mathewhe/aqua_rat huggingface dataset:
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 5 kmph
(B) 6 kmph
(C) 7 kmph
(D) 8 kmph
(E) 9 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
ANSWER:D
Answer: (D) 8 kmph
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
(A) 7
(B) 6
(C) 8
(D) 7/20
(E) 1
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: (D) 7/20
Question: A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.555 in all. For how many days was he absent?
(A) 8
(B) 10
(C) 15
(D) 6
(E) 19
Rationale: 30 * 25 = 750
455
-----------
195
25 + 7.50 = 32.5
195/32.5 = 6
D
Answer: (D) 6
Question: The value of log2 16 is:
A.
1
8
B.	4
C.	8
D.	16
Answer: Option B
Explanation:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Let log2 16 = n.
Then, 2n = 16 = 24 n = 4.
log2 16 = 4.
Answer: Option B
Answer: (B) 4
Question: Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 11 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip?
(A) 37
(B) 42.5
(C) 44
(D) 50
(E) 52.5
Rationale: Total Time taken by jerry = (8/40)*60 Minutes + 11 Minutes + (20/60)*60 Minutes = 45 Minutes
Average Speed = Total Distance / Total Time = (8+20) miles / (45/60)Hours = 28*60 / 45 = 37 Miles per hour
Answer: option A
Answer: (A) 37
Question: The volume of a rectangular box is 330 square inches. The length on one side of the top is 11
inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing
may help you with this one.)
(A) 100
(B) 130
(C) 120
(D) 110
(E) 101
Rationale: 3 x 11 = 33
V = 33 x missing measure
V is 330
330 ÷ 33 = 10 which is the missing
measure of the side of the box top
10 x 11 = 110 sq. ft. which is area
of the top of the box.
correct answer D
Answer: (D) 110
Question: In a room are five chairs to accommodate 3 people. One person to a chair. How many seating arrangements are possible?
(A) 45
(B) 60
(C) 72
(D) 90
(E) 120
Rationale: The first person has 5 options i.e. 5 chairs to choose from
The second person has 4 options i.e. 4 chairs to choose from (first one has already taken a chair)
The third person has 3 options i.e. 3 chairs to choose from (two chairs are already gone)
Total seating arrangements 5*4*3 = 60
ANS:B
Answer: (B) 60
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years.What is the sum ?
(A) Rs. 4462.50
(B) Rs. 8032.50
(C) Rs. 8900
(D) Rs. 8925
(E) None of these
Rationale: Solution
Principal = Rs. (100x4016.25/9x5)= Rs.401625/25= Rs. 8925.
Answer D
Answer: (D) Rs. 8925
Question: The probability of pulling a black ball out of a glass jar is 1/W. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
(A) 1/(XY)
(B) E/Y
(C) Y/X
(D) 1/(X+Y)
(E) 1/(X-Y)
Rationale: P of pulling a black ball out of a glass jar AND breaking the jar = 1/Y
P of pulling a black ball out of a glass jar is 1/W
Lets say P of breaking the jar = n
That means 1/W*n=1/Y
n= W/Y
B is the answer
Answer: (B) E/Y
Question: In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 75000*10^(-3) Petri dishes. How many germs live happily in a single dish?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 48
Rationale: 0.036*10^5 can be written as 3600
75000*10^(-3) can be written as 75
Required= 3600/75= 48
ANSWER:E
Answer: (E) 48
Question: An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 25 times the difference between the two numbers. How many coins did the old man have?
(A)  24
(B)  26
(C)  30
(D)  25
(E)  40
Rationale: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.
x^2 - y^2 = 25(x - y) --> x + y = 25.
Answer: D.
Answer: (D)  25
Question: What is the greatest positive integer n such that 3^n is a factor of 36^100?
(A) 100
(B) 200
(C) 300
(D) 600
(E) 900
Rationale: Prime factorization out is the way to go here!
36 ^100
3^2 times 2^2 and both to the power of 100
[(3^2)*(2^2)]^100
giving you the beautifully simplistic answer of 3^200 and 2^200
Ans is 200
ANSWER:B
Answer: (B) 200
Question: Mrs. Stark paid $6,000 for 100 shares of stock A and $4,000 for 100 shares of stock B. She later sold the same shares of both stocks, gaining 3/8 the amount she paid for stock B. If the prices she had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
(A) The same.
(B) A loss 1 1/2 times as much.
(C) A loss 2 times as much.
(D) A loss 9 times as much
(E) A gain 1 1/2 times as much
Rationale: A = 6000; B = 4000; Profit = (3/8)*4000 = 1500
After prices are reversed:
A = 4000; B = 6000; Profit = (3/8)*6000 = 2250
2250 = 3/2(1500) --> Gain of 3/2 times 1500
Answer: E
Answer: (E) A gain 1 1/2 times as much
Question: There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 25% of all the students at Morse have cars, how many students are in the three lower grades?
(A) 500
(B) 900
(C) 1200
(D) 1350
(E) 1500
Rationale: Let x be the number of students in the lower three grades.
0.1x + 150 = 0.25(x+300)
0.15x = 75
x = 500
The answer is A.
Answer: (A) 500
Question: Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?
(A) 26
(B) 29
(C) 39
(D) 42
(E) 43
Rationale: 39
Option 'C'
Answer: (C) 39
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?
(A) 3 (5/19)
(B) 3 (5/13)
(C) 3 (5/11)
(D) 3 (3/11)
(E) 33(5/11)
Rationale: A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 2 days.
The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.
Answer: C
Answer: (C) 3 (5/11)
Question: professor absentminded has a very peculiar problem that he cannot remember number larger than 15. however he tells his wife, i can remember any number up to 100 by remembering the three numbers obtained as remainder when the numbers is divided by 3,7 and 11 respectively. for example (2,3,6)is 17. professor remembers that he had(2,4,8)rupees in the purse, and he paid(2,5,4) rupees to the servant. how much money is left in the purse?
(A) 45
(B) 46
(C) 47
(D) 48
(E) 49
Rationale: find out the common term in those 3 series for (2,4,8)
3N+2=2,5,8,11,14......71,74
7N+4=4,11,18...67,74
11N+8=8,19,30......63,74
find out the common term in those 3 series for (2,5,4)
3N+2=2,5.....23,26
7N+5=5,12,19,26
11N+4=4,15,26
now 74-26=48
ANSWER:D
Answer: (D) 48
Question: Two trains, 130 and 110 metres long, while going in the same direction, the faster train takes one minute to pass the other completely. If they are moving in opposite direction, they pass each other completely in 3 seconds. Find the speed of trains.
(A) 30 m/s, 40 m/s
(B) 32 m/s, 48 m/s
(C) 40 m/s, 44 m/s
(D) 38 m/s, 42 m/s
(E) None of these
Rationale: Let speed of trains are S1 m/s and S2 m/s.
Then, s1 - s2 = 130+110/60=4 ....(i)
and s1 + s2 = 130+110/3=80....(ii)
on solving (i) and (ii), we get
S1 = 42 m/s , S2 = 38 m/s
Answer D
Answer: (D) 38 m/s, 42 m/s
Question: Mike earns $15 per hour and Phil earns $10per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?
(A) 33.3%
(B) 32.5%
(C) 37%
(D) 37.5%
(E) 40%
Rationale: What % less of 15is 10
let it be x % less ,then
=15(1-x/100)=10
1-x/100=10/15
x=100/3
x=33.3%
Ans A
Answer: (A) 33.3%
Question: x, y, and z are all unique numbers. If x is chosen randomly from the set {9, 10, 11} and y and z are chosen randomly from the set {20, 21, 22, 23}, what is the probability that x and y are prime and z is not?
(A) 1/20
(B) 1/12
(C) 2/15
(D) 3/10
(E) 1/7
Rationale: P(x is prime) = 1/3
P(y is prime) = 1/4
If y is prime, then z is not prime since y and z are unique.
Then the probability is 1/3*1/4 = 1/12
The answer is B.
Answer: (B) 1/12
Question: For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
(A) x + y + z + 1
(B) xyz + xz
(C) xy + z + 1
(D) xyz + 1
(E) xyz + 1/2
Rationale: x appetizers,
y + 1 main courses,
z dessert
Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = xC1*(y+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}
Hence, number of ways = x(y+1)z = xyz + xz
Correct Option: B
Answer: (B) xyz + xz
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 72 kmph
(B) 75 kmph
(C) 30 kmph
(D) 80 kmph
(E) 85 kmph
Rationale: Explanation:
S = (90 + 60)/2 = 75 kmph
ANSWER IS B
Answer: (B) 75 kmph
Question: Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 6 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: if n =7
mark sold 1 box
and Ann sold 5 boxes
total 6 < 7
Answer:E
Answer: (E) 5
Question: If Rs. 600 amounts to Rs. 683.20 in two years compounded annually, find the
rate of interest per annum.
(A) 3% p.a
(B) 4% p.a
(C) 6% p.a
(D) 7% p.a
(E) 8% p.a
Rationale: Sol. Principal = Rs. 500; Amount = Rs. 583.20; Time = 2 years.
Let the rate be R% per annum.. 'Then,
[ 500 (1+(R/100)2 ] = 583.20 or [ 1+ (R/100)]2 = 5832/5000 = 11664/10000
[ 1+ (R/100)]2 = (108/100)2 or 1 + (R/100) = 108/100 or R = 8
So, rate = 8% p.a.
ANSWER E 8% p.a
Answer: (E) 8% p.a
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 4 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R = 1/36
Rate of machine S = 1/18
Rate of R+S = 1/12
To finish the work in 4 hrs, the combined rate needs to be 1/4.
x * 1/12 = 1/4
x = 3
The answer is A.
Answer: (A) 3
Question: The value of a watch depreciates at the rate of 20% every year. It was purchased 4 years ago. If its present value is Rs. 2048, its purchase price was
(A) 3500
(B) 4000
(C) 4500
(D) 5000
(E) 5500
Rationale: Explanation:
= Rs.5000
Answer: D
Answer: (D) 5000
Question: A coin is tossed six times. What is the probability that there is at the least one tail?
(A) 63/64
(B) 31/37
(C) 31/18
(D) 31/10
(E) 31/19
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed six times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/64 ; P(T) = 1 - 1/64 = 63/64
Answer: A
Answer: (A) 63/64
Question: A Cistern is filled by pipe A in 9 hrs and the full Cistern can be leaked out by an exhaust pipe B in 12 hrs. If both the pipes are opened in what time the Cistern is full?
(A) 28 hrs
(B) 24 hrs
(C) 36 hrs
(D) 32 hrs
(E) 34 hrs
Rationale: Explanation:
Pipe A can fill 1/9 of the cistern in 1 hour.
Pipe B can empty 1/12 of the cistern in 1 hour
Both Pipe A and B together can effectively fill 1/9 − 1/12 = 1/36 of the cistern in 1 hour
i.e, the cistern will be full in 36 hrs.
Answer: Option C
Answer: (C) 36 hrs
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 33
(B) 88
(C) 36
(D) 77
(E) 21
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: C
Answer: (C) 36
Question: The Number 3A2105 is divisible by 3.What will be the value of A?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Divisibility of 3 is sum of the digits must be divisible by 3.
So,3+a+2+1+0+5=11+a
Then what gives the value will divisible by 3
So Answer is 1
Option A
Answer: (A) 1
Question: Hardy and Andy start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Andy. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 40 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: let x=length of pool
at first meeting, combined distance=x
at second meeting, combined distance=3x
if andy swims 18.5 m of x, then he will swim 3*18.5=55.5 m of 3x
andy's total distance to second meeting=x+10.5 m
x+10.5=55.5 m
x=45 m
C
Answer: (C) 45
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 40% profit?
(A) 220
(B) 230
(C) 960
(D) 780
(E) 896
Rationale: C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 140% of Rs. 640 = 140/100 * 640 = Rs. 896.
E
Answer: (E) 896
Question: In what time will a train 140 m long cross an electric pole, it its speed be 144 km/hr?
(A) 3.5 sec
(B) 4.25 sec
(C) 5 sec
(D) 12.5 sec
(E) 6 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 140/40 = 3.5 sec.
ANSWER:A
Answer: (A) 3.5 sec
Question: Four of the five parts numbered (a),(b),(c),(d) and (e) in the following sequence are exactly equal. Which part is not equal to the other four? The number of that part is the answer
(A) 120 × 12 – 22 × 20
(B) 10% of 5000 + 2⁄5 of 1200
(C) 80 × 40 – 20 × 110
(D) 8640 ÷ 60 + 53.5 × 16
(E) 5314 – 3029 – 1285
Rationale: The other parts are equal to 1000.
Answer B
Answer: (B) 10% of 5000 + 2⁄5 of 1200
Question: Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?
(A) 435
(B) 440
(C) 450
(D) 460
(E) 512
Rationale: Let suppose total number of students in class are X.
Then from the question we can conclude it that,
X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512
E
Answer: (E) 512
Question: A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?
(A) 3 : 9
(B) 3 : 0
(C) 3 : 3
(D) 3 : 4
(E) 3 : 1
Rationale: Since S # 1/t
S1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4
Answer:D
Answer: (D) 3 : 4
Question: In how many ways can 5 boys be allotted four different COTs such that none of the COTs are empty and all the 5 boys are accommodated?
(A) 240
(B) 260
(C) 280
(D) 290
(E) 300
Rationale: 4 boys can be selected from 5 boys in 5C4 ways = 5
4 boys can be arranged in 4 COTS in 4! ways
and since 1 boy has to share a COT with one of the 4 boys, therefore total ways = 2! = 2
Hence total number of ways in which allocation can be done = 5C4 * 4! * 2! = 5*2*4!
240
A
Answer: (A) 240
Question: 154 pencils are distributed to children with the same number. What can’t be the range including the number of children?
(A) 50~60
(B) 10~20
(C) 20~30
(D) 1~10
(E) 70~80
Rationale: 154 candies are distributed to children with the same number. What can’t be the range including the number of children?
A. 1~10 B. 10~20 C. 20~30 D. 40~50 E. 70~80
-> In 154=1*154=2*77=7*22=11*14, you can come up with 4 cases. One is distributing 77 candies to 2 children each. Another is distributing 2 candies to 77 children each. Also, you can distribute 22 candies to 7 children. The other is distributing 7 candies to 22 children. Amongst these cases, what is not included is a. 50~60. Therefore, the answer is A.
Answer: (A) 50~60
Question: An employer has 5 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?
(A) a) 1,490
(B) b) 132
(C) c) 60
(D) d) 68
(E) e) 23
Rationale: 5C3 * 4C2 = 60. Answer C.
Answer: (C) c) 60
Question: In the recent, cyber security conference in London, out of 800 men, 900 women, 200 children present inside the building premises, 20% of the men, 30% of the women and 50% of the children were Indians. Find the percentage of people who were not Indian?
(A) 73.22
(B) 72.11%
(C) 79.22
(D) 74.66
(E) 88.22
Rationale: Solution: Number of Indians men present there = 800*20/100 = 160
Indian women = 900*30/100 = 270
Indian children = 200*50/100 = 100.
Total member present in cyber security conference = 800+900+200 = 1900
Total Indian = 160+270+100 = 530
Hence, % of Indian present there = 530*100/1900 = 27.89%
% of people who were not Indian = 100-27.89 = 72.11%.
Answer B
Answer: (B) 72.11%
Question: Salesperson A's compensation for any week is $210 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?
(A) $3500
(B) $5500
(C) $7500
(D) $9500
(E) $11,500
Rationale: 210+0.06(x-1000) = 0.08x
0.02x = 150
x = $7,500
The answer is C.
Answer: (C) $7500
Question: If w and s are positive integers such that (2^w)(4^s) = 16, then 2w + s =
(A)  2
(B)  3
(C)  4
(D)  5
(E)  6
Rationale: lets get the eq into simplest orm..
(2^w)(4^s) = 16..
(2^w)(2^2s) = 2^4..
or w+2s=4..
since w and s are positive integers, only w as 2 and s as 1 satisfy the Equation..
so 2w+s=2*2+1=5..
D
Answer: (D)  5
Question: In the following sequence of alphabets, which letter would be at the middle of the fourth and sixteenth letters from the right ? A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
(A) a)2^(1/3)
(B) W
(C) c)2^(1/2)
(D) d)2^(3/2)
(E) e)2^(1/4)
Rationale: Ans is B
Answer: (B) W
Question: The length of the room is 6m and width is 6m. Find the cost of paving the floor by slabs at the rate of Rs.200 per sq meter?
(A) 6200
(B) 6300
(C) 2700
(D) 7200
(E) 8000
Rationale: l=6m w=6m
area of the floor = 6 x 6 = 36 sq m
cost of paving = 200 x 36= Rs. 7200
Answer: D
Answer: (D) 7200
Question: 12^3+12^3+12^3=?
(A) a)72^3
(B) b) 72^4
(C) c) 72^5
(D) d) 72^6
(E) e) 72^2
Rationale: The correct answer is E 72^2
Answer: (E) e) 72^2
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively?
(A) Rs. 5280
(B) Rs. 5500
(C) Rs. 6000
(D) Rs. 6480
(E) Rs. 7680
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 54 * 24 = 1296 m.
Total cost of levelling = Rs. 6480
D
Answer: (D) Rs. 6480
Question: A and B can do a work in 20days, B and C in 25days, C and A in 30days. If A,B and C work together , they will complete the work in?
(A) 10days
(B) 12days
(C) 16days
(D) 20days
(E) 25days
Rationale: A+B 1day work = 1/20
B+C 1day work = 1/25
C+A 1day work = 1/30
Adding we get 2(A+B+C) = 1/20 + 1/25 + 1/30 = 37/300
A+B+C 1 day work = 37/600
A,B,C can finish the work in 600/37 days = 16days approximately
Answer is C
Answer: (C) 16days
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 16%
(B) 88%
(C) 12%
(D) 89%
(E) 56%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: (C) 12%
Question: The speed of a boat in still water in 65 km/hr and the rate of current is 15 km/hr. The distance travelled downstream in 25 minutes is:
(A) 55.55 km
(B) 44.44 km
(C) 33.33 km
(D) 22.22 km
(E) 11.11 km
Rationale: Explanation:
Speed downstream = (65 + 15) = 80 kmph
Time = 25 minutes = 25/60 hour = 5/12 hour
Distance travelled = Time × speed = (2/5)×80 = 33.33 km
Answer: Option C
Answer: (C) 33.33 km
Question: In each of the following questions, there are four options. The numbers, in these options, are alike in a certain manner. Only one number does not fit in. Choose the one which is different from the rest.
(A) 24
(B) 90
(C) 54
(D) 36
(E) 25
Rationale: 24
remaing number are divisible by '9'
ANSWER:A
Answer: (A) 24
Question: Machine P takes 40 hours longer than machine Q to produce 1080 Widgets. Machine Q produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine P produce
(A) 100
(B) 65
(C) 2.5
(D) 11
(E) 4.5
Rationale: Machine Q produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine P produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Q:P).
i.e. speed of their work (P:Q) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (P:Q)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 40
So, x = 40.
Hence 6x = 6*40 = 240 hours.
Hence P takes 240 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/240
= 4.5
Hence option (E).
Answer: (E) 4.5
Question: Calculate 469160 x 9999 = ?
(A) 4691130840
(B) 4686970743
(C) 4691100843
(D) 4586870843
(E) NONE
Rationale: Answer
469160 x 9999 = 469160 x (10000-1)
= 4691600000 - 469160
= 4691130840.
Option: A
Answer: (A) 4691130840
Question: What is the ratio whose term differ by 45 and the measure of which is 2/7?
(A) A)32:23
(B) B)16:56
(C) C)16:63
(D) D)32:39
(E) E)41:52
Rationale: Let the ratio be x:(x+45)
Then, x/(x+45) = 2/7
x=18
required ratio = 16:63
Answer is C
Answer: (C) C)16:63
Question: The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?
(A) 58kgs
(B) 58.85kgs
(C) 58.95kgs
(D) 59kgs
(E) 59.85kgs
Rationale: Actual total weight is (20X 58.4 - 56 + 65) = 1177 Kgs
Actual average weight is 1177/20 = 58.85kgs
B
Answer: (B) 58.85kgs
Question: Two trains, each 100 metre long are moving in opposite directions. They cross each other in 8 seconds. If one is moving twice as fast the other, the speed of the faster train is
(A) 65 km/hr
(B) 60 km/hr
(C) 45 km/hr
(D) 75 km/hr
(E) 80 km/hr
Rationale: tot dist = (100+100) = 200 m
time = 8 sec
let speed of slower train = vm/s
then speed of the faster train = 2vm/s
relative speed = (v+2v)=3v m/s
3v=200/8
v=25/3
speed of the faster train = 2v = 50/3 m/s
50/3*8/5km/hr = 60km/hr
ANSWER B
Answer: (B) 60 km/hr
Question: What is the decimal equivalent of (1/4)^6?
(A) 0.0016
(B) 0.0625
(C) 0.16
(D) 0.0002
(E) 0.5
Rationale: (1/4)^6 = 1/4096 = 0.0002
Answer : D
Answer: (D) 0.0002
Question: 23 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
(A) 22
(B) 23
(C) 44
(D) 46
(E) 45
Rationale: last member can shake with the 1st one.
hence (n-1+1)=23
ANSWER:B
Answer: (B) 23
Question: what will be the next number in the following series??
2, 1, (1/2), (1/4),...
(A) 1/3
(B) 1/8
(C) 2/8
(D) 1/16
(E) 3/8
Rationale: 4/2=2
2/2=1
1/2=1/2
(1/2)/2=1/4
(1/4)/2=1/8
so answer is 1/8
ANSWER:B
Answer: (B) 1/8