mathewhe/aqua_rat huggingface dataset:
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
(A) 32 m
(B) 31 m
(C) 30 m
(D) 35 m
(E) 38 m
Rationale: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
ANSWER A
Answer: (A) 32 m
Question: 1/2, 1/4, ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?
(A) 0.1 < x < 1
(B) 0.01 < x < 0.1
(C) 0.001 < x < 0.01
(D) 0.0001 < x < 0.001
(E) 0.00001 < x < 0.0001
Rationale: In the Sequence notice that the sequence is just the 1/(2^n) ...
so for 1st term=1/2^1=1/2
2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...
Thus the 10th term will be 1/(2^10)=1/1024
Roughly, 1/1024 can be 1/1000=0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.
thus the ans will lie btw. 0.1 and 1.(A)
Answer: (A) 0.1 < x < 1
Question: If d is a positive integer greater than 1, what is the sum of the multiples of d from d to d^2, inclusive?
(A)  d(d + 1)(d-1)
(B)  d^2(d + 1)/2
(C)  d^2(d-1)
(D)  (x^3 + 2x)/2
(E)  x(x-1)^2
Rationale: Ans :- B=d^2(d + 1)/2
I substituted 3 in all answer choices.
Option B and C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
Only B option satisfied.
Answer: (B)  d^2(d + 1)/2
Question: At a certain zoo, the ratio of sea lions to penguins is 4 to 11. If there are 84 more penguins than sea lions at the zoo, how many sea lions are there?
(A) 24
(B) 36
(C) 48
(D) 72
(E) 132
Rationale: The ratio as mentioned = 4/11
also
sea lion + 84 = penguins
or,
4x+84=11x
x=84/7=12
number of sea lions= 12*4=48
ANSWER:C
Answer: (C) 48
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent W?
(A) 20%
(B) 80%
(C) 100%
(D) 180%
(E) 200%
Rationale: C.
Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
W=[(2 - 1)/1] * 100% = 100%
Answer: (C) 100%
Question: if length of rectangle is increased by 10%, and breadth is decreased by 10%.what will it effect on area of rectangle?
(A) it will have no effect
(B) 1% increase
(C) 1% decrease
(D) 2% increase
(E) 2% decrease
Rationale: let initial length=l,and breadth=b
area=l*b
new length=l*110%=[l*110/100]=11l/10,new breadth=9b/10
new area=11l/10*9b/10=99/100lb
decrease in area=[lb-99/100lb]=lb/100=% decrease=[lb/100*1/lb*100]=1%
answer C
Answer: (C) 1% decrease
Question: if p/q=3/4
then3p+6q=?
(A) 25/4
(B) 25/2
(C) 20/4
(D) 33/4
(E) 25/3
Rationale: 3p+6q=?
Divided by q,
3(p/q)+6=x
3*(3/4)+6=33/4
ANSWER:D
Answer: (D) 33/4
Question: If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?
(A) 9
(B) 8
(C) 7
(D) 5
(E) 3
Rationale: Consider 9x - 3y = 12.........divide both sides by 3: 3x - y = 4............now multiply both sides by 2: 6x - 2y
= 8
Answer:B
Answer: (B) 8
Question: Anand and Deepak started a business investing Rs. 6,000 and Rs. 8,000 respectively. Out of a total profit of Rs.4,600. Deepak's share is?
(A) s. 2600.31
(B) s. 2628.57
(C) s. 2450.32
(D) s. 3400.41
(E) s. 2400.32
Rationale: Ratio of their shares = 6000 : 8000 = 3 : 4
Deepak's share = Rs. (4600 * 4/7) = Rs. 2628.57 ANSWER "B
Answer: (B) s. 2628.57
Question: The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 34 ?
(A) 440
(B) 512
(C) 550
(D) 620
(E) 750
Rationale: Large numbers are made in two ways:
Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.
31*2 = 62 (large prime number)
2^6 = 64 (many small prime numbers)
To get a sum as large as 34 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.
You are left with 620 which is 31*2*2*5 (sum greater than 34)
Answer (D)
Answer: (D) 620
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.2
(B) 1.9
(C) 1.7
(D) 1.5
(E) 1.1
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Answer: (D) 1.5
Question: The factorial expression 13!/2! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 6
(D) 7
(E) none of these
Rationale: 13!/2! => 13 x 12 x 11 x 10 x 9 x8x7x6x5x4x3
(A) 3 Can divide 12 or 9
(B) 5 Can divide 10
(C) 6 Can divide 12
(D) 7 can divide 7, 21,42
Hence answer will be (E)
Answer: (E) none of these
Question: 16.02 Ã— 0.0001 = ?
(A) 0.1602
(B) 0.001602
(C) 1.6021
(D) 0.01602
(E) None of these
Rationale: 16.02 Ã— 0.0001 = 0.001602
The answer is B.
Answer: (B) 0.001602
Question: For how many different pairs of positive integers (a, b) can the fraction 2/15 be written as the sum 1/a + 1/b ?
(A) 4
(B) 5
(C) 8
(D) 9
(E) 10
Rationale: (1/a)+(1/b)=215
I. 1/a+1/b=1/15+1/15(a,b)=(15,15)
II. 1/a+1/b=2∗2/15∗2=1/30+3/30(a,b)=10,30)and(30,10)
III.1/a+1/b=2∗3/15∗3=1/45+5/45(a,b)=(45,9)and(9,45)
IV.1/a+1/b=2∗4/15∗4=3/60+5/60(a,b)=(20,12)and(12,20)
Now, we know that the no of different pairs can only be of the form 2k+1. We already have 7 such combinations. Thus, the only value which will satisfy from the given options is 9.
Answer : D
Answer: (D) 9
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 18 sec
(B) 16 sec
(C) 19 sec
(D) 11 sec
(E) 12 sec
Rationale: :
Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35
= 16 sec
Answer: B
Answer: (B) 16 sec
Question: The maximum number of students among them 1340 pens and 1280 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
(A) 25
(B) 30
(C) 20
(D) 45
(E) 90
Rationale: number of pens = 1340
number of pencils = 1280
Required number of students = H.C.F. of 1340 and 1280 = 20
Answer is C
Answer: (C) 20
Question: If x + y = 3 and y/x= 2 then y = ?
(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2
Rationale: from the given data :
y/(3-y) = 2
=> y= 6- 2y
=> y=2
ANSWER:E
Answer: (E) 2
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?
(A) 6
(B) 12
(C) 14
(D) 16
(E) 28
Rationale: Equate the fat:
0.1x + 0.35*8 = 0.2(x + 8) --> x = 12.
Answer: B.
Answer: (B) 12
Question: The positive integer f is divisible by 10. What is the remainder of dividing f(2+4)(1+f) by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: When we multiply any of these options: 10*6*11 (f=10) or 20*6*21 (f=20) we end up with numbers ending in 0 which are exactly divisible by 5 leaving no remainder. Hence answer is A.
Answer: (A) 0
Question: A certain number when divided by 39 leaves a remainder 19, what is the remainder when the same number is divided by 13?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 4
Rationale: Explanation:
39 + 19 = 58/13 = 6 (Remainder)
Answer: D
Answer: (D) 6
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 7. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 7 receives how many more dollars per hour than an employee with a salary grade of 1?
(A) $0.50
(B) $1.00
(C) $1.25
(D) $1.50
(E) $1.75
Rationale: Salary grade of 7 is p(7)=9.50+0.25(7–1)=9.50+0.25*6;
Salary grade of 1 is p(1)=9.50 + 0.25(1–1)=9.50;
p(7)-p(1)=9.50+0.25*6-9.50=1.5.
Answer: D.
Answer: (D) $1.50
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 30?
(A) 30
(B) 14
(C) 50
(D) 42
(E) 70
Rationale: Greatest common factor n and 16 is 4 = 2*2 * 2*2
Greatest common factor n and 45 is 3 = 3*3 *5
Greatest common factor n and 30 is = 2*3*5 =30
A
Answer: (A) 30
Question: Working alone, sawyer finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. sawyer alone cleans the entire house in 6 hours. How many hours will it take Nick and sawyer to clean the entire house if they work together?
(A) 1.5
(B) 2
(C) 2.4
(D) 3
(E) 3.6
Rationale: Answer is 3.6 hours.
sawyer does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
answer is E
Answer: (E) 3.6
Question: A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability W that the game will end after the fourth throw?
(A) 1/16
(B) 3/32
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: Another approach:
Two likely scenarios would be : HHTH or THTH
for each of the scenarios probability would be 1/16
So Probablilty W is 1/16 + 1/16 = 1/8.C
Answer: (C) 1/8
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
(A) 52.6 m2
(B) 58.8 m2
(C) 52.8 m2
(D) 52.3 m2
(E) 51.8 m2
Rationale: 42/360 * 22/7 * 12 * 12 = 52.8 m2
Answer: C
Answer: (C) 52.8 m2
Question: A motor starts with the speed of 70 kmph with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms?
(A) 2 1⁄4 hours
(B) 4 1⁄2 hours
(C) 4 hours 5 minutes
(D) Cannot be determined
(E) None of these
Rationale: Distance covered in first two hours = 70 × 2 = 140 km
Distance covered in next two hours = 80 × 2 = 160 km
Distance covered in first four hours
140 + 160 = 300 km
Remaining distance = 345 – 300 = 45 km.
Now, this distance will be covered at the speed of 90 km/hr.
∴ Time taken = 45⁄90 = 1⁄2 hour.
Total time= 4 + 1⁄2 = 41⁄2 hour
Answer B
Answer: (B) 4 1⁄2 hours
Question: 0.5, 0.55, 0.65, 0.8, ?
(A) 3
(B) 1
(C) 5
(D) 8
(E) 9
Rationale: B
1
The pattern is + 0.05, + 0.10, + 0.15, .....
Answer: (B) 1
Question: The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 150. What is the number of frogs in the pond ?
(A) 148
(B) 154
(C) 156
(D) 144
(E) None
Rationale: Solution:
Ratio of Ducks and Frogs in Pond,
= 37 : 39.
Average of Ducks and Frogs in Pond,
= 150.
So, total number of Ducks and Frogs in the Pond,
= 2* 150 = 300.
Therefore,
Number of Frogs, = (300 *39)/76 = 154.
Answer: Option B
Answer: (B) 154
Question: If each digit in the set of A = (6,7,8,9) is exactly used once, in how many ways can the digits be arranged such that the 6 and 7 are not adjacent?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 22
Rationale: The answer should be = total arrangements - arrangements when 2 and 5 are together.
= 4! - 3! * 2! = 24 -12 = 12
take (6,7),8,9 here there are 3 entities whose number of arrangements are 3! and 2! is the arrangement between 3 and 4
Answer is A
Answer: (A) 12
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 13%, then the cost price of the article is:
(A) 545
(B) 334
(C) 555
(D) 664
(E) 5598
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/113 = Rs. 545
Answer: Option A
Answer: (A) 545
Question: The largest 4 digit number exactly divisible by 88 is:
(A) 9800
(B) 9824
(C) 9944
(D) 10000
(E) 11000
Rationale: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
C
Answer: (C) 9944
Question: A 80 cm long wire is to be cut into two pieces so that one piece will be 3/5th of the other, how many centimeters will the shorter piece be?
(A) A)30
(B) B)20
(C) C)83
(D) D)21
(E) E)52
Rationale: Explanation:
1: 3/5 = 5: 3
3/8 *80 =30
Answer: Option A
Answer: (A) A)30
Question: What is the are of an equilateral triangle of side 16 cm?
(A) 10
(B) 99
(C) 88
(D) 77
(E) 12
Rationale: 36 * 5/18 = 10 mps
Answer: A
Answer: (A) 10
Question: A batsman scored 150 runs which included 3 boundaries and 8 sixes. What % of his total score did he make by running between the wickets
(A) 40%
(B) 50%
(C) 65%
(D) 70%
(E) 75%
Rationale: Number of runs made by running = 150 - (3 x 4 + 8 x 6)
= 150 - (60)
= 90
Now, we need to calculate 60 is what percent of 120.
=> 90/120 * 100 = 75 %
E
Answer: (E) 75%
Question: A man sells 12 candies for rs12 and loses rs 2.40. if he sells 12 candies for rs 16. how much does he gain or loss?
(A) gain rs4
(B) loses rs6
(C) gain rs6.40
(D) loses rs 1.60
(E) gains rs1.60
Rationale: 12 candles = 12 rupees . Lose = 2.4
So actual cost = 12+2.4=14.4 rupees .
So if he sells for 16 rupees then he gains 16-14.4=1.6 rupees
ANSWER:E
Answer: (E) gains rs1.60
Question: A mixture of 150 liters of wine and water contains 10% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 10
(B) 30
(C) 20
(D) 15
(E) 16
Rationale: Number of liters of water in150 liters of the mixture = 10% of 150 = 10/100 * 150 = 15 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (15 + P) and total volume of mixture is (150 + P).
(15 + P) = 25/100 * (150 + P)
60+4P = 150+P
P = 30 liters.
Answer: B
Answer: (B) 30
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
(A) Â¹Â²Câ‚… * 10
(B) Â¹Â²Câ‚‡ * 10
(C) Â¹Â²Câ‚‡ * Â¹â°Câ‚…
(D) 12 * Â¹â°Câ‚…
(E) None of these
Rationale: Explanation:
Here, five seniors out of 12 seniors can be selected in Â¹Â²Câ‚… ways. Also, five juniors out of ten juniors can be selected Â¹â°Câ‚… ways. Hence the total number of different ways of selection = Â¹Â²Câ‚… * Â¹â°Câ‚… = Â¹Â²Câ‚‡ * Â¹â°Câ‚…
= Â¹Â²Câ‚… = Â¹Â²Câ‚‡
ANSWER IS C
Answer: (C) Â¹Â²Câ‚‡ * Â¹â°Câ‚…
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 4 months
(B) 5 months
(C) 6 months
(D) 8 months
(E) 9 months
Rationale: Suppose B joined for x months. Then,
Then,(85000 x 12)/(42500 x x) = 3/1
x = 85000 x 12/42500 x 3 = 8.
So, B joined for 8 months.
Answer:D
Answer: (D) 8 months
Question: A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.
The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625.
The answer is B.
Answer: (B) 5
Question: The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.180 and Rs.120 respectively. What is the sum and the time?
(A) Sum = Rs.380 and Time = 4 years
(B) Sum = Rs.400 and Time = 6 years
(C) Sum = Rs.320 and Time = 4 years
(D) Sum = Rs.360 and Time = 5 years
(E) None of these
Rationale: Explanation :
BD = Rs.180
TD = Rs.120
R = 10%
F = BD ×TD/(BD – TD)=180×120/(180–120)=180×120/60=Rs. 360
BD = Simple Interest on the face value of the bill for unexpired time =FTR/100
⇒180 = (360×T×10)/100
⇒180 = 36 × T
⇒ T = 180/36 = 5 years Answer : Option D
Answer: (D) Sum = Rs.360 and Time = 5 years
Question: The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 80, then 1/m + 1/n is equal to
(A) 1/35
(B) 3/35
(C) 5/37
(D) 4/63
(E) None
Rationale: Answer
We have, m x n = 6 x 210 = 1260
âˆ´ 1/m + 1/n = (m + n)/mn = 80/1260 = 4/63
Correct Option: D
Answer: (D) 4/63
Question: If f(x) = 2x − √x and g(x) = x^2, what is f(g(3))?
(A) -4
(B) 8
(C) 17
(D) 32
(E) 15
Rationale: g(x) = x²
g(3) = 3² = 9
So, f(g(3)) = f(9)
f(x) = 2x − √x
So, f(9) = 2(9) − √9
= 18 - 3
= 15
= E
Answer: (E) 15
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 45km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
(A) 8.95km/hr
(B) 26.7km/hr
(C) 27.7km/hr
(D) 37.9km/hr
(E) 8.45km/hr
Rationale: average speed = (2*45*20)/45+20 km/hr
=27.7 km/hr
Answer (C)
Answer: (C) 27.7km/hr
Question: 4539,1513,378.25,75.65,12.60 ?
(A) 1.2
(B) 6.87
(C) 1.8
(D) 4.68
(E) 9.87
Rationale: Explanation :
Terms are continuously divided by 3 ,4, 5,6 and so on
4539
4539 Ã· 3 = 1513
1513 Ã· 4 = 378.25
378.25 Ã· 5 =75.65
75.65 Ã· 6= 12.60
12.60Ã·7=1.80
Answer : Option C
Answer: (C) 1.8
Question: If 2A = 3B = 4C, find A : B : C
(A) 2 : 4 : 5
(B) 5 : 3 : 1
(C) 3 : 2 : 1
(D) 7 : 3 : 2
(E) 6 : 4 : 3
Rationale: Let 2A = 3B = 4C = x
So, A = x/2 B = x/3 C = x/4
The L.C.M of 2, 3 and 4 is 12
Therefore, A : B : C = x/2 × 12 : x/3 × 12 : x/4 = 12
= 6x : 4x : 3x
= 6 : 4 : 3
Answer is E
Answer: (E) 6 : 4 : 3
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 2277
(B) 28886
(C) 5550
(D) 2678
(E) 2681
Rationale: Total production of salt by the company in that year
= 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year
= 66600/12 = 5550
Answer: C
Answer: (C) 5550
Question: A square has a side 5 centimeters shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the side of the smaller square and y be the side of the larger square. The statement "A square has a side 5 centimeters shorter than the side of a second square" may be formulated by
x = y - 5
The area of the smaller square is equal to x 2 = (y - 5) 2 and the area of the larger square is equal to y 2
The statement "the area of the larger square is four times the area of the smaller square" may be formulated by
y 2 = 4 (y - 5) 2
Write the above equation so that the right side is equal to 0
y 2 - 4 (y - 5) 2 = 0
The left side is made up of the difference of two squares and can be easily factored as follows
[ y - 2 (y - 5) ] [ y + 2 (y - 5) ] = 0
Solve for y to find
y = 10 and y = 10 / 3.
We now use the equation x = y - 5 to find x
y = 10 and x = 5
For the second solution y = 10 / 3, x is negative and cannot be accepted as the length of the side of a square must be positive.
Answer A
Answer: (A) 5
Question: . A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 16 2/3%
(B) 20%
(C) 18%
(D) 25%
(E) 35%
Rationale: 900 ---- 180
100 ---- ? => 20%
ANSWER:B
Answer: (B) 20%
Question: The simple interest on a sum of money will be Rs.1000 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 8981
(B) 3799
(C) 1200
(D) 2693
(E) 2000
Rationale: P --- 10 ---- 1000
P --- 5 ----- 500
3P --- 5 ----- 1500
------
=> 2000
Answer: E
Answer: (E) 2000
Question: In a 80 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
(A) 3 seconds
(B) 12 seconds
(C) 10 seconds
(D) 18 seconds
(E) 28 seconds
Rationale: B runs 56 m in 7 sec.
=> B runs 80 m in 7/56*80 = 10 seconds
Since A beats B by 7 seconds, A runs 80 m in (10-7) = 3 seconds
Hence, A's time over the course = 3 seconds
ANSWER:A
Answer: (A) 3 seconds
Question: A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year
A).	B)
C) D)
(A) Rs. 5624.32
(B) Rs.5423
(C) Rs.5634
(D) Rs.5976
(E) Rs.5376
Rationale: 5% is the rate of interest. 20% of the interest amount is paid as tax.
i.e 80% of the interest amount stays back.
if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value.
The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest.
= 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32
The amount at the end of 3 years = 5000 + 624.32 = 5624.32 Answer: A
Answer: (A) Rs. 5624.32
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5
(B) 8
(C) 7
(D) 4
(E) 1
Rationale: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer:A
Answer: (A) 5
Question: A shopkeeper sells 500 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
(A) 12
(B) 27
(C) 29
(D) 50
(E) 41
Rationale: SP per metre = 18000/500 = Rs. 36 Loss per metre = Rs. 5 CP per metre = 36+ 5 = Rs. 41.Answer: E
Answer: (E) 41
Question: An empty pool being filled with water at a constant rate takes 6hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool?
(A) 5hr 30min
(B) 5hr 20min
(C) 4hr 48min
(D) 3 hr 12min
(E) 2hr 40 min
Rationale: As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).
Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours =3 hours 12 minutes.
Answer: D.
Answer: (D) 3 hr 12min
Question: How many meters are there in 660 centimeters?
(A) 6.6 meters
(B) 660 meters
(C) 600 meters
(D) 6.5 meters
(E) 6 meter
Rationale: Solution:
1 meter = 100 centimeters
Just divide 660 by 100
660 Ã· 100 = 6.6, so there are 6.6 meters in 660 centimeters
Option A
Answer: (A) 6.6 meters
Question: Consider a Number 3.1n2
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 3
Rationale: In this ques we are given the thousandth digit as 2, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 2, the hundreth digit has to go up by 0, and correspondingly, the tenth digit should remain same.i.e 0-9.say 1
A
Answer: (A) 1
Question: If x and y are integers and x=50y + 39, which of the following must be odd?
(A) xy
(B) x + y
(C) 3X-1
(D) X+2Y
(E) 3x+1
Rationale: x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd
you don't know whether Y is even or odd, so you need to try.
A: odd * even = even ; odd*odd= odd ->not true
B: odd + odd = even ; odd+even = odd -> not true
D: odd + 2*odd = odd ; odd + 2*even = odd -> TRUE, stop here.
C: EVEN ...E - EVEN
Answer D
Answer: (D) X+2Y
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?
(A) 72
(B) 80
(C) 120
(D) 150
(E) 100
Rationale: Answer: Option E
Let the number of students be x. Then,
Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% OF X= 48+2/3 OF 48
80/100 X=80
X=100
Answer: (E) 100
Question: In the Bombay Stock Exchange there are 45% female employees and thus the number of male employees is exceeded by 72. Hence the total no. of employees in the BSE is:
(A) 540
(B) 720
(C) 800
(D) 550
(E) None
Rationale: Solution: Female employees = 45%
Male employees = 55%
Difference = 55 - 45 = 10%
→ 10% = 72
→ 1% = 72 /10
→ 100 = 7.2 * 100 = 720.
Answer: Option B
Answer: (B) 720