D) D)5000
(E) E)3100
Rationale: Let the number of meters to be examined be x
Then, 0.04% of x = 2
(4/100)*((1/100)*x = 2
x = 5000
Answer is D
Answer: (D) D)5000
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 150, the runs scored by B are?
A. 15 B. 18
(A) 22
(B) 18
(C) 99
(D) 36
(E) 24
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 150 = 36
Answer: D
Answer: (D) 36
Question: An bus covers a certain distance at a speed of 250 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 1520 km/hr
(B) 1250 km/hr
(C) 1256 km/hr
(D) 1231 km/hr
(E) 1220 km/hr
Rationale: Distance = (250 x 5) = 1250 km.
Required speed = 1250km/hr.
B
Answer: (B) 1250 km/hr
Question: Number of prime numbers between 30 and 50 is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: total 5=31,37,41,43,47
ANSWER:B
Answer: (B) 5
Question: If V = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in V than the median of the numbers in V?
(A)  1.0
(B)  1.5
(C)  2.0
(D)  2.5
(E)  3.0
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (1 + 7 + 18 + 20 + 29 + 33)/6 = 18
Median = (18 + 20)/2 = 19
Difference = 1
Option A
Answer: (A)  1.0
Question: The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
(A) Rs.10529
(B) Rs.10528
(C) Rs.10560
(D) Rs.10508
(E) Rs.10568
Rationale: Let the rate of interest be R% p.a.
4400{[1 + R/100]2 - 1} = 11193.60
[1 + R/100]2 = (44000 + 11193.60)/44000
[1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625
[1 + R/100]2 = 784/625 = (28/25)2
1 + R/100 = 28/25
R/100 = 3/25
Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100
=Rs.10560
Answer:C
Answer: (C) Rs.10560
Question: A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed.
If there is a lekage also which is capable of draining out the liquid from the tank at half of the rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?
(A) 3 hours
(B) 4 hours
(C) 5 hours
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Rate of leakage = 8.33% per hour
Net efficiency = 50 - (16.66 + 8.33)= 25%
Time required = 100/25 = 4 hours
Answer: B
Answer: (B) 4 hours
Question: P & Q sitting in a circular arrangement with 10 persons. What is the probability that P & Q will sit together?
(A) 1/13
(B) 2/11
(C) 3/14
(D) 1/15
(E) 2/17
Rationale: n(S)= number of ways of sitting 12 persons at round table:
=(12-1)!=11!
Since two persons will be always together, then number of persons:
=10+1=11
So, 11 persons will be seated in (11-1)!=10! ways at round table and 2 particular persons will be seated in 2! ways.
n(A)= The number of ways in which two persons always sit together =10!×2
So probability = 10!*2!/11!= 2/11
B
Answer: (B) 2/11
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 26 sec
(B) 76 sec
(C) 48 sec
(D) 27 sec
(E) 22 sec
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km
= 2000 m.
Required time = 2000 * 3/125
= 48 sec.
Answer:C
Answer: (C) 48 sec
Question: On a certain day, Tim invested $600 at 10 percent annual interest, compounded annually, and Lana invested 800 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
(A) $5
(B) $15
(C) $44
(D) $100
(E) $105
Rationale: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
600(1.10)^2 = 600(1.21) = 726
and Lana would have
800(1.05)^2 = 800(1.1025) = 882
Thus, Tim earned 126 dollars, while Lana earned 82 dollars
The difference is $44 and the answer is C.
Answer: (C) $44
Question: Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1310, how much does he invest in 12% stock at Rs. 120?
(A) s. 4000
(B) s. 4500
(C) s. 5500
(D) s. 6000
(E) s. 6500
Rationale: Let investment in 12% stock be Rs. x.
Then, investment in 15% stock = Rs. (12000 - x).
12/120 * x + 15/125 * (12000- x) = 1310
x/10 + 3/25(12000-x) = 1310
5x + 72000 - 6x = 1310 x 50
x = 6500.
Answer = E
Answer: (E) s. 6500
Question: When an amount was distributed among 14 boys, each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount?
(A) 5000
(B) 5030
(C) 5010
(D) 5040
(E) 5020
Rationale: Let the total amount be Rs. X the,
x/14 - x/18 = 80 <=> 2x/126 = 80 <=>x/63
= 63 x 80 = 5040.
Hence the total amount is 5040
Answer is D.
Answer: (D) 5040
Question: A table is bought for Rs.950/- and sold at Rs.800/- find the loss percentage
(A) 10% Loss
(B) 10% Gain
(C) 15% Loss
(D) 20% Gain
(E) 30% Gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (800 ~ 950)/950 = 15% Loss
C
Answer: (C) 15% Loss
Question: It takes eleven minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video, rounded to the nearest hundredth?
(A) 13.48
(B) 13.85
(C) 14.21
(D) 14.67
(E) 14.92
Rationale: The laptop can load the video at a rate of 1/15 of the video per second.
The phone can load the video at a rate of 1/(60*11) = 1/660 of the video per second.
The combined rate is 1/15 + 1/660 = 45/660 of the video per second.
The time required to load the video is 660/45 = 14.67 seconds.
The answer is D.
Answer: (D) 14.67
Question: A sum of money deposited at C.I. amounts to Rs.1980 in 3 years and to Rs.2492 in 4 years. Find the rate percent?
(A) 30%
(B) 10%
(C) 25%
(D) 19%
(E) 50%
Rationale: 1980--- 512
100 --- ? => 25%
Answer: C
Answer: (C) 25%
Question: 13 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?
(A) 80
(B) 160
(C) 720
(D) 1100
(E) 2184
Rationale: No. of ways of picking 2 biology books(from 13 books) = 13c2 = (13*12)/2 = 78
No. of ways of picking 2 chemistry books(from 8 books) = 8c2 = (8*7)/2 = 28
Total ways of picking 2 books of each type = 78*28 =2184
(Option E)
Answer: (E) 2184
Question: Madhu started a business and he invested in 76000, After some month, Amar came to join with him and invest 57000.The end of the year the total profit was divided among them into ratio form 2 : 1.Find after how many months Amar join?
(A) 5 months
(B) 3 months
(C) 7 months
(D) 4 months
(E) 8 months
Rationale: we can assume that Amar join into business after x months. So Amar money was invest into (12 – x ) months.
912000 = 114000 ( 12 – x ) = 114 ( 12 – x ) = 912Rightarrow x = 4
After 4 months amar join the business.
Answer: D
Answer: (D) 4 months
Question: Steve traveled the first 2 hours of his journey at 35 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?
(A) 60 mph
(B) 56.67 mph
(C) 53.33 mph
(D) 62 mph
(E) 66.67 mph
Rationale: Distance traveled in 2 hours = 2 * 35 = 70 m
Distance traveled in 3 hours = 3 * 80 = 240m
Total distance covered = 240 + 70 = 310m
Total time = 2 + 3 =5 h
Hence avg speed = total distance covered / total time taken
= 310/5 = 62 mph
Answer: D
Answer: (D) 62 mph
Question: A train covers a distance of 12 km in 10 min. If it takes 7 sec to pass a telegraph post, then the length of the train is?
(A) 177 m
(B) 189 m
(C) 140 m
(D) 178 m
(E) 188 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 7
= 140 m.
Answer: C
Answer: (C) 140 m
Question: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 42
(B) 52
(C) 60
(D) 32
(E) 15
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42
ANSWER A
Answer: (A) 42
Question: If a/x = 1/3 and a/y =1/ 5, then (x + y) =
(A) A)2a
(B) B)a/2
(C) C)6a
(D) D)7a
(E) E)8a
Rationale: Ratio 1:
3a = x
Ratio 2:
5a = y
x+y = 8a
Answer is E
Answer: (E) E)8a
Question: A scooter costs 45,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years?
(A) 10,000
(B) 23,040
(C) 12,800
(D) 12,000
(E) None of these
Rationale: After first year, the value of the scooter = 36,000
After second year, the value of scooter = 28,800
After third year, the value of scooter = 23,040
Answer B
Answer: (B) 23,040
Question: Which of the following equivalent to (1/343)^2?
(A) (0.019)^3
(B) (0.020)^3
(C) (0.021)^3
(D) (0.022)^3
(E) (0.023)^2
Rationale: (1/343)^2 = (1/7^3)^2 = (1/7)^6 = (1/49)^3 = (0.020)^3
Answer: Option B
Answer: (B) (0.020)^3