RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Let Y be the smallest positive integer such that 12 and 8 are factors of 20*Y, So the value of Y is:
A.7
B.9
C.11
D.13
Answer: B.9
Explanation: You can calculate the LCM(12,8) (Least commom multiple of 12 and 8) = 36
and calculate the LCM(36,20) = 180
And making 180/20 we obtain 9.
So, the Answer is B.
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of $ 8400 ?
A.14
B.24
C.34
D.12
Answer: A.14
Explanation: Required difference = [3 1/2 % of $8400] – [3 1/3 % of $8400]
= [(7/20)-(10/3)]% of $8400 =1/6 % of $8400
= $ [(1/6)*(1/100)*8400] = $ 14.
Answer A.
Question: A number, x is chosen at random from the set of positive integers less than 20. What is the probability that (18/x) > x?
A. 1/5
B. 2/9
C. 3/19
D. 4/19
Answer: D. 4/19
Explanation: Number x has to be chosen from numbers 1-19
(18/x) > x
=> 18 > x^2
=>x^2 - 18 < 0
x can have 2 values only 1 , 2 , 3 , 4
Therefore , probability = 4 / 19
Answer D
Question: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 4 times his original investment. What is the value of n?
A.50 years
B.25 years
C.12 years 6 months
D.37 years 6 months
Answer: D.37 years 6 months
Explanation: Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $400.
Therefore, the Simple Interest earned = 400 - 100 = $300.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 300 = (100 * n * 8) / 100
Or 8n = 300
Or n = 37.5 years.
choice is (D)
Question: A train covers a distance of 12 km in 10 min. If it takes 3 sec to pass a telegraph post, then the length of the train is?
A.60 m
B.188 m
C.120 m
D.80 m
Answer: A.60 m
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 3
= 60 m.
Answer:A
Question: A lady bought five books namely A,B,C,D,E to distribute her 3 child. How many ways she can distribute books?
A.3^3
B.3^4
C.3^5
D.3^6
Answer: C.3^5
Explanation: 3*3*3*3*3
3^5
ANSWER:C
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
A.8%
B.6%
C.7%
D.9%
Answer: A.8%
Explanation: By investing 1552 income = 128
by investing rs 97 income = (128/1552 * 97) = rs 8
=>8%
ANSWER A
Question: 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
A.55 days
B.77 days
C.20 days
D.88 days
Answer: C.20 days
Explanation: 16 * 25 = 20 * x => x
= 20 days
Answer: C
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 22 in two years, at the same percent rate per annum?
A.s. 520
B.s. 480
C.s. 420
D.s. 100
Answer: D.s. 100
Explanation: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 22
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(22 – 20) / 20] * 100
= 10 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 10% p.a.
SI = (PRT/100)
20 = (X*10*2) / 100
X = Rs. 100
ANSWER: D
Question: When positive integer N is divided by positive integer J, the remainder is 25. If N/J = 204.05, what is value of J?
A.600
B.500
C.800
D.200
Answer: B.500
Explanation: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 204.05
Here 204 is the quotient.
Given that Remainder = 25
So, 204.05= 204 + 25/J
So, J = 500
Answer: B
Question: If log72 = m, then log4928 is equal to
A.2(1 + 2m)
B.(1 + 2m)/2
C.2/(1 + 2m)
D.1 + m
Answer: B.(1 + 2m)/2
Explanation: log4928 = 1/2log7(7x4) = 1/2(1 + log74)
= 1/2 + (1/2). 2log72
= 1/2 + log72
= 1/2 + m = (1 + 2m)/2.
ANSWER:B
Question: The simple interest accrued on an amount of ₹ 84000 at the end of 3 yr is ₹ 30240. What would be the compound interest accrued on the same amount at the same rate in the same period?
A.22
B.77
C.66
D.88
Answer: D.88
Explanation: Answer:D
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
A.2333
B.2777
C.2688
D.1000
Answer: D.1000
Explanation: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
Answer: D
Question: ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets for $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces and sells 987 sets of horseshoes, what was their profit?
A.$20,874.25
B.$30,943.25
C.$41,308.50
D.$51,817.50
Answer: A.$20,874.25
Explanation: The numbers are ugly, and the answer choices are widely spread out. This problem is absolutely screaming for estimation!
So here’s some more fast and furious estimation. Initial manufacturing outlay: round that from $11450 to $10000. Cost per set: round to $20. Sales revenue per set: $50. Number produced & sold: 1000. OK, now we’re in business.
Cost equals 10000 + 20*1000 = 10000 + 20000 = $30000. Sales revenue = 50*1000 = $50000. Profit = (Sales Revenue) – (Cost) =$50000 – $30000 = $20000. Answer choice (A) is the only answer even close to that. Single digit calculations all the way, and it was enough to get the answer!
Answer A
Question: a man owns 2/3 of market reserch beauro buzness,and sells 3/4 of his shares for 45000rs,what is the value of buzness?
A.150000
B.90000
C.85000
D.190000
Answer: B.90000
Explanation: If value of business=x
Total sell (2x/3)(3/4)=45000
->x=150000
ANSWER:B
Question: here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 84 and 92 respectively. the average of the whole class is 86, what is the value of x?
A.a) 6
B.b) 4
C.c) 8
D.d) 10
Answer: B.b) 4
Explanation: 12(84)+92x/12+x=86
1008+92x/12+x=86
1008+92x=86(12+x)
1008+92x=1032+86x
X's one side, numbers one side we get,
92x - 86x=1032-1008
6x=24
hence, x=4
Answer B
Question: In the quadratic equation ax2 - 11x + 40 = 0, if the sum of two roots is 1.1, what is the product of the two roots?
A.7
B.6
C.5
D.4
Answer: D.4
Explanation: Explanation:
The sum of the roots of the quadratic equation ax2 - bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 11 and c = 40.
we get, sum of the roots = - (- 11) / a = 1.1
a = 11 / 1.1 = 10
Product of the roots = 40 / 10 = 4
ANSWER: D
Question: How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?
A.6
B.7
C.5
D.8
Answer: B.7
Explanation: Explanatory Answer
Find the number of such integers existing for a lower power of 10 and extrapolate the results.
Between 10 and 100, that is 101 and 102, we have 2 numbers, 11 and 20.
Similarly, between 100 and 1000, that is 102 and 103, we have 3 numbers, 101, 110 and 200.
Therefore, between 106 and 107, one will have 7 integers whose sum will be equal to 2.
Alternative approach
All numbers between 106 and 107 will be 7 digit numbers.
There are two possibilities if the sum of the digits has to be '2'.
Possibility 1: Two of the 7 digits are 1s and the remaining 5 are 0s.
The left most digit has to be one of the 1s. That leaves us with 6 places where the second 1 can appear.
So, a total of six 7-digit numbers comprising two 1s exist, sum of whose digits is '2'.
Possibility 2: One digit is 2 and the remaining are 0s.
The only possibility is 2000000.
Total count is the sum of the counts from these two possibilities = 6 + 1 = 7
Choice B is the correct answer.
Question: Rashmi walks to her bus stop at 5 kmph and reaches there late by 10 minutes. On the next day,she increases her speed to 6 kmph and reaches the bus stop 10 minutes early.How far is the bus stop ?
A.13
B.12
C.11
D.10
Answer: D.10
Explanation: Let the distance to the bus stop is "d"km
Time taken by her(at 5kmph)=d/5hour, and
Time taken by her(at 6kmph)=d/6 hour
As per given condition,
d/5 - d/6 = 20/60
d= 10 kms
ANSWER:D
Question: There are two sticks of which the longer one is 10 cm longer than the short stick. Find the length of the shorter stick if the total length of both the sticks is 24 cm?
A.6
B.7
C.8
D.12
Answer: B.7
Explanation: Since, 24 is the total length. Shorter is any one from answers.
Try Back solving from first answer, i.e. 6. 6+(6+10) = 22<24
Hence, Select next greater no. : 7 +(7+10) =24. So, 7 is the answer
Question: At a florist shop on a certain day, all corsages sold for either $20 or $30. If 10 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 20 percent. What was the store's actual revenue from corsages that day?
A.$200
B.$400
C.$500
D.$800
Answer: C.$500
Explanation: Let, No. of corsages @ $20 = x, no. of corsages @ $30 = y and revenue= r
so, 20x+30y=r.........(1)
Now,
Given the situation, 20(x+10) + 30(y-10)= r-.2r
=> 20x+200+30y-300 = .8r
=> 20x+30y = .8r+100............(2)
so, r = .8r+100
=> r = 500
The answer is C.
Question: If a rod is sold for Rs.34.80, there is a loss of 25%. Find out the CP of the rod?
A.45
B.46
C.46.4
D.47.23
Answer: C.46.4
Explanation: SP=34.80Loss=25%CP=100(100−Loss%)×SP=100(100−25)×34.80=10075×34.80=4×34.803=4×11.60=46.40
C
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 18 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
A.2
B.4
C.8
D.12
Answer: C.8
Explanation: You are considering a case when cat dogs and rabbit are not exactly equal to 12 .
The solution shall be 60=30+40+18-12-2x
and hence x shall be 8.
Answer C
Question: Which is greater than 4?
A.5
B.-5
C.-1/2
D.-25
Answer: A.5
Explanation: 5 greater than 4.
Answer: A
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
A.24
B.28
C.30
D.32
Answer: C.30
Explanation: Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
ANSWER:C
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km
A.200 Km
B.222 Km
C.224 Km
D.248 Km
Answer: C.224 Km
Explanation: Explanation:
Let time taken to travel the first half = x hr
Then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x [because, distance = time*speed]
Distance covered in the the second half = 24(10 - x)
Distance covered in the the first half = Distance covered in the the second half
So,
21x = 24(10 - x)
=> 45x = 240
=> x = 16/3
Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]
Option C
Question: Ravi bought 5 pencil and 10 eraser for Rs 4 . Sheetal bought 3 pencil and 9 eraser for Rs 3 then what would be the cost of pencil and eraser.
A..15p, .30p
B..50p,.27p
C..40p,.20p
D..20p,.40p
Answer: C..40p,.20p
Explanation: Let pencil be x and eraser be y so
5x+10y=4
3x+9y=3
By solving the above two equations we get x=.40p and y=.20p correct ans is C
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.31/32
B.31/17
C.31/19
D.31/12
Answer: A.31/32
Explanation: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32
=31/32
Answer:A
Question: The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score.
A.172
B.173
C.174
D.175
Answer: C.174
Explanation: Total runs = 40 × 50 = 2000
Let his highest score be = x
Then his lowest score = x – 172
Now 200−x−(x−172) /38=48
⇒ 2x = 2172 – 1824
⇒ x = 174
Answer C
Question: The product of the digits of the four-digit number T is 36. No two digits of are identical. How many different numbers are possible values of T ?
A.6
B.12
C.24
D.36
Answer: C.24
Explanation: The main question here is how can you arrange 4 different digits T. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.
Therefore no of ways to arrange 4 diff. digits is 4! which is 24
hence C
Question: Set A of 8 positive integers may have the same element and have 37. And set B of 8 positive integers must have different elements and have 37. When m and n are the greatest possible differences between 37 and other elements’ sums in set A and set B, respectively, m-n=?
A.21
B.22
C.23
D.25
Answer: B.22
Explanation: This is maximum-minimum. Hence, 37-(1+1+1+1+1+1+1)=30 and 37-(1+2+3+4+5+6+7)=9. So, 30-9=21. The correct answer is B.
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
A.1.6
B.1.5
C.1.9
D.1.2
Answer: B.1.5
Explanation: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Question: A boats man can row in still water at speed of 7 km/hr. It takes 6 hours more to travel the same distance in upstream than in downstream if the speed of the river is 3 km/hr. what is the distance between the two destinations?
A.40
B.87
C.126
D.18
Answer: A.40
Explanation: Explanation:
x = 7 km/hr ; y = 3 km/hr
Ds = 10 km/hr ; Us = 4 km/hr
Distance (d) is same. Therefore, if time taken for downstream is t hours, the time for upstream is (t + 6) hours.
10*t = 4*(t + 6)
6t = 24 ; t = 4 hours
d = 10*4 = 40 km
ANSWER: A
Question: How many integers between 100 and 190, inclusive, cannot be evenly divided by 3 nor 5?
A.42
B.44
C.46
D.48
Answer: D.48
Explanation: The total numbers between 100 and 190, inclusive, is 91.
3*34=102 and 3*63=189 so the number of multiples of 3 is 30.
5*20=100 and 5*38=190 so the number of multiples of 5 is 19.
However, the multiples of 15 have been counted twice.
15*7=105 and 15*12=180 so the number of multiples of 15 is 6.
Thus the total number is 91-30-19+6=48.
The answer is D.
Question: If selling price is doubled, the profit triples. Find the profit percent:
A.227
B.100
C.278
D.266
Answer: B.100
Explanation: Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
Answer: B
Question: Each of 435 bags contains at least one of the following three items: raisins, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?
A.256
B.260
C.316
D.320
Answer: D.320
Explanation: there are total of 435 bags and 210 bags contain almonds.
From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320.
Answer: D.
Question: If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 25% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st?
A.50%
B.75%
C.120%
D.133 1/3%
Answer: D.133 1/3%
Explanation: The price on June 1st = 12 (assume);
The price on May 1st = 2/3*12 = 8;
The price on July 1st = 8*1.25 = 10.
The average price of the bond on May 1st and July 1st = (8+10)/2 = 9.
The price of the bond on June 1st (12) is 4/3 times (134%) the average price of the bond on May 1st and July 1st.
Answer: D.
Question: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?
A.a)	8
B.b)	23
C.c)	29
D.d)	32
Answer: C.c)	29
Explanation: Thats 29 in C.
Question: Alice and Heather are 20 miles apart and walk towards each other along the same route. Alice walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Alice, how far from the original destination has Heather walked when the two meet?
A.4 miles
B.8 miles
C.10 miles
D.6 miles
Answer: B.8 miles
Explanation: Original distance between S and H = 20 miles.
Speed of A = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by A = t+24/60 = t+2/5 hours.
Now, the total distances traveled by A and H = 20 miles ---> 6*(t+2/5)+5*t=20 ---> t= 8/5 hours. Thus H has traveled for 8/5 hours giving you a total distance for H = 5*8/5 = 8 miles.
B is thus the correct answer.
P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Question: Let p be a prime number greater than 2, and let N = 32p. How many odd divisors does N have?
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: The answer is A, there is exactly one. Since is the largest (and only) even prime number, any p larger than 2 is odd. Then since 32 = 2*2*2*2, all of which are even, this means that p must be the only odd prime factor.
Question: Given two fair dice, what is the probability Z that the sum of their numbers is 4 if exactly one die shows a 3?
A.a) 2/11
B.b) 1/18
C.c) 3/11
D.d) 2/39
Answer: A.a) 2/11
Explanation: If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.
Z=2/11 would be the answer if 'at least one of the die shows a 3'.A
Question: If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value W of the product xy?
A.	-12
B.	-3
C.	0
D.	2
Answer: C.	0
Explanation: How to deal with inequalities involving absolute values? First example shows us the so callednumber case
In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:
y + 3 ≤ 3
y ≤ 0
So y is 0 or negative
Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:
y + 3 >= -3
y >= -6
Therefore we have a possible range for y: -6=<y<=0
Ok, so far so good, we're half way through. What about x?
Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.
You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers W(-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value.
Hence, Answer Choice C is the one to go.
Question: One-third of 1206 is what percent of 200?
A.3
B.201
C.300
D.None of these
Answer: B.201
Explanation: Answer
Let one-third of 1206 is N% of 200.
∵ 1206/3 = (N x 200)/100
∴ N = (402 x 100) / 200 = 201
Correct Option: B
Question: In a clock (Conventional clock with numbers 1 to 12 in order)is cut into 3 pieces such that the sum of each piece in AP with a common difference of 1. What is the count of numbers in each piece? and what are the numbers?
A.25
B.26
C.27
D.28
Answer: B.26
Explanation: Sum of the 12 numbers=1+2+3+......+12=12*13/2=78
So we have to divide it into 3 slots such that the sum is 78 and sum of each slot is in AP, thus the 3 slots are 25,26,27. So the numbers can be:
3+4+5+6+7=25
8+9+10=27
11+12+1+2=26
ANSWER:B
Question: Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 30ft how many poles do he need?
A.20
B.30
C.40
D.50
Answer: B.30
Explanation: If each side is 120 feet..then total perimeter is 150*4=600
poles every 20 feet hence no of poles= 600/20=30
ANSWER:B
Question: Find the number of ways in which 8 different beads can be arranged to form a necklace.
A.30
B.20
C.2520
D.60
Answer: C.2520
Explanation: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,8 beads can be arranged to form a necklace in(8-1)! /2ways
= 7*6*5*4*3*2/2 = 2520 ways
Answer is C
Question: Double of Quarter of 1 percent written as a decimal is :
A.0.003
B.0.0005
C.0.25
D.0.005
Answer: D.0.005
Explanation: Explanation :
Solution: (2)*(1/4)*1% = 2*(1/4 * 1/100) = 1/400 = 2*0.0025 = 0.005.
Answer : D
Question: A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
A.48
B.12
C.36
D.60
Answer: A.48
Explanation: Explanation:
If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.
Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.
Answer: A
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43 , 46,51 ,x
A.23
B.26
C.54
D.35
Answer: C.54
Explanation: (C)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 51 + 3 = 54.
Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
A.0
B.1
C.4
D.5
Answer: B.1
Explanation: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
B)
Question: A box contains 5 green, 4 yellow and 3 white marbles, 3 marbles are drawn at random. What is the probability that they are not of the same colour?
A.13⁄44
B.41⁄44
C.13⁄55
D.52⁄55
Answer: B.41⁄44
Explanation: Total no. of ways of drawing 3 marbles
= 12C3 = 12×11×10/1×2×3=220
Total no. of ways of drawing marbles, which are of same colour = 5C3 + 4C3 + 3C3 = 10 + 4 + 1 = 15
\Probability of same colour = 15⁄220 = 3⁄44
\ Probability of not same colour = 1 - 3⁄44 =
Answer B
Question: The product of all the prime numbers less than 12 is closest to which of the following powers of 10 ?
A. 10^9
B. 10^3
C. 10^7
D. 10^6
Answer: B. 10^3
Explanation: P = 2*3*5*7*11
~ 10^ 3
Answer : B
Question: In a class of 20 students, 3 students did not borrow any books from the library, 9 students each borrowed 1 book, 4 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
A.13
B.14
C.15
D.16
Answer: B.14
Explanation: The total number of books the students borrowed is 20*2=40.
The students who borrowed zero, one, or two books borrowed 9*1+4*2=17 books.
The 4 students who borrowed at least three books borrowed 40-17=23 books.
If 3 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 23-9= 14 books.
The answer is B.
Question: 9773 + x = 13200, then x is ?
A.3427
B.3237
C.3337
D.2337
Answer: A.3427
Explanation: Answer
x = 13200 - 9773 = 3427
Option: A
Question: 8 coins are tossed. Whats is the probability that one and only one turns up head ?
A.1/256
B.1/32
C.1/64
D.1/128
Answer: B.1/32
Explanation: Explanation :
Possible outcomes(Sample space) when 8 coins are tossed are: (H, H, H, H, H, H, H, H), (H, H, H, H, H, H, H, T), (H, H, H, H, H, H, T, H), (H, H, H, H, H, H, T, T), ....... (T, T, T, T, T, T, T, T) = 28
Required outcomes: (H, T, T, T, T, T, T, T), (T, H, T, T, T, T, T, T), (T, T, H, T, T, T, T, T), (T, T, T, H, T, T, T, T), (T, T, T, T, H, T, T, T), (T, T, T, T, T, H, T, T), (T, T, T, T, T, T, H, T), (T, T, T, T, T, T, T, H) = 8
So the required probability = 8/28 = 1/32
Answer : B