RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: It takes Jake 15 minutes to do one oil change, and it takes Bob 10 minutes. If Jake and Bob both begin doing oil changes at exactly 10:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?
A.10:00 a.m.
B.10:15 a.m.
C.10:30 a.m.
D.10:45 a.m.
Answer: C.10:30 a.m.
Explanation: Since Jake will finish s oil changes after s × 15 minutes and Bob will finish c oil changes after c × 10 minutes, they both will finish doing an oil change at the same time when s × 15 = c × 10. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 15 and 10. The question asks for the first time they will finish a car simultaneously, so you must find the least common multiple. The least common multiple of 15 and 10 is 30, so in the context of the question, this would be 30 minutes. Therefore, the first time they will finish changing the oil of a car at the same time is 10:00 + 30 minutes, or 10:30 a.m. The answer is (C).
Question: The average weight of 8 person's increases by 2.5 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.80 kg
B.85 kg
C.95 kg
D.100 kg
Answer: B.85 kg
Explanation: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
B)
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?
A.11 years
B.31 years
C.81 years
D.61 years
Answer: B.31 years
Explanation: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102 = 31 years.
Answer:B
Question: With 630 ml mixture of milk & water in the ratio 7:2. How much water mustbe added to make the ratio 7:3?
A.60 ml
B.80 ml
C.70 ml
D.90 ml
Answer: C.70 ml
Explanation: concentration of water in mixture1
=2/9 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2
=3/10
By rule of alligation,
concentration of water in mixture1
(2/9) concentration of water in pure water (1)
Mean concentration
(3/10)
1−3/10=7/10
=1:19
=> Quantity of water
=630×1/9=70 ml
C
Question: Molly's age in 18 years will be seven times her age six years ago. What is Molly's present age?
A.6
B.8
C.10
D.12
Answer: C.10
Explanation: Let x be Molly's present age.
x + 18 = 7(x-6)
x = 10
The answer is C.
Question: How many words can be formed by using all letters of the word “BIHAR”
A.14
B.20
C.420
D.120
Answer: D.120
Explanation: The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
Option D
Question: 10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many days will a woman finish the work?
A.125 days
B.150 days
C.90 days
D.225 days
Answer: D.225 days
Explanation: 15 women's work of a day = 1⁄6 - 1⁄10 ⇒ 1⁄15 part
∴ for 1 whole part a woman will take
= 15 × 15 = 225 days.
Answer D
Question: In a sample of associates at a law firm, 30 percent are second-year associates, and 60 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?
A.10
B.20
C.C
D.40
Answer: C.C
Explanation: Let the sample be 100.
Given 60% are not first year i.e. there could be second year (x) and more than 2 years(y) possibility.
60% = (x) + y
Given 30% = second year (x)
club both , we get y = 30%.
Answer: option C is correct answer.
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 7.5 m x 6 m x 22.5 cm?
A.6000
B.6410
C.6440
D.6500
Answer: A.6000
Explanation: Number of bricks = Volume of Wall/Volume of Bricks
=750x600x22.5/25x11.25x6= = 6000
answer :A
Question: what is next no. 11 23 47 83 131 191 ???
A.263
B.181
C.191
D.201
Answer: A.263
Explanation: 11+12*1=23
23+12*2=47
47+12*3=83
83+12*4=131
131+12*5=191
191+ 12*6=263
A
Question: Real-estate salesman Z is selling a house at a 30 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 30 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 30 percent discount. Salesman Y's final price is what fraction of salesman X's final price?
A.12/13
B.11/15
C.11/17
D.11/14
Answer: D.11/14
Explanation: Let the retail price be = x
Selling price of Z = 0.70x
Selling price of X = 0.70*0.80x = 0.56x
Selling price of Y = ((0.70x + 0.56x)/2)*0.70 = 0.63x * 0.70 = 0.44x
0.44x = k * 0.56x
k = 0.44/0.56 = 44/56=11/14
Answer: D
Question: It takes John 25 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
A.5:40 a.m
B.7:50 a.m
C.6:55 a.m
D.8:00 a.m
Answer: B.7:50 a.m
Explanation: The time it takes John to get to work: time to walk to car park + time to drive
25 + 45 = 70 minutes = 1 hour and 10 minutes
John needs to get out of the house 1 hour and 10 minutes before 9:00 am at
9:00 - 1:10 = 7:50 a.m
correct answer B
Question: A rectangular rug with side lengths of 3 feet and 6 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
A.A.3/16
B.1/4
C.C.1/2
D.23/32
Answer: D.23/32
Explanation: Area of the rectangular rug = 3*6 = 18
Fraction not covered by the rug = (Total Area - Rug area) / Total Area
= (64 - 18)/64
= 23/32=D
Question: What is the unit digit in {(6374)^1793 x (625)317 x (341^491)}?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: Unit digit in (6374)^1793 = Unit digit in (4)^1793
= Unit digit in [(4^2)^896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)^317 = Unit digit in (5)^317 = 5
Unit digit in (341)^491 = Unit digit in (1)^491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
A)
Question: Solution Y is 30 percent liquid W and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid W?
A.30%
B.33 1/3%
C.37 1/2%
D.40%
Answer: C.37 1/2%
Explanation: Answer:C
Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid W and 70% water, and then I was able to get the answer. That was a bit tricky and nice question=C
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 150 cookies, what percent of the cookies did Nell bake?
A.0.125%
B.1.25%
C.12.6%
D.125%
Answer: C.12.6%
Explanation: 9.18x+5.17x+2.05x = 16.4x = 150 cookies
x= 150/16.4 = 9.1 (approx)
So, Nell baked 9.1*2.05 cookies or 19 cookies (approx)
% share = 19/150 = 12.6 approx
Hence, answer is C.
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.10-
B.99
C.88
D.62
Answer: A.10-
Explanation: Speed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream = (80-60)/2 = 10 kmph.Answer: A
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
B
Question: A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube?
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: Given: positive integer n is a perfect square and a perfect cube --> n is of a form of n=x6 for some positive integer x --> 0<x^6<10^3 --> 0<x^2<10 --> x can be 1, 2 or 3 hence nn can be 1^6, 2^6 or 3^6.
Answer: B.
Question: The ratio of three numbers is 2:3:4 and their sum is 180. The second number of the three numbers is?
A.24
B.60
C.27
D.29
Answer: B.60
Explanation: 2:3:4
Total parts = 9
9 parts --> 180
1 part ---->20
The second number of the three numbers is = 3 * 20 = 60
Answer : B
Question: P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?
A.3
B.5
C.6
D.7
Answer: C.6
Explanation: Let P takes x days to complete the work
Then Q takes x/2 days and R takes x/3 days to finish the work
Amount of work P does in 1 day = 1/x
Amount of work Q does in 1 day = 2/x
Amount of work R does in 1 day = 3/x
Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x
6/x = 2
=> x = 12
=> Q takes 12/2 days = 6 days to complete the work
Answer is C.
Question: A metallic sheet is of rectangular shape with dimensions 100 m x 50 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 10 m, the volume of the box (in m cube) is:
A.42500m cube
B.20000 m cube
C.44140 m cube
D.24000m cube
Answer: D.24000m cube
Explanation: Explanation:
l = (100-20)m = 80 m, [because 10+10=20]
b = (50-20)m = 30 m,
h = 10 m.
Volume of the box = (80X30X8) m cube
= 24000 m cube.
Option D
Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 7 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
A.30
B.20
C.18
D.12
Answer: D.12
Explanation: 21-12 < no of hrs < 21-6
9< no of hrs < 14.
D
Question: If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
A.90
B.100
C.110
D.120
Answer: D.120
Explanation: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)
Therefore, the product should have factors with a difference of 2.
120 = 10*12, so this is a possible value for the original expression.
The answer is D.
Question: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 37 grams of protein daily, how many grams of food X are in the mixture.
A.100
B.140
C.150
D.160
Answer: D.160
Explanation: Let x be the amount of food X.
0.1x + 0.15(300-x) = 37
0.05x = 8
x = 160
The answer is D.
Question: In the Hillside summer camp there are 100 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
A.150.
B.145.
C.100.
D.30.
Answer: C.100.
Explanation: Given there are 100 students , 90% of 50 = 90 boys and remaining 10 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 1000 to existing 90 then the count will be 190 and the girls number will be 10 as it.
Now boys are 95% and girls are 5%. ( out of 200 students = 190 boys + 10 girls ).
IMO option C is correct.
Question: A,B and C enter into partnership. A advances Rs.1200 for 4 months, B Rs. 1400 for 8 Months and C Rs.1000 for 10 months. They gain Rs.585 altogether. Find the share of B.
A.Rs.252
B.Rs.258
C.Rs.296
D.Rs.256
Answer: A.Rs.252
Explanation: ANSWER:A
Question: If 2/a + 3/a + 4/a is an integer, which of the following must also be an integer?
A.12/a
B.3/a
C.6/a
D.9/a
Answer: D.9/a
Explanation: If 2/a + 3/a + 4/a; then (2+3+4)/a is also integer.
i.e. 9/a is an integer..Answer D.
Question: How much is 60% of 40 is greater than 4/5 of 30?
A.8
B.3
C.7
D.0
Answer: D.0
Explanation: (60/100) * 40 â€“ (4/5) * 30
24 - 24 = 0
Answer: D
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $55, how much more remains to be paid?
A.$455
B.$495
C.$525
D.$550
Answer: B.$495
Explanation: 90% remains to be paid so the remaining amount is 9*55=$495.
The answer is B.
Question: Find a sum for 1st 8 prime number's?
A.25
B.28
C.30
D.77
Answer: D.77
Explanation: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19) = 77
Note: 1 is not a prime number
Option D
Question: By selling 50 meters of cloth. I gain the selling price of 18 meters. Find the gain percent?
A.42 7/7%
B.42 5/8%
C.56 1/4%
D.42 6/8%
Answer: C.56 1/4%
Explanation: SP = CP + g
50 SP = 50 CP + 18 SP
32 SP = 50 CP
32 --- 18 CP gain
100 --- ? => 56 1/4%
Answer: C
Question: Indu gave Bindu Rs.3750 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A.5
B.6
C.9
D.3
Answer: B.6
Explanation: 3750
= D(100/4)2
D = 6
Answer: B
Question: If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 432, what is the greatest possible profit that might be made in selling eight books ?
A.23267
B.2677
C.1856
D.2778
Answer: C.1856
Explanation: Explanation:
Least Cost Price = Rs. (200 * 8) = Rs. 1600.
Greatest Selling Price = Rs. (432 * 8) = Rs. 3456.
Required profit = Rs. (3456 - 1600) = Rs. 1856.
Answer: C) 1856
Question: What is the smallest positive perfect square that is divisible by 4, 10, and 18?
A.900
B.1,600
C.2,500
D.3,600
Answer: A.900
Explanation: The number needs to be divisible by 2^2, 2*5, and 2*3^2.
The smallest such perfect square is 2^2*3^2*5^2 = 900
The answer is A.
Question: Claire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?
A.39
B.50
C.66
D.57
Answer: C.66
Explanation: G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300
G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66
C
Question: John's favorite number is odd and has prime factors that do not repeat. Which of the following numbers is his favorite?
A.27
B.75
C.121
D.105
Answer: D.105
Explanation: Factor each option.
A 27 = 3*3*3
B 75 = 3*5*5
C 121 = 11*11
D 105 = 3*5*7
E 147 = 3*7*7
D is the only choice with no repeating prime factors
Question: Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?
A.30%
B.33 1/3%
C.37 1/2%
D.40%
Answer: C.37 1/2%
Explanation: At the beginning, you have 8 KG of solution Y, i.e.
70% * 8KG = 5,6 KG of Water
30% * 8 KG = 2,4 KG of X
2 KG of water evaporate:
5,6KG - 2KG = 3,6KG of Water
2,4KG of X
2 KG of liquid are added:
3,6KG + 2*0,70 = 5 KG of Water
2,4KG + 2*0,30 = 3 KG of X
So you have 3KG of X in 8KG (3 + 5) solution.
Therefore X concentration is 3/8 = 37,5%
ANSWER:C
Question: What will come in place of the x in the following Number series? 4, 8 , 16, x , 44
A.33
B.37
C.28
D.41
Answer: C.28
Explanation: (C)
The pattern is + 4, + 8, + 12, +16 â€¦â€¦â€¦..
So the missing term is = 16+ 12= 28
Question: (0.15)(power 3) - (0.06)(power 3)/ (0.15)(power 2) + 0.009 + (0.06)(power 2) is:
A.0.09
B.0.08
C.0.1
D.0.07
Answer: A.0.09
Explanation: Given expression
= (0.15) (power 3) - (0.06)(power 3) / (0.15)(power 2) + (0.15 x 0.06) + (0.06)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.15 - 0.06)
= 0.09
Answer is A.
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
A.29%
B.20%
C.26%
D.20%
Answer: B.20%
Explanation: 900 ---- 180
100 ---- ? => 20%
Answer: B
Question: Find the wrong number in the series.
3, 8, 15, 24, 34, 48, 63
A.37
B.38
C.34
D.888
Answer: C.34
Explanation: Explanation:
The difference between consecutive numbers of the given series are respectively 5, 7, 9, 11, 13, and 15.
Therefore, 24+11=35 But in your problem it is given as 34.so 34 is wrong number
Answer: C) 34
Question: The value of log343 7 is
A.1/3
B.- 3
C.- 1/3
D.3
Answer: A.1/3
Explanation: Solution
Let log3437	= n.
Then, 343n	= 7
= (73)n = 7.
‹=›3 n = 1
‹=›n = 1/3.
log343 7	= 1/3.
Answer A
Question: A person has to cover a distance of 6km in 45 minutes. If he covers one half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed must be?
A.12km/hr
B.10km/hr
C.15km/hr
D.20km/hr
Answer: A.12km/hr
Explanation: Remaining distance = 3km
Remaining time = 1/3 * 45 = 15min = 1/4 hour
Required speed = 3*4 = 12km/hr
Answer is A
Question: In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday?
A.Thursday
B.Friday
C.Saturday
D.Sunday
Answer: B.Friday
Explanation: Day of week after 64 days after Arman's birthday = 7*9 + 1
Saturday as the period will have 9 weeks and 1 days .
The 1 days in the end will be Friday .
Answer B
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
A.7
B.6
C.4
D.9
Answer: B.6
Explanation: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
Question: A number is said to be prime saturated if the product of all the different positive prime factors of t is less than the square root of t. What is the greatest two digit prime saturated integer ?
A.99
B.98
C.97
D.96
Answer: D.96
Explanation: t=96 = 3 * 32 = 3 * 2^5
Answer is D.
Question: A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $34 to ship a certain package, which of the following was the weight of the package, in pounds?
A.12
B.14
C.16
D.18
Answer: B.14
Explanation: Let the weight of the package be X.
2X + 6= 34
X = 14
The answer is B.
Question: A tap can fill a tank in 8 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?
A.1 hr 20 min
B.4 hr
C.3 hr
D.5 hr 20 min
Answer: D.5 hr 20 min
Explanation: Explanation:
1 tap can fill the tank in 8 hours.
Therefore
1 tap can fill half tank in 4 hours.
3 taps can fill the tank in 8/3 hour.
Therefore
3 taps can fill half tank in 8/6 hour =1hour 20 minutes.
Total time taken=5 hour 20 minutes
Answer: Option D
Question: A thief is noticed by a policeman from a distance of 280 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
A.100
B.277
C.180
D.278
Answer: C.180
Explanation: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 280 - 100 = 180 m.
Answer: C
Question: A tradesman by means of his false balance defrauds to the extent of 32%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
A.74%
B.78%
C.94%
D.75%
Answer: A.74%
Explanation: g% = 32 + 32 + (32*32)/100
= 74%
Answer: A
Question: The speed of a boat in still water is 8 kmph. If it can travel 1 km upstream in 1 hr, What time it would take to travel the same distance downstream?
A.14 minutes
B.4 minutes
C.24 minutes
D.28 minutes
Answer: B.4 minutes
Explanation: Speed of the boat in still water = 8 km/hr
Speed upstream = 1⁄1 = 1 km/hr
Speed of the stream = 8-1 = 7 km/hr
Speed downstream = (8+7) = 15 km/hr
Answer is B
Time taken to travel 1 km downstream = 1/15 hr = (1×60)/15= 4 minutes
Question: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 5 seconds. Find the length of the train and its speed.
A.5.6 m/sec
B.15 m/sec
C.18 m/sec
D.9 m/sec
Answer: D.9 m/sec
Explanation: If length of train is l and speed of train is s, then
l/s = 5
(l+180)/s = 20
(l+180)/l = 20/5 =4
l+180 =5*l
4*l=180
l=45 mtrs
s= l/5 = 45/5 = 9 m/sec
ANSWER:D
Question: The ages of three friends are prime numbers. The sum of the ages is less than 51. If the ages are in Arithmetic Progression (AP) and if at least one of the ages is greater than 10, what is the difference between the maximum possible median and minimum possible median of the ages of the three friends?
A.0
B.1
C.13
D.6
Answer: D.6
Explanation: Let the numbers are a-d, a , a+d
sum <51 => a-d+a+a+d < 51 => middle number a <17
prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
a can be 3,5,7,11,13
if a is 3 -> a-d can be 2 only; a+d not possible thus reject this.
if a is 5, a-d can be 2 and 3; only a-d = 3 satisfies
=> three numbers can be 3,5,7 ->reject this , as it is given at least one is >10
if a = 7 ; a-d can be 3 and a+d can be 11
This satisfies all the conditions hence the median is 7=> min median.
if a = 11, the three element pair is 3,11,19 or 5,11,17
median = 11; we are not sure if its the max median possible
if a = 13, 7,13,19 pair is possible
median = 13; reject 11 as the max.
thus difference = 13-7 = 6
ANSWER:D
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.31/32
B.1/16
C.1/2
D.1/32
Answer: A.31/32
Explanation: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
P(T)= There is not even a single tail.
i.e. all the outcomes are heads.
P(T)= 1/32 ; P(T) = 1 - 1/32 = 31/32
ANSWER:A
Question: Out of 9 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
A.A)5/7
B.B)5/21
C.C)16/21
D.D)5/6
Answer: C.C)16/21
Explanation: P(at least one graduate) = 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃
= 1 - (6 * 5 * 4)/(7 * 9 * 8)
= 16/21
Answer:C
Question: Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
A.7 hours 30 minutes
B.8 hours
C.8 hours 15 minutes
D.8 hours 25 minutes
Answer: C.8 hours 15 minutes
Explanation: Number of pages typed by Ravi in 1 hour =	32/6	=	16/3	.
Number of pages typed by Kumar in 1 hour =	40/5	= 8.
Number of pages typed by both in 1 hour =	(16/3+ 8)	=	40/3	.
Therefore Time taken by both to type 110 pages =	(	110 x	3/40	)	hours
= 8	1/4 hours (or) 8 hours 15 minutes.
Option C
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 6 II. 3 III. 7
A.I only
B.III only
C.II,III only
D.II only
Answer: D.II only
Explanation: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....
Let's TEST VALUES....
IF we use the 6 consecutive integers: 6, 7,8,9,10 and 11, then the sum = 51.
51 is divisible by 3
51 is NOT divisible by 6
51 is NOT divisible by 7
There's only one answer that 'fits' with these facts. Answer : D
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
A.10 kmph
B.21 kmph
C.8 kmph
D.12 kmph
Answer: C.8 kmph
Explanation: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
ANSWER:C