mathewhe/aqua_rat huggingface dataset:
Question: Stacy and Heather are 40 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?
(A) 4 miles
(B) 8 miles
(C) 17 miles
(D) 6 miles
(E) 12 miles
Rationale: Original distance between S and H = 40 miles.
Speed of S = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.
Now, the total distances traveled by S and H = 40 miles ---> 6*(t+2/5)+5*t=40 ---> t= 188/55 hours. Thus H has traveled for 188/55 hours giving you a total distance for H = 5*188/55 = 17 miles.
C is thus the correct answer.
P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Answer: (C) 17 miles
Question: How many different 6-letter sequences are there that consist of 1A, 3B's and 4C's ?
(A) 6
(B) 80
(C) 120
(D) 360
(E) 720
Rationale: How many different 6-letter sequences are there that consist of 1 A, 3B's, and 4 C's?
(A) 6
(B) 80
(C) 120
(D) 360
(E) 720 (ANS B)
Answer: (B) 80
Question: Given distinct positive integers 1, 11, 4, x, 2, and 9, which of the following could be the median?
(A) 2
(B) 3
(C) 6
(D) 8
(E) 9
Rationale: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.
Arrange numbers in ascending order: 1, 2, 4, 9, 11, and x.
Now, x can not possibly be less than 4 as given that all integers are positive and distinct (and we already have 1, 2, and 4).
Next, if x is 4<x<9 then the median will be the average of 4 and x. As all answers for the median are integers, then try odd values for x:
If x=5, then median=(4+5)/2=4.5 --> not among answer choices;
If x=8, then median=(4+8)/2=6 --> OK;
Answer: C
Answer: (C) 6
Question: How many pounds of salt at 80 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?
(A) 5
(B) 15
(C) 40
(D) 50
(E) 25
Rationale: Selling price is 48 cents/lb
For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)
Basically, you need to mix 35 cents/lb (Salt 1) with 80 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg)
weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (80 - 40)/(40 - 35) = 8/1
We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 5 lbs.
Answer (A)
Answer: (A) 5
Question: The average (arithmetic mean) of the even integers from 0 to 200 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 100 inclusive?
(A) 10
(B) 25
(C) 50
(D) 100
(E) 200
Rationale: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 200 is 200/2 = 100
The average of the even numbers from 0 to 100 is 100/2 = 50
The answer is C.
Answer: (C) 50
Question: The distance between Delhi and Mathura is 100 kms. A starts from Delhi with a speed of 50 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 45 kmph at 8 p.m. from Delhi. When will they meet?
(A) 11
(B) 77
(C) 8 3/4
(D) 8 1/2
(E) 8
Rationale: D = 100 – 50 = 50
RS = 45 + 50 = 95
T = 90/45 = 0.5 hours
8 a.m. + 0.5 = 8 1/2 a.m..Answer: D
Answer: (D) 8 1/2
Question: There are 4 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament?
(A) 10
(B) 8
(C) 40
(D) 60
(E) 120
Rationale: Each person is one participant of 4 games. So there are in all 4*4 = 16 instances of one participant games. But each game has 2 participants so total number of games = 16/2 = 8
B
Answer: (B) 8
Question: What is the greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 3, 4, 5, 6 and 7 respectively?
(A) 456780
(B) 678910
(C) 997479
(D) 997917
(E) 997920
Rationale: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 7 when we divide by 10, so D is the only possible answer.
Answer: (D) 997917
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 17 kmph
(C) 19 kmph
(D) 17 kmph
(E) 20 kmph
Rationale: Speed of the boat in still water
= (60+100)/2
= 80 kmph. Speed of the stream
= (100-60)/2
=20 kmph.
Answer: E
Answer: (E) 20 kmph
Question: If Reena says, “Anjali's father Raman is the only son of my father-in-law Ramanand”, then how is Piyu, who is the sister of Anjali, related to Ramanand ?
(A) Grand-daughter
(B) Wife
(C) Daughter
(D) None of these
(E) None of these33
Rationale: Explanation:
Only son of Reena's father-in-law Ramanand is Reena's husband. So, Raman is Reena's husband and Anjali & Piyu are his daughter's, Thus, Piyu is Grand-daughter of Ramanand.
ANSWER: A
Answer: (A) Grand-daughter
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin
(A) 24.58
(B) 24.5
(C) 24.3
(D) 24.9
(E) 24.1
Rationale: If Rahul age is x, then Sachin age is x-7,
so (x-7)/x = 7/9
=> 9x-63 = 7x
=> 2x = 63
=> x = 31.5
So Sachin age is 31.5 - 7 = 24.5
Answer: B
Answer: (B) 24.5
Question: A train covers a distance of 1250 km in 25hrs. Find the speed of the train?
(A) 30km/hr
(B) 40km/hr
(C) 50km/hr
(D) 60km/hr
(E) 100km/hr
Rationale: Speed = 1250/25 = 50km/hr
Answer is C
Answer: (C) 50km/hr
Question: Arrange fractions in descending order
(A) 9/11 > 8/9 > 3/5 > 4/7
(B) 9/11 > 8/9 > 4/7 > 3/5
(C) 8/9 > 9/11 > 3/5 > 4/7
(D) 9/11 >3/5 > 8/9 > 4/7
(E) None of these
Rationale: Explanation:
9/11 = .818 , 8/9 = .88 , 3/5 = .6, 4/7 = .571
So order is 8/9 > 9/11 > 3/5 > 4/7
Option C
Answer: (C) 8/9 > 9/11 > 3/5 > 4/7
Question: In an exam, Bobby scored 38 percent, Bonny scored 56 percent, Vijay scored 66 percent and Libin scored 75 percent. The maximum score awarded in the exam is 500. Find the average mark scored by all the three boys?
(A) 293
(B) 293.75
(C) 294
(D) 295.5
(E) 298.25
Rationale: Average mark scored by all the three boys =
[38/100 (500) + 56/100 (500) + 66/100 (500) + 75/100(500)] / 4
(190+280+330+375)/4
= 293.75
Answer: B
Answer: (B) 293.75
Question: A man borrowed Rs 24000 from two money lenders. For one loan, he paid 15% per annum and for the other 18% per annum. At the end of one year, he paid Rs 4050. How much did he borrow at each rate ?
(A) Rs.16000
(B) Rs.12000
(C) Rs.15000
(D) Rs.13000
(E) None of these
Rationale: Explanation:
Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x).
{(x * 15 * 1)/100 } + { [(24000 – x) * 18 * 1]/100 } = 4050
or 15 x + 432000 - 18x = 405000 or x = 9000.
Money borrowed at 15% = Rs 9000 .
Money borrowed at 18% = Rs 15000.
Answer: C
Answer: (C) Rs.15000
Question: Company Z has 48 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
(A) 6
(B) 7
(C) 8
(D) 9
(E) 12
Rationale: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y = 48.
Now, plug options for x. Only A and E give an integer value for y. But only for E x > y as needed.
Answer: E.
Answer: (E) 12
Question: The faces of pyramid are to be painted by 4 different colors. In how many ways can be this be done?
(A) A.720
(B) B.256
(C) C.24
(D) D.12
(E) E.36
Rationale: If I have to paint 4 sides with 4 different colour...
First face can have 4c1 options,
2nd would have 3c1, and subsequent ones would have 2c1 and 1 options respectively.
Total options = 4c1 x 3c1 x 2c1 x 1 = 24 distinct ways
Correct answer - C
Answer: (C) C.24
Question: Two pipes A and B can fill a tank in 36 hours and 46 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 20.195 hrs
(B) 21.195 hrs
(C) 22.195 hrs
(D) 23.195 hrs
(E) 20.495 hrs
Rationale: a fill in one hour = 1/36
b fill in one hour = 1/46
both fill in one hour = 1/36+1/46
= 82/1656
time taken by both pipes = 1656/82
=20.195 hrs
ANSWER:A
Answer: (A) 20.195 hrs
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 800 per sq.metre.
(A) Rs.15500
(B) Rs.16500
(C) Rs.17500
(D) Rs.18500
(E) Rs.19500
Rationale: Area = 5.5 × 3.75 sq. metre.
Cost for 1 sq. metre. = Rs. 800
Hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = Rs. 16500
Answer: B
Answer: (B) Rs.16500
Question: Which number is the odd one out in the list ?
(A) 38442
(B) 78426
(C) 84029
(D) 67626
(E) 72927
Rationale: C
84029
All the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27.
Answer: C
Answer: (C) 84029
Question: If n is a prime number greater than 3, what is the remainder when n^2 is divided by 13?
(A) 0
(B) 1
(C) 2
(D) 13
(E) 5
Rationale: There are several algebraic ways to solve this question including the one under the spoiler. But the easiest way is as follows:since we can not have two correct answersjust pick a prime greater than 3, square it and see what would be the remainder upon division of it by 13.
n=5 --> n^2=25 --> remainder upon division 25 by 13 is 12.
Answer: D.
Answer: (D) 13
Question: 1,234
1,243
1,324
.....
....
+4,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers?
(A) 24,000
(B) 26,664
(C) 40,440
(D) 60,000
(E) 66,660
Rationale: Using the symmetry in the numbers involved (All formed using all possible combinations of 1,2,3,4), and we know there are 24 of them. We know there will be 6 each with the units digits as 1, as 2, as 3 and as 4. And the same holds true of the tens, hundreds and thousands digit.
The sum is therefore = (1 + 10 + 100 + 1000) * (1*6 +2*6 +3*6 +4*6) = 1111 * 6 * 10 = 66660
ANS:E
Answer: (E) 66,660
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) 227
(B) 299
(C) 270
(D) 585
(E) 271
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer: C
Answer: (C) 270
Question: The average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 107 kg
(B) 80 kg
(C) 120 kg
(D) 90 kg
(E) 100
Rationale: Solution
Total weight increased	= (10 x 4.2)kg
= 42 kg.
Weight of new person	= (65 + 42)kg
= 107kg.
Answer A
Answer: (A) 107 kg
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 22
(B) 21
(C) 22
(D) 28
(E) 11
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m.Answer: D
Answer: (D) 28
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) Rs.128
(B) Rs.129
(C) Rs.125
(D) Rs.198
(E) Rs.120
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2
=Rs.125
Answer:C
Answer: (C) Rs.125
Question: At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?
(A) 24min
(B) 44min
(C) 14min
(D) 21min
(E) 74min
Rationale: In this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart
Case 1 : (5*x + t) * 12/11
(5*5 + 3) * 12/11
28 * 12/11 = 336/11= min
therefore the hands will be 3 min apart at 31 5/11 min past 5.
Case 2 : (5*x - t) * 12/11
(5*5 -3 ) * 12/11
22 *12/11 = 24 min
therefore the hands will be 3 min apart at 24 min past 5
Answer: A
Answer: (A) 24min
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases?
(A) 8:6
(B) 8:7
(C) 8:9
(D) 8:4
(E) 8:1
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer: B
Answer: (B) 8:7
Question: The perimeter of a semi circle is 108 cm then the radius is?
(A) 17
(B) 21
(C) 19
(D) 11
(E) 12
Rationale: 36/7 r = 108 => r
= 21
Answer: B
Answer: (B) 21
Question: In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 8
Rationale: Let us first find the fraction of green, blue and yellow balls
1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator
= 11 / 24 , add numerators
The fraction of white balls is given by
24 / 24 - 11 / 24 = 13 / 24
So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then
(13 / 24) of x = 26 balls
or (13 / 24) ? x = 26
x = 26 ? (24 / 13) = 48 , total number of balls
The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by
(1 / 8) of 48 = 6 balls.
correct answer A
Answer: (A) 6
Question: The number obtained by interchanging the digits of a two-digit number is less than the original number by 36. The sum of the digits of the number is 8. What is the original number ?
(A) 71
(B) 62
(C) 53
(D) 35
(E) 45
Rationale: Explanation :
Let the number be 10x + y.
∴ x + y = 8 .....(i)
10x + y - (10y + x) = 36 ∴ 9(x - y) = 3
∴ x - y = 4 .......(ii)
From equation (i) and (ii): x = 6, y = 2
∴ Number = 62
Answer : Option B
Answer: (B) 62
Question: Solution for 2.12+.004+.345
(A) 2.91
(B) 2.911
(C) 2.469
(D) 2.586
(E) 2.499
Rationale: 2.12+.004+.345
0=0-2.12-0.004-0.345
0=-2.469
answer :C
Answer: (C) 2.469
Question: How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr ?
(A) 25
(B) 30
(C) 40
(D) 45
(E) 55
Rationale: Solution
Speed of train relative to man =(63-3)km/hr=60km/hr
=(60x5/18)m/sec =50/3 m/sec
Time taken to pass the man =(500x3/50)sec =30sec
Answer B
Answer: (B) 30
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
(A) 4000
(B) 345
(C) 5673
(D) 6530
(E) 8154
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 9 = Rs.8154
Answer: Option E
Answer: (E) 8154
Question: There is a right angle triangle inside a circle of diameter 18cm. Inside this triangle ,there is another circle of diameter 6 cm. Find the perimeter of the triangle.
(A) 24cm
(B) 36*2^1/2cm
(C) 36cm
(D) 54cm
(E) 42cm
Rationale: 1)The radius of the incircle of a right triangle with legs a and b and hypotenuse c is r=(a+b-c)/2
2)The radius of the circumcircle is half the length of the hypotenuse R=c/2
3)Thus the sum of the circumradius and the inradius is half the sum of the legs R+r=(a+b)/2
From 2nd Rule c=18cm
From 3rd Rule a+b= 2*(9+3) =24cm
Hence Perimeter a+b+c= 24+18= 42 cm
ANSWER:E
Answer: (E) 42cm
Question: Which is better investment, 12% stock at par with an income tax at the rate of 5paise per rupee or 14 2/7 % stock at 120 free from income tax?
(A) 12%
(B) 14 2/7%
(C) Both are equally good
(D) Cannot be compared
(E) None of these
Rationale: Let the investment in each (100*120)
Income in first case = (12/100*100*120)=1440
Net income =(1440-5/100*1440)=1368
Income in second case=((100/2*20)*100*120)=1428.57
Clearly, 14 2/7 % stock at 120 is better
Option B
Answer: (B) 14 2/7%
Question: If a(a - 4) = 12 and b(b -4) = 12, where a ≠ b, then a + b =
(A) −48
(B) −5
(C) 4
(D) 46
(E) 48
Rationale: i.e. if a = 6 then b = -2
or if a = -2 then b = 6
But in each case a+b = -2+6 = 4
Answer: option C
Answer: (C) 4
Question: Two trains travelling in the same direction at 55 and 40 kmph completely pass off another in 1 minute. If the length of the first train is 139 m, what is the length of the second train?
(A) 387 m
(B) 139 m
(C) 111 m
(D) 125 m
(E) 167 m
Rationale: RS = 55 â€“40 = 15 * 5/18 = 25/6 mps
T = 60 sec
D = 25/6 * 60 = 250 m
139
--------
111 m
Answer: C
Answer: (C) 111 m
Question: In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?
(A) 22
(B) 25
(C) 88
(D) 17
(E) 10
Rationale: The toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2, 2, 1
b. 3, 1, 1
Case a. Number of ways of achieving the first option 2 - 2 - 1
Two toys out of the 5 can be selected in \inline {\color{Black} 5C_{2}} ways. Another 2 out of the remaining 3 can be selected in \inline {\color{Black} 3C_{2}} ways and the last toy can be selected in \inline {\color{Black} 1C_{1}} way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2
Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways \inline {\color{Black} 5C_{2}\times 3C_{2}}= 15 ways
Case b. Number of ways of achieving the second option 3 - 1 - 1
Three toys out of the 5 can be selected in \inline {\color{Black} 5C_{3}} ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3 - 1 - 1 option is \inline {\color{Black} 5C_{3}} = 10 = 10 ways.
Total ways in which the 5 toys can be packed in 3 identical boxes
= number of ways of achieving Case a + number of ways of achieving Case b
= 15 + 10 = 25 ways.
Answer: B
Answer: (B) 25
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: Select 20 b in =>20 ways
one girl ==25 ways
boy and girl 20*25= 500
ANSWER E
Answer: (E) 500
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 76 seconds
(B) 16 seconds
(C) 18 seconds
(D) 27 seconds
(E) 19 seconds
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.
Answer: D
Answer: (D) 27 seconds
Question: What number is obtained by adding the units digits of 734^98 and 347^82?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: The units digit of 734^98 is 6 because 4 raised to the power of an even integer ends in 6.
The units digit of 347^82 is 9 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 82 is in the form 4n+2, the units digit is 9.
Then 6+9 = 15.
The answer is E.
Answer: (E) 15
Question: A prize of $1200 is to be distributed among 40 winners, each of whom must be awarded at least $40. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
(A) $100
(B) $120
(C) $280
(D) $300
(E) $360
Rationale: Total value of the prize =$1200
Number of people = 40
2/5 of 1200 (=$480) should be distributed among 3/5 of 40 (=24 people ) with each getting $40 each. Remaining money = 1200-480 = $720. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $40. Thus, minimising the remaining 15 people (=40-24-1. '-1' to exclude 1 that needs to be maximised) = 15*40=600.
Thus the maximum award can be = 720-600 = $120, hence B is the correct answer.
Answer: (B) $120
Question: What is the product between the place values of two 8's in the numeral 780.38
(A) 0.16
(B) 0.64
(C) 80.08
(D) 64
(E) 6.4
Rationale: Required product = 80 x 0.08 = 6.4
Answer is E
Answer: (E) 6.4
Question: Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R?
(A) Rs.400
(B) Rs.500
(C) Rs.300
(D) Rs.600
(E) None of these
Rationale: Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r
Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400
q = 1/3 (p + r) => 3q = p + r
Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300
r = 1200 - (p + q) => r = Rs.500.
ANSWER:B
Answer: (B) Rs.500
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
(A) 1
(B) 24
(C) 18
(D) 11
(E) 12
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.
Answer:B
Answer: (B) 24
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
(A) 4
(B) 10
(C) 15
(D) 16
(E) 18
Rationale: Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes,they will together (30/2)+1=16 times. Answer: D
Answer: (D) 16
Question: Two trains 150 meters and 180 meters long are running in the same direction with speeds of 102 km/hr, 66km/hr. In how much time will the first train cross the second
(A) 37 sec
(B) 22 sec
(C) 27 sec
(D) 35 sec
(E) 33 sec
Rationale: Explanation:
Relative speed of the trains = (102 - 66) km/hr = 36 km/hr
= (36Ã— 5/18) m/sec = 10 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (150 + 180) m at 10 m /sec = (330/10) sec = 33 sec.
Answer: Option E
Answer: (E) 33 sec
Question: The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
(A) 277
(B) 665
(C) 288
(D) 267
(E) 256
Rationale: 8 * 84 = 672 – 7
= 665
Answer:B
Answer: (B) 665
Question: A, B and C shared profits in ratio of 5 : 7 : 6. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ?
(A) 10 : 49 : 45
(B) 20 : 49 : 48
(C) 10 : 19 : 64
(D) 20 : 29 : 64
(E) 30 : 29 : 63
Rationale: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.
Let X is the total investment
â‡’14 x = 5
â‡’ 8 x = 7
â‡’ 7x = 6
â‡’ Final investment ratio = 20 : 49 : 48
B
Answer: (B) 20 : 49 : 48
Question: When p is divided by 9, the remainder is 7. All of the following are possible values of p, except for which of the following?
(A) 16
(B) 34
(C) 52
(D) 60
(E) 70
Rationale: Four of these numbers can be expressed in the form of 9x+7, where x can be 0,1,2,3,4....
However, 60 = 9(6) + 6
The answer is D.
Answer: (D) 60
Question: There are 10 points on a circle. A hexagon can be formed by linking 3 of the 10 points. How many such hexagons are possible?
(A) 60
(B) 120
(C) 200
(D) 210
(E) 600
Rationale: 3 points can be selected out of 10 points in 10C3 ways
=10 !/7!*3!=120
Ans B
Answer: (B) 120