RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If one positive integer is greater than another positive integer by 3, and the difference of their cubes is 189, what is their sum?
A.6
B.7
C.8
D.9
Answer: D.9
Explanation: 1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
The two numbers are 3 and 6.
The answer is D.
Question: Which of the following functions does not intersect with R = 3x^2 + 2x + 1
A.R = 3x^2 + 3x + 1
B.R = 2x^2 + 3x + 1
C.R = 3x^2 + 2x + 3
D.R = 4x^2 + 2x - 3
Answer: C.R = 3x^2 + 2x + 3
Explanation: Let’s find the actual intersecting point of given function and each choice R
A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0
B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1
C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.
D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2
E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.
So only choice (C) has no intersecting point. The answer is (C).
Question: The owner of a furniture shop charges his customer 30% more than the cost price. If a customer paid Rs. 8450 for a computer table, then what was the cost price of the computer table?
A.Rs. 5725
B.Rs. 5275
C.Rs. 6275
D.Rs. 6500
Answer: D.Rs. 6500
Explanation: CP = SP * (100/(100 + profit%))
= 8450(100/130) = Rs. 6500.
ANSWER:D
Question: Twenty times a positive integer is less than its square by 96. What is the integer?
A.20
B.24
C.30
D.34
Answer: B.24
Explanation: Let the integer be x. Then,
x2 - 20x = 96
(x + 4)(x - 24) = 0
x = 24
ANSWER:B
Question: A bag contains 50p,Rs.1/- and Rs2/- coins in the ratio of 4:2:1 respectively. If the total money in the bag is Rs.60/-. Find the number of 50p coins in that bag?
A.20 coins
B.40 coins
C.60 coins
D.70 coins
Answer: B.40 coins
Explanation: 50paisa : Rs.1/- : Rs.2/- = 4 : 2 : 1 ---> coins ratio
= 2 : 2 : 2 ----> money ratio
Rs.2/- * 10 coins = Rs.20/-
Rs.1/- * 20 coins = Rs.20/-
50 Paisa * 40 coins = Rs.20/-
Then 50 paisa coins in that bag = 40 coins
B)
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:
A.3488
B.6240
C.2776
D.2889
Answer: B.6240
Explanation: Explanation:
To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment = = Rs. 6240
Answer: B) 6240
Question: A box contains 5 black, 10 white and 8 yellow marbles. 4 marbles are drawn from the box at random. What is the probability that all three marbles are of the same color?
A.224/8855
B.225/8855
C.245/8855
D.285/8855
Answer: D.285/8855
Explanation: Explanation:
Total marbles in a box = 5 black +10 white + 8 yellow marbles = 23 marbles
4 marbles are drawn from 23 marbles at random. Therefore,
n(S) = 23C4 = 8855 ways
Let A be the event that 4 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 5C4 + 10C4 + 8C4 = 5 +210 + 70= 285
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) =285/8855
ANSWER:D
Question: Two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days. The number of days required by 1 man to complete the work is
A.60 days
B.15 days
C.6 days
D.51 days
Answer: B.15 days
Explanation: Two men and 7 children complete a certain piece of work in 4 days
or 8 men and 28 children complete a certain piece of work in 1 days
4 men and 4 children complete the same work in only 3 days.
or 12 men and 12 children complete the same work in only 3 days.
so 8 men +28 children = 12 men +12 children
1Man = 4 children
4 men and 4 children complete the same work in only 3 days
or 4 men and 1 man ( in place of 4 children ) complete the same work in only 3 days
or 5 men complete the same work in 3 days
or 1 man will complete the same work in 5* 3 =15 days
ANSWER:B
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
A.13
B.31
C.49
D.56
Answer: D.56
Explanation: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
56
Answer: D
Question: Mangala completes a piece of work in 12 days, Raju completes the same work in 18 days. If both of them work together, then the number of days required to complete the work is?
A.5.2 days
B.6.2 days
C.7.2 days
D.8.2 days
Answer: C.7.2 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 12 Ã— 18/30 = 7.2 days.
C)
Question: If 35*s is a perfect square then s can be which of the following numbers?
A.21
B.35
C.54
D.105
Answer: B.35
Explanation: My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 35 are 5 * 7
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice B completes the pairing of 5 and 7. It adds a3, a5, and a7to the prime factors of 35 (5*7) and makes it a perfect square. B
Question: A committee that includes 12 members is about to be divided into 3 subcommittees with 4 members each. On what percent of the possible subcommittees that Michael is a member of is Annie also a member?
A.39%
B.35%
C.31%
D.27%
Answer: D.27%
Explanation: Michael is a member of one of the subcommittees.
P(Annie is on the same subcommittee) = 3/11 which is about 27%.
The answer is D.
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 30% profit by using a false weight. What weight does he substitute for a kilogram?
A.769 1/7 grams
B.769 3/13 grams
C.769 8/3 grams
D.769 1/3 grams
Answer: B.769 3/13 grams
Explanation: If the cost price is Rs.100, then to get a profit of 30%, the selling price should be Rs.130.
If 130kg are to be sold, and the dealer gives only 100kg, to get a profit of 30%.
How many grams he has to give instead of one kilogram(1000 gm).
130 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/130 = 769 3/13 grams.
Answer:B
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 16 miles per hour." What was their average speed in the whole journey?
A.10 miles/hour
B.12.3 miles/hour
C.11 miles/hour
D.13 miles/hour
Answer: B.12.3 miles/hour
Explanation: 2xy/x+y=12.3 miles/hour
ANSWER:B
Question: An amount of money was invested at 10% a year. Five times that amount was invested at 15%. How much was invested at 15% if the total annual return was $1,615?
A.9500
B.1000
C.10500
D.11000
Answer: A.9500
Explanation: Let x and 5x be the amounts invested as 10% and 15% respectively.
Annual return for x = .1x
Annual return for 5x = .75x
Total return = .85x = 1615
x = 1900
So amount invested for 15% = 9500.
ANSWER:A
Question: There are 24 students in Chadâ€™s class. He brought 27 cookies to pass out
for his birthday. How many cookies will each student get? Will there be
any cookies left over?
A.1-9
B.1-7
C.2-8
D.1-3
Answer: D.1-3
Explanation: 27/24 = 1 R 3 Chad will give each student 1 cookie and there will be 3
cookies left over
correct answer D
Question: Mary can do a piece of work in 11 days. Rosy is 10% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?
A.10
B.15
C.20
D.25
Answer: A.10
Explanation: Ratio of times taken by Mary and Rosy = 110:100 =11:10
Suppose Rosy takes x days to do the work.
11:10 :: 11:x => x= 10 days.
Hence, Rosy takes 10 days to complete the work.
Answer: A
Question: If the average (arithmetic mean) of 2x, 4x, and 8x is 140, what is the value of x?
A.20
B.30
C.15
D.33
Answer: B.30
Explanation: AM of 2x, 4x and 8x = 2x + 4x + 8x / 3 = 14x/3
Given that 14x/3 = 140
x = 30
Answer is B
Question: If y is a positive integer, which of the following could NOT be the square of y?
A.4432
B.9426
C.4966
D.6415
Answer: A.4432
Explanation: A number ending in 2 cannot be a perfect square.
4432 ends in a number 2, making that the correct answer
(A) 4432
Question: Find the odd man out. 24,36,52,72,96
A.72
B.52
C.36
D.24
Answer: B.52
Explanation: Explanation :
All except 52 are multiples of 6
Answer : Option B
Question: After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 240 billion gallons, the reservoir was approximately what percentage full before the storm?
A.40%
B.48%
C.54%
D.58%
Answer: C.54%
Explanation: When the storm deposited 120 billion gallons, volume of water in the reservoir = 240 + 120 = 360 billion gallons
If this is only 60% of the capacity of the reservoir, the total capacity of the reservoir = 360/0.6 = 600 billion gallons
Therefore percentage of reservoir that was full before the storm = (240/600)*100 = 40%
Option C
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
A.32 kmph
B.76 kmph
C.34 kmph
D.43 kmph
Answer: A.32 kmph
Explanation: S = (100 + 300)/45
= 400/45 * 18/5
= 32
Answer:A
Question: Nine highschool girls gather at the gym for a game of mini-foot ball. Three teams of 3 people each will be created. How many ways are there to create these 3 teams?
A.27
B.51
C.45
D.175
Answer: C.45
Explanation: Arrange the 6 boys in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (C)
You get 6!/(2! * 2! * 2!) * 2!
Answer : C
Question: A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of y when angle B is 75 degrees?
A.75
B.95
C.105
D.115
Answer: C.105
Explanation: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.
An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.
angle B = 75 degrees
Thus,
arc ADC = 150 degrees
A whole circle has 360 degrees of arc, so arc ABC should be the rest of the circle.
arc ABC = 360 - 150 = 210 degrees
The angle that intersects this arc, angle D, should have half this measure.
angle D = y = 210/2 = 105 degrees
Answer =(C)
Question: Jane makes toy bears. When she works with an assistant, she makes 89 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
A.20%
B.80%
C.110%
D.180%
Answer: C.110%
Explanation: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 75.6 bears per 36 hours a week or 2.1 bears/hr ([40 bears * 1.89] / [40 hrs * .90]).
[(2.1 - 1)/1] * 100% = 110%
ANSWER:C
Question: The least number by which 72 must be multiplied in order to produce a multiple of 112, is:
A.6
B.12
C.14
D.18
Answer: C.14
Explanation: Required number is divisible by 72 as well as by 112, if it is divisible by their LCM, which is 1008.
Now, 1008 when divided by 72, gives quotient= 14.
Therefore, required number= 14.
Answer: C
Question: Which of the following is closer to √0.1+√0.15?
A.0.5
B.0.7
C.0.9
D.1.1
Answer: B.0.7
Explanation: √0.1+√0.15=approximately √0.09+√0.16=0.3+0.4=0.7 . Hence, the correct answer is B.
Question: As x increases from 165 to 163, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)
A. I only
B. III only
C. I and II
D. I and III
Answer: C. I and II
Explanation: I. 2x - 5 --> x increases from 165 to 163 --> 2x increases --> 2x - 5 increases. Correct.
II. 1 - 1/x --> x increases from 165 to 163 --> 1/x decreases --> 1 -1/x increases. Correct.
III. 1/(x^2 - x) --> x increases from 165 to 163 --> x^2-x increases --> 1/(x^2 - x) decreases.
Answer: C.
Question: What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 9), (x, 9)?
A.121
B.132
C.144
D.156
Answer: A.121
Explanation: To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 11.
The area is 11*11 = 121.
The answer is A.
Question: Thirty men can do a work in 24 days. In how many days can 20 men can do the work, given that the time spent per day is increased by one-third of the previous time?
A.27 days
B.77 days
C.88 days
D.66 days
Answer: A.27 days
Explanation: Let the number of hours working per day initially be x. we have M1 D1 H1
= M2 D2 H2
30 * 24 * x = 20 * d2 * (4x)/3
=> d2 = (30 * 24 * 3)/(24 * 4)
= 27 days.
Answer:A
Question: The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 4 type B widgets, and the weight of 3 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?
A.5:4
B.7:6
C.9:8
D.11:10
Answer: D.11:10
Explanation: 3B = 7C and so B = 7C/3
7A = 4B and so A = 4B/7 = 4C/3
A+B = 4C/3 + 7C/3 = 11C/3
B+C = 7C/3 + C = 10C/3
The ratio of A+B:B+C = 11:10
The answer is D.
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
A.20
B.99
C.28
D.18
Answer: A.20
Explanation: Explanation:
There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee = â¶Câ‚ƒ = (6 * 5 * 4)/6 = 20.
Answer:A
Question: In how many ways the letters of the word LOOC be arranged?
A.10
B.11
C.12
D.16
Answer: C.12
Explanation: In this four letters means 4! = 24 ways
But 'O' is repeated two times.
And thus we divide the final ways by 2. I.e. there are only 24/2 = 12 ways of arranging the letters of this word.
LOOK, LOKO, LKOO, KOOL, KOLO, KLOO, OOLK, OOKL, OLOK, OKOL, OLKO, OKLO = 12 Ways
C
Question: A closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
A.0 feet
B.1 feet
C.2 feet
D.3 feet
Answer: D.3 feet
Explanation: 36 pie cubic feet of water and its filled to half tank's capacity...
volume of tank = 72 Pie cubic feet
height of tank = 4*2 = 8 feet ( since tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet.)
72 pie = pie * r2*8
r2=9
r = 3 feet
ANSWER:D
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 60 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
A.22
B.27
C.15
D.99
Answer: C.15
Explanation: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 60) = 90(x - 5)
150 = 10x => x = 15.Answer: C
Question: If the square root of p^2 is an integer, which of the following must be true?
I. p^2 has an odd number of factors
II. p^2 can be expressed as the product of an even number of prime factors
III. p has an even number of factors
A.I
B.II
C.III
D.I and II
Answer: D.I and II
Explanation: I. p^2 is a perfect square and a perfect square has pairs of factors and '1' with it. The total number of factors is odd
II. If p = 3 then p^2 = 9. The prime factors will always remain even as the p is an integer and the pairs have to come out of square root to make p an integer.
III. This is not true always. Let us say p = 4, it has three factors: 1, 2 and 4. Hence it will not hold true always.
Hence D is the answer.
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.22 sec
B.88 sec
C.48 sec
D.18 sec
Answer: C.48 sec
Explanation: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer:C
Question: Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 4 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
A.7/15
B.9/20
C.11/25
D.13/27
Answer: D.13/27
Explanation: Tom paints 1/6 of the room in the first hour.
Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.
The three people then paint the remaining 2/6 in a time of (2/6) / (3/4) = 4/9 hours
Peter worked for 13/9 hours so he painted 13/9 * 1/3 = 13/27 of the room.
The answer is D.
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
A.7%
B.4%
C.9%
D.42%
Answer: B.4%
Explanation: 65*(90/100)*((100-x)/100)
= 56.16
x = 4%
Answer:B
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
A.287
B.270
C.276
D.129
Answer: B.270
Explanation: I = (500*9*6)/100 = 270
Answer: B
Question: If P(A) = 6/17, P(B) = 5/17, and P(A ∪ B) = 4/17 Find P(B|A)?
A.2/3
B.3/5
C.2/7
D.3/7
Answer: A.2/3
Explanation: P(B|A) = P(A ∪ B)/P(A)
P(B|A) = (4/17)/(6/17) = 4/6 = 2/3.
A
Question: A bag contains 2 red, 2 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
A.5/7
B.11/14
C.17/21
D.19/28
Answer: A.5/7
Explanation: P(no red balls) = 5/7*4/6*3/5 = 2/7
P(at least one red ball) = 1 - 2/7 = 5/7
The answer is A.
Question: If A is to be chosen at random from the set {8,1} and B is to be chosen at random from the set {2,7,9,6}, what is the probability that AB will be even?
A.5/9
B.5/4
C.3/8
D.9/7
Answer: B.5/4
Explanation: Method-1
AB will be even when
1) A is even and B is odd, Probability of A even is (1/2) and Probability of B odd is (2/4), so Probability of Case(1) = (1/2)*(2/4) = (2/8)
2) A is Odd and B is Even, Probability of A Odd is (1/2) and Probability of B Even is (2/4), so Probability of Case(2) = (1/2)*(2/4) = (2/8)
3) A is even and B is Even, Probability of A even is (1/2) and Probability of B Even is (2/4), so Probability of Case(1) = (1/2)*(2/4) = (2/8)
Total Favorable Probability = (2/8)+(4/8)+(4/8) = (10/8) = 5/4
Answer: option B
Question: If a^3 is divisible by 240 what is the least possible value of integer a?
A.12
B.30
C.60
D.90
Answer: C.60
Explanation: 240 can be written as (2^4)*3*5.
For a^3 to be divisible by 240 it should contain atleast 2^4 and 3 and 5 in its factors. We can leave out option A because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^3 will have 3 as the maximum power of 2, so we can leave out this option too.
Option C is the right answer if we follow the same method as we followed for other two previous options.
60 = (2^2)*3*5; 60^3 = (2^6)*(3^3)*(5^3). So it shows that 60^3 is divisible by 240 and hence the answer.
Answer : C
Question: If the price of bananas goes down by 10%, find the percentage of increase that a family should effect in its consumption so as not to increase expenditure on this account?
A.13(1/9)%
B.15(1/9)%
C.11(1/9)%
D.12(1/9)%
Answer: C.11(1/9)%
Explanation: Increase in consumption
= [(P/(100 - P)] X 100)%
= [(10/(100 - 10)] X 100)%
= 11(1/9)%
ANSWER:C
Question: A man distributed Rs. 100 equally among his friends. If there had been 5 more friends, each would have received one rupee less. How many friends had he ?
A.20
B.25
C.30
D.35
Answer: B.25
Explanation: firstly we have 20 friends and money wiill be distribute each of them 5 rupee
then 5 more friends
it means total no frnd=25 each recv 4 rupee
which means all recv 1 less rupee
ANSWER:B
Question: If (x - 1)^2 = 361, which of the following could be the value of x - 4?
A.17
B.15
C.-22
D.-24
Answer: C.-22
Explanation: (x - 1)^2 = 361
(x - 1) = 19 or -19
x = 20 or -18
x - 4 = 16 or -22
The answer is C.
Question: A car traveled 35% of the way from Town X to Town Y at an average speed of 35 mph. The car traveled at an average speed of v mph for the remaining part of the trip. The average speed for the entire trip was 50 mph. What is v in mph?
A.45
B.65
C.55
D.75
Answer: B.65
Explanation: Assume total distance = 100miles
Time taken for 35 miles = 35/35 = 1 hour
Time taken for the rest of the 65 miles = 65/v hours.
Average speed = 50
Therefore the total time needed = 2 hours.
2 = 1 + 65/v
Hence v = 65 mph
Answer : B
Question: A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $42,000 commission, how many machines did she sell?
A. 90
B. 103
C. 130
D. 115
Answer: C. 130
Explanation: First 100 machines = 3% commission = 0.03*100*10000 = 30000
Commission from sale of next machines = 42000 - 30000 = 12000
So 30 more machines..
Total = 130 machines
IMO C...
Question: In a class of 50 students, 20 play Basketball, 15 play Cricket and 11 play Football. 7 play both Basketball and Cricket, 4 play Cricket and Football and 5 play Basketball and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
A.67
B.45
C.10
D.675
Answer: C.10
Explanation: Notice that7 play both Basketball and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Basketball/Football.
[color=#ffff00]{Total}={Basketball}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Basketball and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Basketball and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer: C.
Question: Three pieces of timber 30 m, 35 m and 45 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
A.7 m
B.4 m
C.5 m
D.6 m
Answer: C.5 m
Explanation: Answer
Greatest possible length of each plank = H.C.F of 30, 35, 45 = 5 m
Correct Option: C
Question: A software programmer does 30% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?
A.13x /15
B.15x/15
C.7x/15
D.2x/30
Answer: C.7x/15
Explanation: Take X=30 lines
80% of 30 = 24 lines
20% of 30 = 6 lines
W - R - T
6 lines - r1 - 24 (first 80% of the 30 days)
24 lines - r2 - 6 ( last 20% of the 20 days)
r1 = 1/4r2 = 4
Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1
=> 6 * 4 + 8 * 1/4 = 24 + 2 = 26
Insert, X=30 in all options => C is the answer.