RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If x and y are integers and x + y = 6, which of the following must be true?
A.x and y are consecutive integers.
B.If x < 0, then y > 0.
C.If x > 0, then y < 0.
D.Both x and y are even.
Answer: B.If x < 0, then y > 0.
Explanation: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option B is right could you explain
B
Question: The greatest possible length which can be used to measure exactly the length 6m, 3m 85cm, 12 m 95 cm is
A.2
B.7
C.5
D.8
Answer: C.5
Explanation: Explanation:
Required Length = H.C.F of 600 cm, 385 cm and 1295 c
= 5 cm.
Answer: C) 5 cm
Question: A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
A.1 ½ days
B.2 ½ days
C.3 ½ days
D.4 ½ days
Answer: A.1 ½ days
Explanation: A
1 ½ days
3/20 * 2 + (2 + x)/5 = 1
x = 1 ½ days
Question: The probability of having a girl is identical to the probability of having a boy. In a family with four children, what is the probability that all the children are of the same gender?
A.1/8.
B.1/3
C.1/4
D.1/6
Answer: A.1/8.
Explanation: There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2= 1/16
case 2 .all girls.
1/2*1/2*1/2*1/2=1/16
We will add the cases to get 1/8
Question: The sum of two consecutive number is 67. Which is the larger number?
A.34
B.43
C.44
D.45
Answer: A.34
Explanation: Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=67
2x+1=67
2x=66
x=33
Therefore larger number is x+1=34
ANSWER:A
Question: A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train?
A.270 m
B.210 m
C.340 m
D.130 m
Answer: A.270 m
Explanation: Explanation:
Speed= 72 kmph = 72×10/36 = 20 m/s
Distance covered = 250+ x where x is the length of the train
Time = 26 s
(250+x)/26 = 20
250+x = 26×20 = 520 m
x = 520-250 = 270 m
Answer: Option A
Question: Simplify (3^y + 3^y + 3^y) (3^y + 3^y + 3^y)
A. 4^4y * 3^3y
B. 9^y+1
C. 16^y + 9^y
D. 12^y
Answer: B. 9^y+1
Explanation: B
(3^y + 3^y + 3^y) (3^y + 3^y + 3^y)
(3*3^y)(3*3^y)
9*9^y=9^(y+1)..
Question: A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out.
A.40m3
B.42m3
C.44m3
D.46m3
Answer: C.44m3
Explanation: Explanation:
Volume=πr2hVolume=(22/7∗1∗1∗14)m3=44m3
Option C
Question: D and E are two points respectively on sides AB and AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 144:25 and BC=13 cm, then find the length of DE.
A.12
B.13
C.14
D.11
Answer: C.14
Explanation: ABC and ADE are similar triangles.
So (side of ABC/side of ADE)^2=25/169
side of ABC/side of ADE = 5/13
So the length of DE = 5
Answer - C
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
A.20/67
B.20/63
C.20/68
D.20/28
Answer: B.20/63
Explanation: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126
= 20/63
Answer:B
Question: Which of the following inequalities is always true for any non-negative real number 'x' and 'y'?
A.√(x+y) <= √x + √y
B.√(x-y) <= √x - √y
C.√(x+y) = √x + √y
D.√(x-y) >= √x - √y
Answer: A.√(x+y) <= √x + √y
Explanation: Using the principle of subadditivity which we know applies with square roots, we know that evaluating the function for the sum of two elements will always produce something less than or equal to the sum of the function's values at each element. Therefore, the answer is A.
Question: The number 83 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
A.17
B.16
C.15
D.14
Answer: C.15
Explanation: 7^2+5^2+3^2=49+25+9 = 83
7+5+3 =15
Hence answer is C
Question: After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?
A.37
B.29
C.11
D.15
Answer: D.15
Explanation: Explanation:
i) Let the ages of the five members at present be a, b, c, d & e years.
And the age of the new member be f years.
ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)
iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years
So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)
==> a + b + c + d + e = 5x + 15
==> a + b + c + d = 5x + 15 - e ------ (3)
iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,
The new average is: (5x + 15 - e + f)/5
Equating this to the average age of x years, 3 yrs, ago as in (2) above,
(5x + 15 - e + f)/5 = x
==> (5x + 15 - e + f) = 5x
Solving e - f = 15 years.
Thus the difference of ages between replaced and new member = 15 years.
Answer: D
Question: Suppose you flip a fair coin 8 times. What is the probability that, in 8 flips, you get at least one head?
A.55/256
B.255/256
C.155/256
D.5/256
Answer: B.255/256
Explanation: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads
probability of flipping either a head or a tail = 1/2
probability of flipping 3 tails in a row (1/2)^5
probability of flipping at least 1 head = 1 - (1/2)^8 = 255/256
Answer : B
Question: If athul rows 16 km upstream and 24 km down steam taking 4 hours each, then the speed of the stream
A.1kmph
B.2 kmph
C.1.5 kmph
D.12 kmph
Answer: A.1kmph
Explanation: Speed upstream = 16/4 = 4 kmph
Speed down stream = 24/4 = 6 kmph
Speed of stream = ½ (6-4) = 1 kmph
ANSWER:A
Question: The breath of a rectangular landscape is 6 times its length. There is a playground in it whose area is 4200 square mtr & which is 1/7 th of the total landscape. What is the breath of the landscape?
A.520
B.420
C.320
D.550
Answer: B.420
Explanation: Sol. 6x * x =7* 4200
x = 70
Length = 6* 70 = 420 B
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 12 years at the same rate?
A.2P
B.3P
C.4P
D.5P
Answer: B.3P
Explanation: P ---- 2P ---- 8 years
3 P ---- 12 years
ANSWER:B
Question: A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?
A.50
B.8
C.60
D.42
Answer: C.60
Explanation: in the first case the lady takes up 32 red colour
then he takes up 24 y (cause he should take up pair)
then he takes up 1y+1blue
then 2blue(cause to make sure he has a pair of each color in hand)
32+24+2+2=60
ANSWER:C
Question: What is the greatest positive integer n such that 3^n is a factor of 36^300?
A.100
B.200
C.300
D.600
Answer: D.600
Explanation: 36 = 3^2 * 2^2.
36^300 = 3^600 * 2^600
The answer is D.
Question: If x and y are different prime numbers, each greater than 6, which of the following must be true? I. x+y is an even integer II. xy is an odd integer III. (x/y) is not an integer
A.II only
B.II,III only
C.I,II and III
D.III only
Answer: C.I,II and III
Explanation: Given: x and y are different prime numbers, both greater than 6
Statement I: x+y is an even integer
Since x and y are prime numbers greater than 6, they will be odd
Therefore sum will be even.
Correct
Statement II: xy is an odd integer
Since x and y are prime numbers greater than 6, they will be odd
Therefore multiplication will be odd.
Correct
Statement III: (x/y) is not an integer
Since x and y are prime integers, therefore they will not have any common factor apart from 1
Hence (x/y) will not be an integer
Correct
Hence all three statements I, II and III are correct
Answer : C
Question: A sum of Rs. 2795 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
A.1642
B.1640
C.1720
D.2795
Answer: C.1720
Explanation: (x*8*3)/100 = ((2795 - x)*3*5)/100
24x/100 = 41925/100 - 15x/100
39x = 41925 => x = 1075
Second sum = 2795 – 1075
=1720
Answer:C
Question: A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.0 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
A.63,000
B.2,000,000
C.2,030,000
D.2,040,000
Answer: C.2,030,000
Explanation: Let's assume in 2006 he has sold X. Therefore in 2007 he should have sold 97/100×X.
97/100×2100=2037
-->2,037,000 sold in 2007. When rounded to the nearest 10,000 :
2,030,000
C
Question: If 50! × 50!/50^n is an integer, what is the largest possible value of n?
A.36
B.24
C.8
D.4
Answer: B.24
Explanation: 50! × 50!/50^n is an integer.
Or 50! × 50!/(5^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 50! = [50/5] + [50/25] = 12
Since there are 2 20!'s, power of 12 in the numerator = 2*12 = 24
Hence the largest value of b for which 50! × 50!/50^n is integer = 24
Correct Option : B
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
A.56.8 m2
B.82.9 m2
C.52.8 m2
D.17.9 m2
Answer: C.52.8 m2
Explanation: 42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer:C
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3:7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
A.Rs. 15.50
B.Rs. 16.90
C.Rs. 13.50
D.Rs. 16.50
Answer: D.Rs. 16.50
Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer:D
Question: A car averages 75 mph for the first 4 hours of a trip and averages 60 mph for each additional hour. The average speed for the entire trip was 70 mph. How many hours long is the trip?
A.6
B.78
C.8
D.9
Answer: A.6
Explanation: Let the time for which car averages 60 mph = t
70*(t+4)= 75*4 + 60 t
=>10 t= 20
=> t = 2
Total duration of the trip = 4+2=6
Answer A
Question: Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
A.7
B.8
C.6
D.5
Answer: B.8
Explanation: Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise she has four different routes.
Total routes = 8
Answer: B
Question: In covering a distance of 42 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
A.5 kmph
B.6 kmph
C.6.25 kmph
D.7 kmph
Answer: D.7 kmph
Explanation: Let Abhay's speed be x km/hr.
Then,	42/X	-	42/2X	= 3
6x = 42
x = 7 km/hr. Answer: Option D
Question: On a map, 1 inch represents 28 miles. How many C inches would be necessary to represent a distance of 383.6 miles?
A.5.2
B.7.4
C.13.7
D.21.2
Answer: C.13.7
Explanation: C inches necessary to represent a distance of 383.6 miles = 383.6/28
= 13.7
Answer C
Question: Each side of a certain parallelogram has length 8. If the area of the parallelogram is 16. Which of the following is the measure of one of its angles?
A.14.5
B.45
C.60
D.90
Answer: A.14.5
Explanation: Ans is 30deg
area of a parallelogram = b*h
b*h=16
h=16/8=2
sin theta =opp/hyp = 2/8 = 1/4
theta = sin inv of 1/4 = 14.5 deg
A
Question: Half a number plus 5 is 11.What is the number?
A.10
B.11
C.12
D.13
Answer: C.12
Explanation: Solution
Let x be the number. Always replace "is" with an equal sign
(1/2)x + 5 = 11
(1/2)x + 5 - 5 = 11 - 5
(1/2)x = 6
2 × (1/2)x = 6 × 2
x = 12
Answer C
Question: How many seconds will a 900 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.400
Answer: D.400
Explanation: Let length of tunnel is x meter
Distance = 900+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
900+x = (65/3) * 60
900+x = 20 * 65 = 1300
x = 1300 - 900 = 400 meters
Answer: D
Question: If 15 students in a class average 70% on an exam and 10 students average 95% on the same exam, what is the average in percent for all 25 students?
A.77%
B.78%
C.79%
D.80%
Answer: D.80%
Explanation: (15*70 + 10*95) / 25 = 80%
The answer is D.
Question: The ages of 2 persons differ by 32 years. If 12 years ago the elder one be 6 times as old as the younger one, find the present age of elder person.
A.30
B.48.5
C.50.4
D.62.6
Answer: C.50.4
Explanation: age of the younger person = x
age of the elder person = x+32
6(x-12) = x+32-12
x= 18.4
age of elder person = 18.4+32=50.4
Answer is C
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
A.12808
B.12800
C.12805
D.12801
Answer: B.12800
Explanation: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Question: A woman is 20 years older than her son. In 5 years, her age will be twice the age of her son. The present age of her son is
A.15
B.14
C.13
D.12
Answer: A.15
Explanation: Explanation:
Let the son's present age be x years. Then, woman's present age = (x + 20) years
=> (x + 20) + 5 = 2(x + 5)
=> x + 25 = 2x +10
So, x = 15. Answer: A
Question: A rectangular with dimensions 40 inches by 65 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
A.a) 4 inches
B.b) 6 inches
C.c) 7 inches
D.d) 5 inches
Answer: D.d) 5 inches
Explanation: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
40=2*2*2*5
65=5*13
GCF = 5
P.S you can make squares with side of 5
Answer : D
Question: If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 30 percent decrease in y would result in which of the following changes in z?
A.decrease of 7.5%
B.decrease of 26.5%
C.increase of 16.5%
D.increase of 24.5%
Answer: B.decrease of 26.5%
Explanation: After the changes, z = 1.5x*(0.7y)^2 = (1.5*0.49)xy^2 = 0.735*z
The answer is B.
Question: You keep tossing a fair coin for twenty times. Each time, the coin lands up with tails up.
What is the probability that if you toss it now, the coin will land with heads up this time?
A.50 %
B.60 %
C.70 %
D.80 %
Answer: A.50 %
Explanation: Solution:
50%
Explanation:
The probability will be 50% only as it always was. The next flip of coin is not dependent on what the results were in the previous flips.
Answer A
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
A.18 sec
B.77 sec
C.48 sec
D.28 sec
Answer: C.48 sec
Explanation: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer: C
Question: The diagonals of a rhombus are 15 cm and 17 cm. Find its area?
A.277
B.127.5
C.150
D.288
Answer: B.127.5
Explanation: 1/2 * 15 * 17 = 127.5
Answer: B
Question: Two pipes P and Q can fill a tank in 10 hours and 14 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
A.4 hours 20 min
B.5 hours 49 min
C.3 hours 50 min
D.3 hours 22 min
Answer: B.5 hours 49 min
Explanation: Explanation:
Part filled by P in 1 hour = 1/10
Part filled by Q in 1 hour = 1/14
Part filled by (P + Q) in 1 hour = ( 1/10 + 1/14) = (6/35)
Time taken to fill the tank is (35/6) = 5 hours 49 min
ANSWER B
Question: D is the set of all the multiples of 3 between 20 and 100. E is the set of all the factors of 700. Set D and Set E have how many numbers in common?
A.None of these
B.1
C.3
D.5
Answer: A.None of these
Explanation: D is a set of multiples of 3.
700 is NOT a multiple of 3, hence none of its factors is a multiple of 3.
Therefore, those two sets won't have any overlap.
Answer: A.
Question: There are 6 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 15 other amateurs, what is the total number of chess games possible to be played in the tournament?
A.10
B.20
C.45
D.60
Answer: C.45
Explanation: Each person is one participant of 6 games. So there are in all 6*15 = 90 instances of one participant games. But each game has 2 participants so total number of games = 90/2 = 45
C
Question: There are 27 different three-digit integers that can be formed using only the digits 4, 5 and 6. If all 27 of the integers were listed, what would their sum be?
A.14,785
B.14,885
C.14,985
D.15,085
Answer: C.14,985
Explanation: There must be nine 4's in the hundreds place, nine 4's in the tens place, and nine 4's in the units place. This is also true for the 5's and 6's. Then the sum is:
9(444+555+666)=9*(1665)=14,985.
The answer is C.
Question: A does half as much work as B in three-fourth of the time. If together they take 18 days to complete
the work, how much Ɵme shall B take to do it
A.40 days
B.35 days
C.30 days
D.25 days
Answer: C.30 days
Explanation: Explanation:
Suppose B takes x days to do the work.
As per question A will take
2
∗
34
∗
x=3x2days
(A+B)s 1 days work= 1/18
1/x + 2/3x = 1/18 or x = 30 days
Answer: C
Question: If d is the standard deviation a, b, and c, what is the standard deviation of a +6, b + 6, c + 6 ?
A.d
B.6d
C.6d+6
D.6d+12
Answer: A.d
Explanation: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
When 6 is added in each term of set {a, b,c} then the new set {a+6, b+6, c+6} will remain same as the previous standard deviation i.e. d
Answer: A
Question: The distance between 2 cities A and B is 100km. A train starts from A at 8 a.m. and travels towards B at 50 km/hr. Another starts from B at 9 a.m. and travels towards A at 60 km/hr. At what time do they meet?
A.9.45a.m.
B.10a.m.
C.10.25a.m.
D.11.10am.
Answer: A.9.45a.m.
Explanation: Suppose they meet x hrs after 8 a.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 100
50x + 60 (x-1) = 100
x = 1.45
They meet at 8+1.45 = 9.45 a.m.
Answer is A
Question: In how many ways the letters in the word MANAGEMENT can be arranged such that A’s does not come together.
A.181440
B.191440
C.171440
D.182440
Answer: A.181440
Explanation: Methods to arrange all the letters leaving A = 8*7*6*5*4*3*2*1/(2*1)*(2*1)*(2*1)= 5040
Now between these 8 letters , there are 9 places so methods to place A and A in these positions = 9*8/2*1 = 36
thus total methods are 5040*36 = 181440
ANSWER:A
Question: The remainder of the division of a number by 66 is 27. What will be the remainder when that number is divided by 7?
Please explain
A.2
B.5
C.6
D.7
Answer: A.2
Explanation: The easiest way to solve this question is by plugging in a number. Here are the steps I followed:
1) Choose a number X that when divided by 66 gives you 27 as a remainder. So I did x = 66 + 27 = 93.
2) Divide that number by 7. 93/7 = 13R2
Since the remainder is 2, the correct answer is choice A.
Question: Mohan purchased 15 kgs of rice at the rate of Rs.25 per kg and 8 kgs of pulses at the rate of Rs.25 per kg. Whaat is the total amount that he paid to the shopkeeper?
A.A)Rs.598
B.B)Rs.575
C.C)Rs.596
D.D)Rs.595
Answer: B.B)Rs.575
Explanation: Explanation:
Price of 15 kgs of rice at Rs.25/kg = 15x25 = Rs.375
Price of 8 kgs of pulses at Rs.25/kg = 8x25 = Rs.200
Therefore, Total amount = Rs.375+Rs.200 = Rs.575
Answer: Option B
Question: Vishal and Raghu jointly started a business. Vishal invested three times as Raghu did and invested his money for double time as compared to Raghu. Raghu earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?
A.Rs. 28,000
B.Rs. 18,000
C.Rs. 14,000
D.Rs. 8,000
Answer: A.Rs. 28,000
Explanation: Explanation:
Investments ratio is = 3:1
Time period ratio is = 2:1
As they are proportional to gain
------
Gain ratio of Vishal and raghu = 6:1
But given Raghu got Rs. 4000,
=? 1 ----- 4000
7 ----- ?
=> Rs.28,000
The total gain = Rs.28,000
ANSWER IS A
Question: 2,7,14,32,58,?
A.112
B.154
C.123
D.132
Answer: D.132
Explanation: 1^2+1=2
2^2+3=7
3^2+5=14
5^2+7=32
7^2+9=58
11^2+11=132
ANSWER:D
Question: If 30 honey bees make 30 grams of honey in 30 days, then 1 honey bee will make 1 gram of honey in how many days?
A.1
B.3.5
C.30
D.49
Answer: C.30
Explanation: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 30 :: 30 : x
Honey 30 : 1
=> 1 x 30 x x = 30 x 1 x 30
=> x =30.
Answer : C
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability Q that the sum of the two integers will equal 9 ?
A. 0.15
B. 0.20
C. 0.25
D. 0.30
Answer: B. 0.20
Explanation: Rearrange the first set:
A = {5,4,3,2}
B = {4,5,6,7, 8}
As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5=20. Q=favorable/total=4/20=0.2.
Answer: B.
Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: Q=1*1/5.
Answer: B.
Question: In a group of 65 people,40 like cricket,10 like both cricket and tennis. How many like tennis?
A.30
B.35
C.40
D.45
Answer: B.35
Explanation: Make a Venn diagram, and enter your data.
Let the number of people who like only tennis be x
x + 10 + 30 = 65
x = 25
so number who like tennis = 10+25 = 35
Answer B
Question: 16 men and 12 children can complete work in 26 days 13 men can complete the same work in 48 days in how many days’ will12 men and 6 children complete half of the work?
A.12
B.15
C.13
D.14
Answer: D.14
Explanation: Explanation:
16 men and 12 children can do work in 26 days =>in one day
16 *26=416 men and 12*26=312 children can do same work
also, 13 men can do same work in 48 days =>13 *48=624 men
thus 624 men = 412 men + 312 children
=> 2mne = 3 children
24 men can do a work in 26 days
16 men can do same work in =26*24/16 = 39 days
Answer: Option D
Question: A man can row with a speed of 19 kmph in still water. If the stream flows at 8 kmph, then the speed in downstream is?
A.28
B.26
C.20
D.27
Answer: D.27
Explanation: M = 19
S = 8
DS = 19 + 8
=27
Answer: D
Question: A 60 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
A.A)73
B.B)20
C.C)83
D.D)17.1
Answer: D.D)17.1
Explanation: Explanation:
1: 2/5 = 5: 2
2/7 * 60 = 20
Answer: Option D