mathewhe/aqua_rat huggingface dataset:
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
(A) 25years
(B) 45years
(C) 12years
(D) 6years
(E) 16years
Rationale: Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (_(61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25 years.
Ans: A
Answer: (A) 25years
Question: In the first 10 overs of a cricket game, the run rate was only 3.6. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.25
(B) 6.5
(C) 6.15
(D) 7
(E) 8
Rationale: 10 overs - run rate = 3.6
runs scored in first 10 overs = 36
remaining overs 40
total runs to be scored= 282
32 runs already scored 282-36=246
246 runs to be scored in 40 overs
let required runrate be x
40*x=246
x=246/40
x=6.15
the required runrate is 6.15
ANSWER:C
Answer: (C) 6.15
Question: John has $1,600 at the beginning of his trip, after spending money, he still has exactly $600 less than he spent on the trip. How much money does John still have?
(A) $200
(B) $400
(C) $600
(D) $800
(E) $500
Rationale: Suppose total money spent = x
Not spend (Money he still has)= x-600
x+x-600 = 1600
x= 1100
Money not spend= 1100-600= 500
Answer : E
Answer: (E) $500
Question: Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 48 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 6
Rationale: One way of approaching this question is by Relative speed method
1. Speed/ Rate of Donovan = Distance/ time => 400/48 =>50/6
2. Speed/ Rate of Michael = Distance/ time => 400/40 => 10
Relative Speed between them = 10 - 50/6 => 10/6 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)
In order to pass Donovan-
Distance to be covered = 400, Relative Rate = 10/6
Total Time taken by Micheal to surpass Donovan = Distance / rate => 400*6/10 => 2400/10 => 240
No. of laps taken by Michael = Total time / Michael's rate => 240/40 => 6
Hence correct answer is 6 Laps.
E
Answer: (E) 6
Question: A cab driver 5days income was $25, $50, $60, $65 , $70. Then his average income is?
(A) A)$58
(B) B)$54
(C) C)$65
(D) D)$48
(E) E)$62
Rationale: avg = sum of observations/number of observations
avg income=(25+50+60+65+70)/5 = 54
Answer is B
Answer: (B) B)$54
Question: If a committee of 3 people is to be selected from among 7 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
(A) 20
(B) 40
(C) 50
(D) 180
(E) 280
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
14*12*10 / 6 = 280. Answer E.
Answer: (E) 280
Question: What is the remainder when 14,456 × 15,657 × 16,788 is divided by 10?
(A) 6
(B) 8
(C) 4
(D) 3
(E) 2
Rationale: Only the unit's digit of the product will decide the remainder when divided by 10.
Hence, 6*7*8= will give units digit as 6
So, whatever be the number, if it ends in 6, the remainder after dividing with 10 will be 6.
OptionA
Answer: (A) 6
Question: In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,6). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
(A) 1/5
(B) 1/3
(C) 1/2
(D) 2/3
(E) 4/5
Rationale: The area of the right triangle is (1/2)*4*6 = 12.
Only the points (a,b) below the line y=x satisfy a - b > 0.
The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.
P(a - b > 0) = 8/12 = 2/3
The answer is D.
Answer: (D) 2/3
Question: Rs. 6000 is lent out in two parts. One part is lent at 4% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 5:1
(B) 5:7
(C) 5:2
(D) 5:8
(E) 5:2
Rationale: Let the amount lent at 4% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 4/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 2500
Amount lent at 10% = 3500
Required ratio = 5:7
Answer:B
Answer: (B) 5:7
Question: 88% OF 370+24% OF 210-?=118
(A) 256
(B) 258
(C) 268
(D) 358
(E) NONE OF THESE
Rationale: LET 88% OF 370+240% OF 210-X=118
THEN, X=(88/100*370)+(24/100*210)-118-325.60+50.40-118=376-118=258
CORRECT OPTION: B
Answer: (B) 258
Question: The smallest number which when diminished by 8, is divisible 8, 16, 24, 32 and 40 is:
(A) 1008
(B) 1015
(C) 488
(D) 490
(E) 590
Rationale: Required number = (L.C.M. of 8, 16, 24, 32, 40) + 8
= 480 + 8
= 488
Answer: Option C
Answer: (C) 488
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 72.25, the number of the member is the group is:
(A) 57
(B) 67
(C) 77
(D) 85
(E) 97
Rationale: Explanation:
Money collected = (72.25 x 100) paise = 7225 paise.
∴ Number of members = √(7225) = 85.
Answer: D
Answer: (D) 85
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is
(A) 25/42
(B) 25/47
(C) 25/32
(D) 25/48
(E) 25/41
Rationale: :
Total fruits = 9
Since there must be at least two apples,
= 25/42.
Answer: A
Answer: (A) 25/42
Question: How many words can be formed by using all letters of the word ‘BIHAR’ ?
(A) 110
(B) 120
(C) 130
(D) 140
(E) None
Rationale: Solution
The word BIHAR contains 5 different letters.
Required number of words = 5P5 = 5 ! = (5 x 4 x 3 x 2 x 1) = 120
Answer B
Answer: (B) 120
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 4 : 1 ?
(A) 6 months
(B) 3 months
(C) 2 months
(D) 8 months
(E) 9 months
Rationale: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 4. or x = (85000 * 12) / (42500 * 4) = 6.
So, B joined for 6 months.
Answer: A
Answer: (A) 6 months
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: (A) 1
Question: A, B and C rents a pasture for Rs.928. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 289
(C) 288
(D) 255
(E) 552
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 928 = 288
Answer: C
Answer: (C) 288
Question: What is the difference between the place values of two sevens in the numeral 54707429 ?
(A) 699990
(B) 693000
(C) 99980
(D) 699930
(E) None of these
Rationale: Explanation:
Required Difference
= 700000 - 7000 = 693000
Answer is B
Answer: (B) 693000
Question: In an election between two candidates first candidate got 65% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
(A) 7000 votes
(B) 8000 votes
(C) 9000 votes
(D) 9800 votes
(E) 9900 votes
Rationale: Total = 100 %,
First person got 65%
second person got remaining 35 % of votes.
than 35 % = 2800
35% = 35Ã—80 = 2800
100% =100Ã—80 =8000 votes
B
Answer: (B) 8000 votes
Question: What is the sum of the 1st 5 prime numbers greater than 20?
(A) 121
(B) 151
(C) 168
(D) 164
(E) 161
Rationale: Required sum = (23 + 29 + 31 + 37 + 41) = 161
Note: 1 is not a prime number
Answer E
Answer: (E) 161
Question: Jason flips a coin three times. What is the probability W that the coin will land on the same side in all three tosses?
(A) 1/16
(B) 1/8
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Total outcome is 2^3=8
Favorable cases HHH or TTT
Therefore, probability W is 2/8 or 1/4.C
Answer: (C) 1/4
Question: From 5 positive numbers and 7 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
(A) 720
(B) 625
(C) 250
(D) 960
(E) 355
Rationale: The number of ways to choose 4 positive numbers is 5C4 = 5.
The number of ways to choose 4 negative numbers is 7C4 = 35.
The number of ways to choose 2 positive and 2 negative is 5C2*7C2 = 10*21 = 210.
The total number of groups is 5+35+210 = 250.
The answer is C.
Answer: (C) 250
Question: If 2x^2 – y^2 = 2xy, then (x - y)^2 =
(A) x^2
(B) 3x^2
(C) 4xy
(D) 2y^2-x^2
(E) – y^2
Rationale: (x-y)^2 = x^2 + y^2 - 2xy = x^2 + y^2- 2x^2+y^2 = 2y^2-x^2
correct option : D
Answer: (D) 2y^2-x^2
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference?
(A) 10 feet
(B) 8 feet
(C) 13 feet
(D) 15 feet
(E) 18 feet
Rationale: total circuit=16/4=4
total feet squirrel travels=4*2=8 feet
ANSWER:B
Answer: (B) 8 feet
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 216 marks in the second test and failed by 36 marks in that test. Find the pass mark in the first test?
(A) 277
(B) 266
(C) 111
(D) 121
(E) 224
Rationale: Let the maximum mark in each test be M.
The candidate failed by 36 marks in the second test.
pass mark in the second test = 216 + 36 = 252
45/100 M = 252
Pass mark in the first test = 40/100 M = 40/45 * 252 = 224.
Answer:E
Answer: (E) 224
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 11
(B) 444
(C) 420
(D) 287
(E) 221
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 14 + 21 = 35
T = 12
D = 35 * 12 = 420
Answer:C
Answer: (C) 420
Question: How many of the positive factors of 56 , 96 and how many common factors are there in numbers?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 1
Rationale: factors of 56- 1, 2, 4, 7, 8, 14, 28, 56
factors of 96- 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Comparing both, we have three common factors of 56 and 96- 1,2,4
Answer(C)
Answer: (C) 3
Question: Two airplanes take off from one airfield at noon. One flies due east at 204 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
(A) 166
(B) 408
(C) 400
(D) 483
(E) 566
Rationale: B
In two hours:
the plane flying East will be 408 miles away from airport.
the other plane will be 566 miles away from airport.
566/408 = ~1.4 = ~sqrt(2)
This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 408 miles apart.B
Answer: (B) 408
Question: What is the smallest five digit number that is divisible by 15, 36, 40, and 54?
(A) 10400
(B) 10800
(C) 11200
(D) 11600
(E) 12000
Rationale: 15 = 3 * 5
36 = 2^2 * 3^2
40 = 2^3 * 5
54 = 2 * 3^3
LCM = 2^3 * 3^3 * 5 = 1080
The smallest five-digit number that is a multiple of 1080 is 10*1080 = 10,800
The answer is B.
Answer: (B) 10800
Question: Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many E miles will Tom drive before Karen wins the bet?
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him E: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer.
Answer: (D) 24
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is a + 2?
(A) a - 5
(B) a
(C) a - 1
(D) a - 3
(E) a + 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= a+2
n= a+1
1st integer= a+1-4= a-3
D is the answer
Answer: (D) a - 3
Question: The ratio of radius of a circle and the side of a square is 2 : 3. Find the ratio of their areas:
(A) 2 : 1
(B) 4 : 9
(C) 8 : 77
(D) 4 : 121
(E) None
Rationale: radius/side = 2/3
â‡’ area of circle/area of square= 4/9
Answer: B
Answer: (B) 4 : 9
Question: On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.7, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.063
(B) 0.128
(C) 0.488
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probablity of rain = 0.7
Therefore, probability of no rain = 0.3
0.3*0.3*0.7 = 0.063
Hence A
Answer: (A) 0.063
Question: Of the three-digit integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A) 120
(B) 116
(C) 108
(D) 107
(E) 72
Rationale: # of three-digit integers greater than 600 is 399 (999-600);
Numbers with all distinct digits: 4*9*8=288. First digit can take 4 values: 6, 7, 8 or 9, second digit can take 9 values (10 minus the one we used for the first digit) and third digit can tale 8 values (10 minus 2 digits we've already used for the first two digits);
Numbers greater than 600 which have all alike digits: 4 (666, 777, 888, 999);
{Total}-{all distinct}-{all alike}={two alike, one different} --> 399-288-4=107.
Answer: D.
Answer: (D) 107
Question: How many seconds will a 500 meter 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) 287
(B) 288
(C) 500
(D) 277
(E) 121
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Answer: (C) 500
Question: For a sequence to be considered an arithmetic sequence, there must be a constant difference between the terms. If a,b,c,d,e is an arithmetic sequence, which of the following is also an arithmetic sequence?
I. 7a,7b,7c,7d,7e
II. a-5, b-5, c-5, d-5, e-5
III. a^3, b^3, c^3, d^3, e^3
(A) III only
(B) I and II
(C) II and III
(D) II only
(E) I and III
Rationale: lets look at the three choices...
I. 7a,7b,7c,7d,7e
since the difference is constant, it is an arithmetic sequence...
II. a-5, b-5, c-5, d-5, e-5
since the difference is constant, it is an arithmetic sequence
III. a^3, b^3, c^3, d^3, e^3
since the difference is not constant it is not be an arithmetic sequence...
Answer is B)
Answer: (B) I and II
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
(A) XB < AX
(B) XB < YD
(C) AX > XB
(D) AX < AB
(E) AX > AB
Rationale: A--X------B
C------Y--D
AX < AB.
Answer: D.
Answer: (D) AX < AB
Question: If cost of sugar increases by 25%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
(A) 20
(B) 40
(C) 15
(D) 16
(E) 12
Rationale: 100
125
-----
125 ----- 25
100 ------ ? => 20%
ANSWER A
Answer: (A) 20
Question: A train takes 18 seconds to pass completely through a statin 162 m long and 15 seconds through another station 120 m long. The length of the train is:
(A) 30
(B) 60
(C) 90
(D) 100
(E) 120
Rationale: Sol.
Let the length of the train be x metres.
∴ x + 162 / 18 = x + 120 / 15 ⇔ 15 (x + 162) = 18 (x + 120) ⇔ x = 90 m.
Answer C
Answer: (C) 90
Question: 20 machines can do a work in 5days. How many machines are needed to complete the work in 10days?
(A) 10
(B) 15
(C) 8
(D) 12
(E) 20
Rationale: Required number of machines = 20*5/10 = 10
Answer is A
Answer: (A) 10
Question: If x^2 - 1 = 0 and x > 0, which of the following must be equal to 0 ?
(A)  x^2 - 9x
(B)  x^2 - 9x + 8
(C)  x^2 - 2x + 3
(D)  x^2 + 2x - 3
(E)  x^2 + 5x + 6
Rationale: x^2-1 = 0
x= +1 or x = -1
if we substitute x= 1 in the equation x^2 -9x+8 = 1-9+8 = 0
B is also the answer
Answer: (B)  x^2 - 9x + 8
Question: 12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
(A) 6
(B) 8
(C) 10
(D) 20
(E) 40
Rationale: we have 1 litre = 1000cm³ (thanks Bunuel)
=>12 litres = 12*1000 = 12000cm³
Let call the height of the water is x
the breadth and length of the water will equal the aquarium
The volume of the water:
50 * 30 * x = 12000cm³
=> x = 12000/(50*30) = 8 cm
Answer is B
Answer: (B) 8
Question: A travel agent offers a vacation plan which costs x dollars for the first day, and x/3 for each additional day. How much does a vacation of y days cost, where y > 1.
(A) (yx-3x)/3
(B) (yx+4x)/2
(C) (yx+5x)
(D) (yx+2x)/3
(E) (yx-x)/3
Rationale: Cost = x + (y-1)*x/3 = (3x + (y - 1)*x)/3 = (yx+2x)/3
Answer is D
Answer: (D) (yx+2x)/3
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
(A) 5
(B) 6
(C) 8
(D) 4
(E) 1
Rationale: 28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer: D
Answer: (D) 4
Question: A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $6.00?
(A)  72
(B)  60
(C)  90
(D)  120
(E)  240
Rationale: Cost price of 1 pound of bananas = 0.5/3 = 1/6
Selling price of 1 pound of bananas = 1/4
Profit per pound = (1/4 - 1/6) = (1/12)
Total profit is given as 6
(1/12)*x = 6
x = 72
Answer: A
Answer: (A)  72
Question: The price of an article is cut by 10%. To restore it to the former value, the new price must be increased by
(A) 10%
(B) 9 1/11 %
(C) 11 1/9%
(D) 11%
(E) None
Rationale: Explanation:
Let original price = Rs.100
Then, new price = Rs.90
Increase on Rs.90=Rs.100
Increase % = (10/90×100)% =11 1/9 %
Correct Option: C
Answer: (C) 11 1/9%
Question: Crew A can build a complete car in 20 minutes and Crew B can build a complete car in 25 minutes. If both crews work independently and start at the same time, what is the shortest amount of time V it could take for 10 cars to be complete?
(A) 111 1/9 minutes
(B) 115 2/5 minutes
(C) 116 minutes
(D) 120 minutes
(E) 125 minutes
Rationale: A builds 4 cars in 80 min
B builds 4 cars in 100 min
So A builds another car in another 20 min (i.e total 5 cars)
B builds another car in another 25 minutes (i.e, total 5 cars)
However, A can build another car in next 20 min (i.e total 6 cars)
So total time V= 125 min by B, which is > 120 min by A
B - 4 cars, A - 6 cars
Answer = D
Answer: (D) 120 minutes
Question: What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 69.12 = ?
(A) 229
(B) 225
(C) 235
(D) 220
(E) 240
Rationale: ? = 33 1⁄3% of 768.9 + 25% of 1691.2 – 69.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 6.12
= 256.3 + 40.3 – 69.12 ≈ 229
Answer A
Answer: (A) 229
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 16%?
(A) 26%
(B) 28%
(C) 27%
(D) 40%
(E) 70%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 84
2/3 SP1 = 84
SP1 = 126
100 --- 26 => 26%
Answer:A
Answer: (A) 26%
Question: A vendor sells 20 percent of the pears he had and throws away 50 percent of the remainder. The next day, the vendor sells 20 percent of the remaining pears and throws away the rest. In total, what percent of his pears does the vendor throw away?
(A) 56
(B) 60
(C) 64
(D) 68
(E) 72
Rationale: Let x be the original number of pears.
On day one, the vendor throws away (0.5)(0.8)x=0.4x.
The remaining pears are (0.5)(0.8)x = 0.4x.
On day two, the vendor throws away (0.8)(0.4)x=0.32x.
The vendor throws away a total of 0.4x + 0.32x = 0.72x.
The vendor throws away 72 percent of the pears.
The answer is E.
Answer: (E) 72
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) 6
(B) 5
(C) 7
(D) 8
(E) 2
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
Question: At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 7:3. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?
(A) 45/21
(B) 46/2
(C) 13/30
(D) 23/6
(E) 4/6
Rationale: Red: Blue = 7:3
Let Red = 7x and Blue = 3x
1/3 of Red are left handed => 1/3 * 7x = 7x/3 Red left handed
2/3 of Blue are left handed => 2/3 *3x = 6x/3 blue left handed
fraction of participants who are left handed = total left handed/ total participants = (red left handed + blue left handed)/total participants = (7x/3 + 6x/3)/(7x+3x) = 13/30
Answer : C
Answer: (C) 13/30
Question: The perimeter of a semi circle is 113 cm then the radius is?
(A) 17
(B) 28
(C) 19
(D) 11
(E) 22
Rationale: 36/7 r = 113 => r
= 22
Answer: E
Answer: (E) 22
Question: A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders W when the order of the divisors is reversed.
(A) 8,5,3
(B) 4,2,1
(C) W=3,2,1
(D) W=6,4,2
(E) None of above
Rationale: My approach would be
Three Divisors : 3, 5, 8
Three Remain: 1, 4, 7
Start from the bottom of the last column i.e. from the third remainder:
Go up diagonally and multiply by the second divisor: 5*7 = 35
Go down and add the second remainder: 35 + 4 = 39
Go up diagonally and multiply by the first divisor: 39* 3 = 117
Go down and add the first remainder: 117 + 1 = 118
Divide 118 by 8, 5, 3
118/8 gives quotient = 14 and remainder = 6
14/5 gives quotient = 2 and remainder = 4
2/3 gives quotient = 0 and remainder = 2
Ans is D i.e. 6,4,2
Answer: (D) W=6,4,2
Question: The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
(A) 7 years
(B) 5 years
(C) 4 years
(D) 6 years
(E) 3 years
Rationale: 100 ---- 300 --- 3
900 --- 3
----
6 years
Answer:D
Answer: (D) 6 years
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:12. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 19
(B) 17
(C) 13
(D) 10
(E) 12
Rationale: 7*5: 5*x = 7:12
x = 12
Answer: E
Answer: (E) 12
Question: Jane started baby-sitting when she was 20 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Check two extreme cases:
Jane = 20, child = 10, years ago = 32-20 = 12 --> child's age now = 10+12 = 22;
Jane = 22, child = 11, years ago = 32-22 = 10 --> child's age now = 11+10 = 21.
Answer: C.
Answer: (C) 22