RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The letters in the word "PLACES" are permuted in all possible ways and arranged in the alphabetical order.Find the word at 48 position.
A.AESPCL
B.ALCEPS
C.ALSCEP
D.AESPLC
Answer: D.AESPLC
Explanation: for words AC**** possible ways for arranging * will be 4!=24
now next seq in alphabatical order will be AE**** so....
same way for AE**** possible ways for arranging * will be 4!=24
..
..
Thus, 48th element will be last element in AE**** that means AE followd by reverse alphabatical order! which is AESPLC
ANSWER:D
Question: In some quantity of alcohol, 50% of pure alcohol and 30% of is water. If 20liters of pure alcohol is added, then the strength of alcohol solution becomes 20%. The original quantity was?
A.1.42liters
B.2.5liters
C.3liters
D.5.6liters
Answer: A.1.42liters
Explanation: Let the original quantity be x liters
alcohol solution in x liters = 30/100 *x = 3x/10 kg
(3x/10)/(x+20) = 20/100
3x = x/5 + 4
14x = 20
x = 1.42liters
Answer is A
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A.24000
B.25100
C.25150
D.25200
Answer: D.25200
Explanation: Explanation:
Number of ways of selecting 3 consonants from 7
= 7C3
Number of ways of selecting 2 vowels from 4
= 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 × 4C2
=
(
7
×
6
×
5
3
×
2
×
1
)
×
(
4
×
3
2
×
1
)
=
210
=(7×6×53×2×1)×(4×32×1)=210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves
=
5
!
=
5
×
4
×
3
×
2
×
1
=
120
=5!=5×4×3×2×1=120
Hence, required number of ways
=
210
×
120
=
25200
D)
Question: f(x) is defined as the largest integer n such that x is divisible by 2^n. Which of the following numbers is the biggest?
A.f(24)
B.f(42)
C.f(62)
D.f(76)
Answer: A.f(24)
Explanation: So, we have an integer x. It has some power of 2 in its prime factorization (2^n) and f(x) is the value of that n. Basically f(x) is the power of 2 in prime factorization of x.
For example, if x is say 40, then f(x)=3. Why? Because the largest integer n such that 40 is divisible by 2^n is 3: 40/2^3=5, or 40=2^3*5 --> the power of 2 in prime factorization of 40 is 3.
Hence all we need to do to answer the question is to factorize all options and see which one has 2 in highest power.
A. f(24) --> 24 = 2^3*3
B. f(42) --> 42 = 2*21
C. f(62) --> 62 = 2*31
D. f(76) --> 76 = 2^2*19
E. f(84) --> 84 = 2^2*21
Answer: A.
Question: In a certain series, each term is m greater than the previous term. If the 16th term is 660 and the 13th term is 600, what is the first term?
A.120
B.180
C.360
D.300
Answer: C.360
Explanation: a + 15m = 660 (16th term)
a + 12m = 600 (13th term)
You get a = 360 and m = 20
Answer:C
Question: A 10 Liter mixture of milk and water contains 30 percent water. Two liters of this mixture is taken away. How many liters of water should now be added so that the amount of milk in the mixture is double that of water?
A.3.3
B.3.4
C.0.4
D.4.9
Answer: C.0.4
Explanation: Explanation:
Two liters were taken away So we have only 8 liters of mixture.
Amount of milk in 8 liters of mixture = 8 × 70% = 5.6 liters
Amount of water in 8 lit of mix = 8 - 5.6 = 2.4 liters.
Half of milk i.e half of 5.6 = 2.8 liters.
We need (2.8 - 2.4) liters water more = 0.4 lit
Answer: C
Question: 10 friends meet for movie 20 for picnic and 5 for games 4 for movie & picnic 2 for movie & games, 0 for picnic & games, 2 for all, how many are students are there in all?
A.30
B.31
C.32
D.33
Answer: B.31
Explanation: n(A U B U C)=n(A) + n(B) + n(C) - n(A INTERSECTION B) - n(A INTERSECTION C) - n(C INTERSECTION B) + n(A INTERSECTION B - INTERSECTION C)
Hence,
Total no. of Students = 10 + 20 + 5 - 4 - 0 - 2 + 2
= 31.
ANSWER:B
Question: 60 percent of movie theatres in Town X have 2 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?
A.12
B.18
C.32
D.40
Answer: D.40
Explanation: Lets take numbers here.
Assume that the total number of movie theaters in the town = 100
Then number of movie theaters with 3 screens or less = 60
=> Number of movie theaters with 4 screens or more = 40
Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12
Number of movie theaters selling popcorn at $300 or less = 56
=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44
Of these 44 theaters, 12 are those with 3 screens or less
Therefore 40 (44-12) must be those with four screens or more
D is the answer
Question: Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04)
A.0.56
B.0.58
C.0.6
D.0.57
Answer: A.0.56
Explanation: 0.56
Option 'A'
Question: The length of a rectangle is four times its width. If the area is 100 m2 what is the length of the rectangle?
A.20
B.40
C.50
D.80
Answer: A.20
Explanation: Let L be the length and W be the width of the rectangle. Hence
L = 4 W
We now use the area to write
100 = L ? W
Substitute L by 4 W in the equation above
100 = 4 W ? W = 4 W2
Solve for W and find L
4 W2 = 100
W2 = 25 , W = 5 and L = 4 W = 20 m
correct answer A
Question: How many integral divisors does the number 120 have?
A.14
B.16
C.12
D.20
Answer: B.16
Explanation: Explanatory Answer
Express the number in terms of its prime factors
120 = 2(3) * 3 * 5.
The three prime factors are 2, 3 and 5.
The powers of these prime factors are 3, 1 and 1 respectively.
Find the number of factors as follows
To find the number of factors / integral divisors that 120 has, increment the powers of each of the prime factors by 1 and then multiply them.
Number of factors = (3 + 1) * (1 + 1) * (1 + 1) = 4 * 2 * 2 = 16.
Choice B
Question: The value of land increases by x% during June and decreases by y% during July. If the value of the land is the same at the end of July as at the beginning of June, what is y in terms of x?
A.200x/(100+2x)
B.100x/(100+x)
C.x(2+x)/(1+x)2
D.x(200+x)/10000
Answer: B.100x/(100+x)
Explanation: The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...
Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.
Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.
Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.
Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.
Answer E: (50/25) + 50 = 52. ELIMINATE E.
B
Question: power windows: 60%
anti-lock brakes: 25%
CD player: 45%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
A.25
B.8
C.11
D.3
Answer: B.8
Explanation: Answer: B
Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.
If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation:
45=15+22+x
x=8, choice B.
Question: 30 quintals is what percent of 2 metric tonnes ?
A.15%
B.1.5%
C.150%
D.30%
Answer: C.150%
Explanation: Answer
Required percent = {30/(2 x 10)} x 100 % = 150%
Correct Option: C
Question: Q is a set of nine distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: 2 + 3 + 5 + 7 +11 + 13 + 17 + 23 + 29 = 100 ( sum is even)
Least number = 2
A
Question: Three positive integers a, b, and c are such that their average is 12 and a ≤ b ≤ c. If the median is (a + 5), what is the least possible value of c?
A.11
B.13
C.15
D.17
Answer: C.15
Explanation: Solution
Given Data
3 positive integers
Average of a, b, and c = 12.
So, a+b+c3a+b+c3 = 36 or a + b + c = 36
a ≤ b ≤ c
Median = (a + 5)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 5
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 5) + (a + 5) = 36 (b and c are equal and b, the median, is a + 5)
Or 3a = 26 or a = 8.66
So, b = c = 8.66 + 5 = 13.66
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 5) + (a + 6) = 36
Or 3a = 25. The value of the numbers is not an integer in this scenario as well.
Let us increment c again by 1. i.e., c = b + 2
Now, a + (a + 5) + (a + 7) = 36
Or 3a = 24 or a = 8.
If a = 8, b = 13 and c = 15.
The least value for c that satisfies all these conditions is 15.
Correct answer is choice C.
Question: A number, x is chosen at random from the set of positive integers less than 12. What is the probability that (9/x) > x?
A. 1/11
B. 2/9
C. 2/11
D. 2/3
Answer: C. 2/11
Explanation: Number x has to be chosen from numbers 1-11
(9/x) > x
=> 9 > x^2
=>x^2 - 9 < 0
x can have 2 values only 1 , 2
Therefore , probability = 2 / 11
Answer C
Question: The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is
A.40
B.37
C.35
D.45
Answer: B.37
Explanation: LCM of 3,5,7 and 8 = 840
28523/840 = 33 remainder = 803
least no which should be added = 840-803 = 37
ANSWER B
Question: What is the sum of all even numbers from 1 to 601?
A.122821
B.281228
C.90300
D.122850
Answer: C.90300
Explanation: Explanation:
600/2 = 300
300 * 301 = 90300
Answer: C
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
A.333
B.200
C.288
D.276
Answer: B.200
Explanation: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 5300
[4L - 40] = 5300 / 26.50 = 200
4L = 240
L = 240/4= 60 meters.
Answer: B
Question: The ratio of the number of females to males at a party was 1:2 but when 7 females and 7 males left, the ratio became 1:3. How many people were at the party originally?
A.28
B.32
C.36
D.42
Answer: D.42
Explanation: The total number of people are x females + 2x males.
3*(x-7) = 2x - 7
x = 14
There were 3x = 42 people at the party originally.
The answer is D.
Question: The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 5 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?
A.$200
B.$375
C.$400
D.$500
Answer: B.$375
Explanation: C for cost.
P price per person.
C= 3*P
C=5*P-250
Substituting the value of P from the first equation onto the second we get P = 125.
Plugging in the value of P in the first equation, we get C= 375. Which leads us to answer choice B
Question: If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability R that N is divisible by 3?
A.1/3
B.¼
C.9/25
D.5/16
Answer: D.5/16
Explanation: Prime digits are: 2, 3, 5, 7
Total number of 2 digit #s with both digits prime are: 4*4 = 16
out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.
=> prob = 5/16.
Ans D. Took me 3:20 mins.
Question: In a camp, there is a meal for 100 men or 200 children. If 150 children have taken the meal, how many
men will be catered to with the remaining meal ?
A.25 men
B.32 men
C.34 men
D.30 men
Answer: A.25 men
Explanation: Explanation:
There is meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 100 men
So, 50 Children = 100/200 * 50 = 25 men
Answer: A
Question: When you multiply a number by 4 and
then subtract 8, the result is the same as
if you first subtracted 4 from the same
number and then multiplied by 12. What
is the number?
A.A)5
B.B)13
C.C)19
D.D)31
Answer: A.A)5
Explanation: Let x equal the number and then change the words into an equation and solve for x:
4x – 8 = 12(x – 4)
4x – 8 = 12x – 48
40 = 8x
5 = x
correct answer A)5
Question: Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 742.
A.120 ,122 , 124 ,126
B.120 ,122 , 124 ,128
C.120 ,121 , 122 ,123
D.123 ,125 , 127 ,129
Answer: A.120 ,122 , 124 ,126
Explanation: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two
x + (x + 2)
twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 742 is written as
x + (x + 2) + 4 x + 20 = 742
Solve for x and find all four numbers
x = 120 , x + 2 = 122 , x + 4 = 124 , x + 6 = 126
Answer A
Question: If 3/p=8 & 3/q=18 then p-q=?
A.5/24
B.6/24
C.7/24
D.8/24
Answer: A.5/24
Explanation: p=3/8 , q=3/18=>q=1/6
therefore
p-q=(3/8)-(1/6)=5/24
ANSWER:A
Question: A group of three girls and three boys have tickets for six adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 6 theatre-goers?
A.6! – 2!3!2!
B.6! – 6!3!
C.7 × 2!3!2!
D.6! – 4!3!
Answer: D.6! – 4!3!
Explanation: There are 3 boys and 3 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 6 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 6 is 6!.
2. # of arrangements when 3 boys are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 4 units: {MMM}{W}{W}{W} The # of arrangements of these 4 units is 4!.
Hence total # of arrangements when 3 men sit together is: 3!4!.
# of arrangements when 3 boys do not sit together would be: 6!-3!4!.
Answer: D
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
A.16.39
B.16.33
C.16.35
D.16.3
Answer: D.16.3
Explanation: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 130% of Rs. 630 = 130/100 * 630 = Rs. 819.
S.P. per kg = 819/50 = Rs. 16.38 = 16.30.
Answer: D
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 38 years and that of the grandchildren is 6 years. What is the average age of the family?
A.28 4â„7 years
B.31 5â„7 years
C.32 4â„7 years
D.27 1â„2 years
Answer: C.32 4â„7 years
Explanation: Required average = (67Ã—2+38Ã—2+6Ã—3/2+2+3)
=228/7
= 32 4â„7 years
Answer C
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
A.277
B.270
C.288
D.266
Answer: B.270
Explanation: I = (500*9*6)/100 = 270
Answer: B
Question: A is twice as good a work man as B and together they finish a piece of work in 36 days.The number of days taken by B alone to finish the work is :
A.100 days.
B.108 days.
C.98 days.
D.47 days.
Answer: B.108 days.
Explanation: Solution
(A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.
(A + B)'s 1 day’s work = 1/36
Divide 1/36 in the ratio 2 : 1.
∴ B’s 1 day’s work = (1/36 x1/3)= 1/108
Hence,B alone can finish the work in 108 days.
Answer B
Question: When positive integer A is divided by positive integer B, the remainder is 5. If A/B = 58.25, what is the value of B?
A.18
B.19
C.15
D.20
Answer: D.20
Explanation: When positive integer A is divided by positive integer B, the remainder is 5 --> A=qB+5;
A/B=58.25 --> A=58B+0.25B (so q above equals to 58);
0.25B=6 --> B=20.
Answer: D.
Question: How many numbers between 11 and 90 are divisible by 7?
A.11
B.13
C.15
D.12
Answer: A.11
Explanation: The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, Tn = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Required number of terms = 11
Answer is A.
Question: The cash realised on selling a 14% stock is Rs.108.25, brokerage being 1/4% is?
A.366
B.106
C.108
D.192
Answer: C.108
Explanation: Cash realised= Rs. (108.25 - 0.25)
= Rs. 108.
Answer: C
Question: 4^x +4* 4^-x = 4 What is the value of x?
A.1/2
B.-1/2
C.-1
D.1/2
Answer: A.1/2
Explanation: let 4^x = t
t+4/t =4
t^2 -4t +4 =0
(t-2)^2=0
(t- 2)=0
t=2
4^x= 4^1/2
x=1/2
Ans: A
Question: A box contains 4 black and 5 red balls and another box contains 5 black and 4 red balls. One ball is to drawn from either of two boxes. What is the probability of drawing a black ball ?
A.1/9
B.2/9
C.4/9
D.1/2
Answer: D.1/2
Explanation: Explanation :
Probability of choosing first box is 1/2 and second box is 1/2.
∴ Probability of choosing one balck ball from the first box is 4C1 / 9C1 x 1/2 = 4/9 x 1/2 = 2/9
Probability of choosing one black ball from the second box is = 1/2 x 5C1 / 9C1 = 5/18
∴ P(E) = 2/9 + 5/18 = 4 + 5/18 = 9/18 = 1/2
Answer : Option D
Question: The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?
A.1650
B.1700
C.1750
D.1800
Answer: C.1750
Explanation: If the population increases by 50% then you're multiplying the previous number by 3/2. So to work backwards, divide by 3/2 (which is the same as multiplying by 2/3).
So we have:
1950: 810
1900: 810*(2/3) = 540
1850: 540*(2/3) = 360
1800: 360*(2/3) = 240
1750: 240*(2/3) = 160
Answer is C
Question: In a group of ducks and cows, the total number of legs are 26 more than twice the no. of heads. Find the total no.of buffaloes.
A.10
B.12
C.13
D.15
Answer: C.13
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 26
=> 2x = 26 => x = 13
C
Question: Rs.1300 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
A.s.528
B.s.600
C.s.528
D.s.540
Answer: B.s.600
Explanation: A+B+C = 1300
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1300 = Rs.600
Answer: B
Question: g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(r) is divisible by 4^11, what is the smallest possible value for r?
A. 22
B. 24
C. 28
D. 32
Answer: B. 24
Explanation: g(r)=4^11=2^22. So we have to find a product with atleast 22 2's in it.
in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
Question: In a camp, there is a meal for 120 men or 200 children. If 125 children have taken the meal, how many men will be catered to with remaining meal?
A.30
B.20
C.40
D.45
Answer: D.45
Explanation: There is a meal for 200 children.
125 children have taken the meal.
Remaining meal is to be catered to 75 children.
Now, 200 children 120 men.
75 children = (120/200)x 75 = 45 men.
D
Question: How many combinations of numbers less than 8 make their sum=8 (repetation of numbers is allowed)
A.102
B.103
C.104
D.105
Answer: C.104
Explanation: 8 digit no, =11111111
7 digit no.= 1111112,1111121,1111211........= total 7 numbers
6 digit no. = 111113,111131...........111122,111221....= total 21 numbers
5 digit no.= 11114,11141........11123....11231.....=total 25 numbers
4 digit no.= 2222,1115,1151,1511,5111....1133.....1124....= total 22 numbers
3 digit no.= 116,161,611,224,242,422,332,323,233....125....134...= total 21 numbers
2 digit no. = 44,17,71,26,62,35,53 = total 7 numbers.
now total possible numbers are (without zero) = 104
ANSWER:C
Question: In a workshop there are 4 kinds of beds, 5 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
A.A)168.
B.B)96.
C.C)56.
D.D)48.
Answer: B.B)96.
Explanation: ways to select one shelf = 2
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 7+5 = 12
ways to select all of them together = 2*4*12 = 96
Hence, B is the answer.
Question: Anne bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?
A.3%
B.4%
C.7%
D.D.10%
Answer: B.4%
Explanation: For Anne
Cost of Computer = $2000
Sales tax = (5/100)*2000 = $100
Total Cost of Computer = 2000 + 100 = 2100
For Henry
Cost of Computer = $1800
Sales tax = (12/100)*1800 = $216
Total Cost of Computer = 1800 + 216 = 2016
% that Henry paid less than Anne = (2100 - 2016)*100/2100 =4%
Answer: Option B
Question: 2646 can be expressed as a product of primes as
A.2 × 2 × 3 × 3 × 7 × 7
B.2 × 3 × 3 × 3 × 7 × 7
C.2 × 2 × 2 × 3 × 3 × 7
D.2 × 3 × 3 × 3 × 3 × 7
Answer: B.2 × 3 × 3 × 3 × 7 × 7
Explanation: Explanation:
It is clear that 2646 = 2 × 3 × 3 × 3 × 7 × 7
Answer: Option B
Question: If B and C are digits and 8BC is a 2-digit number that is divisible by 2, which of the following is a possible product of B and C?
A.1
B.2
C.4
D.6
Answer: C.4
Explanation: Try with the options -
A. If BC = 1 , both B and C must be 1
B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3
C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3
D. If BC = 6 , then we can have the following possibilities
i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3
ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3
E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 2
Thus answer is (C)
Question: The sum of the cube of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
A.20
B.21
C.22
D.24
Answer: A.20
Explanation: Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.
(a + b + c) = 400 = 20
A
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is :
A.36.0
B.36.5
C.36.2
D.36.1
Answer: B.36.5
Explanation: Explanation:
Correct Sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = = 1825/50 = 36.5
Answer: B) 36.5
Question: Find the third proportion to 12, 36?
A.106
B.107
C.108
D.109
Answer: C.108
Explanation: let x be 3rd pro.
then 12:36=36:x
so x=108
ANSWER:C