RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/12 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
A.23/30
B.11/15
C.47/60
D.1/6
Answer: C.47/60
Explanation: 1/5 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/5) = 1/15
therefore only video cassette recorder = 1/12 - 1/15 = 1/60
Total = 1/5+1/60+neither cable tv nor videocassette recorders
1 =13/60+ neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-13/60 = 47/60
Hence C.
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1792?
A.1600
B.2777
C.2889
D.27670
Answer: A.1600
Explanation: 1792 = P [1 + (5*12/5)/100]
P= 1600.Answer:A
Question: The ratio of ducks and frogs in a pond is 31 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?
A.148
B.152
C.156
D.169
Answer: D.169
Explanation: Solution:
Ratio of Ducks and Frogs in Pond,
= 31 : 39.
Average of Ducks and Frogs in Pond,
= 152.
So, total number of Ducks and Frogs in the Pond,
= 2* 152 = 304.
Therefore,
Number of Frogs, = (304 *39)/70 = 169.
Answer: Option D
Question: If n is an integer greater than 7, which of the following must be divisible by 3?
A.1. n (n+1) (n-4)
B.2. n (n+2) (n-1)
C.3. n (n+3) (n-5)
D.4. n (n+4) (n-2)
Answer: D.4. n (n+4) (n-2)
Explanation: We need to find out the number which is divisible by three,
In every 3 consecutive integers, there must contain 1 multiple of 3.
So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three
1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)
2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)
3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)
4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)
5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)
from the above onlyoption Ais product of consecutive three numbers.
D
Question: A miniature roulette wheel is divided into 9 equal sectors, each bearing a distinct integer from 1 to 9, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun four times, approximately what is the probability that the product of the four winning sectors’ integers will be even?
A.50%
B.67%
C.80%
D.90%
Answer: D.90%
Explanation: The only way to have an odd product is if all 4 integers are odd.
P(odd product) = 5/9*5/9*5/9*5/9 = 625/6561
P(even product) = 1 - 625/6561 = 5936/6561 which is about 90%
The answer is D.
Question: The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?
A.5100
B.7550
C.10100
D.15500
Answer: B.7550
Explanation: First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
2550+(100*50)=7550;ANSWER:B
Question: In what time will a train 120 meters long cross an electric pole, if its speed is 184 km/hr
A.5 seconds
B.4.5 seconds
C.3 seconds
D.2.3 seconds
Answer: D.2.3 seconds
Explanation: Explanation:
First convert speed into m/sec
Speed = 184*(5/18) = 51 m/sec
Time = Distance/speed
= 120/51 = 2.3 seconds
Option D
Question: A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally?
A.15 days
B.16 days
C.17 days
D.18 days
Answer: D.18 days
Explanation: clearly 11mornings and 12 afternoons = 23 half days
since 13 days raining means 13 half days.
so 23-13 =10 halfdays ( not effecetd by rain )
so 10 halfdays =5 fulldays
total no. of days = 13+5 =18 days
ANSWER:D
Question: A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
A.1.4
B.1.5
C.1.6
D.1.8
Answer: D.1.8
Explanation: Let the speed be 's' and let the distance between rose and poppy be 'x'
The problem boils down to:
Rose to Poppy: s+3=x/6 ------- 1
Daisy to Rose: s=(x+18)/10------ 2
so from 1 we can re write x as x=6s+18
substitute the value of x in 2 gives us s=1.8 m/s
D
Question: A train 100m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
A.45kmph
B.55kmph
C.32kmph
D.61kmph
Answer: B.55kmph
Explanation: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
100/[(x+5)*5/18] = 6
30(x+5) = 1800
x = 55kmph
Answer is B
Question: A, B, C hired a car for Rs.520 and used it for 7,8 and 11 hours respectively. Hire charges paid by B were
A.Rs.140
B.Rs.160
C.Rs.180
D.Rs.220
Answer: B.Rs.160
Explanation: Solution
A : B : C	= 7 : 8 : 11.
Hire charges paid by B	= Rs(520×8/26)
= Rs.160.
Answer B
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.7. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?
A.0.12
B.0.24
C.0.28
D.0.66
Answer: D.0.66
Explanation: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )
=0.6*0.2+0.4*0.3+0.6*0.7
= 0.12+0.12+0.42
=0.66
D
Question: A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
A.(320 - y)/(5x)
B.(y +220)/(5x)
C.5(80 - y)/(4x)
D.(y + 400)/(4x)
Answer: B.(y +220)/(5x)
Explanation: Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20 = 65 houses per week
total time they took = (40/20) + (40/65) = 2.6 weeks
Putting the values of x and y in equation B
(y +220)/(5x) = (40+220)/5*20 = 260/100 = 2.6
Question: In the xy-plane, a line has slope 3 and x-intercept 6. What is the y-intercept of the line?
A.-18
B.-3
C.0
D.3
Answer: A.-18
Explanation: Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 6.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 3*6 + b => b = -18. Hence A.
Question: On a purchase of $110, a store offered a payment plan consisting of a $10 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
A.9.5%
B.10.5%
C.11.5%
D.9.1%
Answer: D.9.1%
Explanation: 12*10 + 10 = 130
(10/110)* 100 = 9.1
Answer : D
Question: If the price of an article went up by 50%, then by what percent should it be brought down to bring it back to its original price?
A.2/3%
B.2/8%
C.2/1%
D.33.3%
Answer: D.33.3%
Explanation: Let the price of the article be Rs. 100.
50% of 100 = 50.
New price = 100 + 50 = Rs. 150
Required percentage = (150 - 100)/150 * 100
= 50/150 * 100= 33.33%.
Answer:D
Question: A man 24 years older than his son. In two year his age will be twice of his son. what is the present age of his son?
A.23
B.22
C.21
D.20
Answer: B.22
Explanation: Correct Answer : B
present age of son = x years
present age of man = ( x +24 )years
In two year his age will be twice of his son.
(x +24)+2=2(x+2)
x=22
Question: The total of the ages of Jayant, Prem and Saransh is 75 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Prem?
A.25 years
B.32 years
C.34 years
D.38 years
Answer: A.25 years
Explanation: Solution
Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,
(2x + 10)+(3x + 10)+(4x + 10)	= 75.
‹=›9x = 45
x = 5.
∴ Prem's present age = 3x + 10 = 25 years.
Answer A
Question: 6^b + 6^b + 6^b + 6^b + 6^b + 6^b =
A.7^b
B.7^(b + 1)
C.7^(7b)
D.6^(b + 1)
Answer: D.6^(b + 1)
Explanation: Easy one.
6*6^b = 6^(b+1)
Ans. D
Question: A chemical is composed of hydrogen, oxygen and nitrogen. If 20 moles of the chemical is to be made containing twice as much hydrogen as oxygen and three times as much oxygen as nitrogen how many moles of oxygen is required?
A.5 moles
B.6 moles
C.8moles
D.2 moles
Answer: D.2 moles
Explanation: Amount of chemical=20 moles
hydrogen=2 oxygen
oxygen=3 nitrogen
hydrogen+oxygen+nitrogen=20
2 oxygen+oxygen+1/3 oxygen=20
10 oxygen=20
oxygen=2
Answer is D
Question: 3889 + 12.597 - ? = 3854.002
A.A)47.095
B.B)47.595
C.C)47.932
D.D)47.95
Answer: B.B)47.595
Explanation: Let 3889 + 12.597 - x = 3854.002.
Then x = (3889 + 12.597) - 3854.002
= 3901.597 - 3854.002
= 47.595.
Answer = B
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 8 runs. His new average is:
A.22 runs
B.24 runs
C.26 runs
D.28 runs
Answer: D.28 runs
Explanation: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 8
= 11x + 88 = 10x + 108
= x = 20.
New average = (x + 8) = 28 runs.
Answer:D
Question: If 1 added to the age of the elder sister, then the ratio of the ages of two sisters becomes 0.5:1, but if 2 is subtracted from the age of the younger one, the ratio becomes 1:3, the age of the younger sister will be?
A.7 years
B.5 years
C.8 years
D.10 years
Answer: B.5 years
Explanation: Explanation :
Let, the age of the elder sister be x year, and younger sister be y year.
Now, according to the question,
y/(x+1)=0.5/1.
=>y/(x+1)=1/2.
=>2y= x + 1
=>x−2y =−1 -------(i)
And,
=>(y−2)/x=1/3.
=>x−3y =−6 -------(ii)
On solving these equations, we get :-
x=9 and y=5
Hence, the age of the younger sister is 5 years.
Answer : B
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.7
B.6
C.8
D.5
Answer: C.8
Explanation: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Question: There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?
A.100
B.90
C.50
D.45
Answer: D.45
Explanation: 1. first child out of 10 - 10 possibilities
2. second child out of 9 - 9 possibilities. the total number of pairs = 9*10=90
3. exclude xy yx cases: 90/2=45
Second way
N=10C2=10!/(8!2!)=10*9/2=45
ANS:D
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
A.11
B.10
C.9
D.8
Answer: A.11
Explanation: (5 + x)/20 + 5/25 = 1 => x = 11 days
ANSWER A
Question: Of the three-digit integers greater than 900, how many have two digits that are equal to each other and the remaining digit different from the other two?
A. 94
B. 82
C. 80
D. 45
Answer: A. 94
Explanation: To satify the given condition,
required no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same,
number greater than 700;
total numbers = 1*10*10 = 100
numbers with all digits different = 1*9*8 = 72
numbers when all three digits are same (777) = 1
req. = 100- 72 - 1 = 27
considering the numbers between 700999 = 27*3=95
Answer is 94 ('cause 700 can't be included)
Answer (A).
Question: The distance between a gym and a pharmacy is approximately 1.2 x 10^5 inches. Which of the following is closest to the distance between the gym and a pharmacy, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
A.3.1
B.3.9
C.3.7
D.4.2
Answer: A.3.1
Explanation: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the gym and a pharmacy is approximately 1.2 x 10^5 inches. To convert inches to kilometers, we need to multiply 1.2 x 10^5 inches by the ratio we just found out.
kilometers = 1.2 x 10^5 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 1.2 x 10^5/3.9x10^4 km
km = 3.08 = 3.1 km
Therefore, we can see that the closest answer is A.
Question: A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examinaiton?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: Explanation :
Let the full marks of each subject is 100. So, total marks in 5 subject is 500.
Student gets 60% aggregate marks i.e 60% of 500 = 300.
=> 10x + 9x +8x +7x + 6x = 300
=> 40x = 300.
=> x = 300/40 = 7.5.
Hence,
The marks in first subject = 10x = 7.5 x 10 = 75.
The marks in 2ndsubject = 9x = 7.5 x 9 = 67.5.
The marks in 3rd subject = 8x = 7.5 x 8 = 60.
The marks in 4th subject = 7x = 7.5 x 7 = 52.5.
The marks in 5th subject = 6x = 7.5 x 6 = 45.
Thus , he passed in all 5 subjects.
Answer : D
Question: if f(f(X))=81. then. value of x=?
when f(X)=2X-1+f(X-1). is not equal to zero and f(X=0)=0
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: f(X=0) = 0
f(X=1) = 2*1-1+f(1-1)
= 2-1+0
= 1
f(X=2) = 2*2-1+f(2-1)
= 4-1+1
= 4
f(X=3) = 2*3-1+f(3-1)
= 6-1+4
= 9
===>f(X=n) = n^2
f(f(X)) = 81
X = sqrt(sqrt(81)) = 3
ANSWER:B
Question: The ratio of male to female in a class is 6:6. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
A.a)180 degree
B.b) 168 degree
C.c)191 degree
D.d)192 degree
Answer: A.a)180 degree
Explanation: here is my approach => males => 6x and females =6x => total =12x
now 12x=> 360
therefore 6x => 180 degree .
P.S => 6x is nothing but total number of students with the given preference
Answer A
Question: A firm is comprised of partners and associates in a ratio of 2:61. If 60 more associates were hired, the ratio of partners to associates would be 4:137. How many partners are currently in the firm?
A.12
B.14
C.16
D.18
Answer: C.16
Explanation: The ratio 2:61 = 4:122 so the ratio changed from 4:122 to 4:137.
137-122 = 15 which is 1/4 of the increase in 60 associates.
The ratio changed from 16:488 to 16:548.
Thus the number of partners is 16.
The answer is C.
Question: Difference of 2 numbers is 1660. If 7.5% of one number is 12.5% of the other number, find the 2 numbers?
A.125,150
B.5124,4515
C.4150,2490
D.3250,4510
Answer: C.4150,2490
Explanation: Let the numbers be x and y
7.5% of x = 12.5% of y
x = 125y/75 = 5y/3
x-y = 1660
5y/3 - y = 1660
y = 2490
x = 5y/3 = 4150
Answer is C
Question: Rahul is younger than Karthi by 7 years. If the ratio of their ages is 7:9, find the age of Rahul
A.20
B.24
C.24.5
D.23
Answer: C.24.5
Explanation: karthi age is x and rahul x-7
=> (x-7)/x = 7/9
=> 9x-63 = 7x
=> 2x = 63
=> x = 31.5
then Rahul age is 31.5- 7 = 24.5
ANSWER C
Question: A cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
A.5.2 hrs
B.13.3 hrs
C.1.9 hrs
D.7.2 hrs
Answer: B.13.3 hrs
Explanation: Net part filled in 1 hour = (1/5 - 1/8) = 3/40
The cistern will be filled in 40/3 hrs i.e., 13.3 hrs.
Answer:B
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
A.18% p.a.
B.22% p.a.
C.20% p.a.
D.24% p.a.
Answer: C.20% p.a.
Explanation: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
ANSWER:C
Question: There are 13 cans in the refrigerator. 7 of them are red and 6 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
A.460
B.490
C.493
D.455
Answer: A.460
Explanation: Answer: A.
Question: The average (arithmetic mean) of eight numbers is 8. If 4 is added from each of five of the numbers, what is the new average?
A.4.5
B.8.9
C.10.5
D.4.5
Answer: C.10.5
Explanation: Sum of 8 numbers = 8*8=64
If 4 is added from each of five of the numbers , we added 4*5=20 from the total sum
Sum of 8 number after adding 4 from each of five of the numbers =64+20=84
New average = 84/8=10.5
Answer C
Question: In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
A.10 m
B.20 m
C.30 m
D.40 m
Answer: B.20 m
Explanation: A - distance of (500 - 140)m =>360 m
A cover 3 m , B covers 4 m => 480 m
when A reaches the winning post B covers 480 m and remains 20 m behind
= > A wins by 20 m
ANSWER B
Question: In a company of 10 employees, 5 employees earn $30,000, 3 employees earn $40,000, and the 2 highest-paid employees earn the same amount. If the average annual salary for the 10 employees is $65,000, what is the annual salary for each of the highest-paid employees?
A.$190,000
B.$170,000
C.$150,000
D.$130,000
Answer: A.$190,000
Explanation: 5*30,000+3*40,000+2x=10*65,000
2x=650,000-150,000-120,000
2x=380,000
x=190,000
The answer is A.
Question: How many pieces of 75 cm can be cut from a rope 45 meters long?
A.30
B.40
C.60
D.None
Answer: C.60
Explanation: Explanation :
Total pieces of 75 cm that can be cut from a rope of 45 meters long is
= (45 meters)/(75 cm)
= (45 meters)/(0.75 meters)
= 60
Answer : C
Question: If grapes are 90% water and raisins are 15% water, then how many kilograms did a quantity of raisins, which currently weighs 12 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
A.96
B.98
C.100
D.102
Answer: D.102
Explanation: Let x be the original weight of the grapes.
The weight of the grape pulp was 0.1x.
Since the grape pulp is 85% of the raisins, 0.1x = 0.85(12 kg).
Then x = 8.5*12 = 102 kg.
The answer is D.
Question: The number 106 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?
A.6
B.5
C.7
D.8
Answer: A.6
Explanation: Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-4, +/-3 and +/-9, so the difference could be 6, or 12. Since only one of them is among the choices, then it must be the correct answer.
Answer:A
Question: A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work.
A.27 days
B.54 days
C.56 days
D.68 days
Answer: B.54 days
Explanation: Explanation:
As per question, A do twice the work as done by B.
So A:B = 2:1
Also (A+B) one day work = 1/18
To get days in which B will finish the work, lets calculate work done by B in 1 day =1/18*1/3=1/54
[Please note we multiplied by 1/3 as per B share and total of ratio is 1/3]
So B will finish the work in 54 days
ANSWER IS B
Question: Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?
A.20
B.24
C.48
D.72
Answer: C.48
Explanation: J = Juan, F = Jamal
Since J is always fixed, set J, set F relative to J, then see how many options there are:
J F 4 3 2 1 = 24 or
F J 4 3 2 1 = 24
24+24=48 … C
ANSWER:C
Question: When a positive integer A is divided by 11 and 3, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 11 and 3, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)?
A.14
B.28
C.33
D.42
Answer: C.33
Explanation: A = 11k+1 = 3j+2
B = 11m+1 = 3n+2
A-B = 11(k-m) = 3(j-n)
A-B is a multiple of both 11 and 3, so it is a multiple of 33.
The answer is C.
Question: In a group of ducks and cows, the total number of legs are 36 more than twice the number of heads. Find the total number of cows.
A.12
B.14
C.16
D.18
Answer: D.18
Explanation: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 36 more than twice the number of heads
=> 2(d + 2c) = 36 + 2(c + d)
=> d + 2c = 18 + c + d
=> 2c = 18 + c
=> c = 18
i.e., total number of cows = 18
Answer is D.
Question: The banker's gain on a sum due 3 years hence at 12% per year is Rs. 270. The banker's discount is:
A.960
B.840
C.1020
D.760
Answer: C.1020
Explanation: T.D. =(B.G. x 100/R x T)
= Rs.(270 x 100/12 x 3)= Rs. 750.
Therefore, B.D. = Rs.(750 + 270) = Rs. 1020.
Answer is C
Question: There are 4 books on fairy tales,5 novels and 3 plays.In how many ways can you arrange these so that books on fairy tales are together,novels are together and plays are together and in the order,books on fairy tales,novels and plays.
A.22000
B.19261
C.17280
D.18168
Answer: C.17280
Explanation: There are 4 books arranged in 4!ways
Similarly,5 novels arranged in 5!ways.
And 3 plays arranged in 3!ways.
Counting principle all of them together can be arranged=4!*5!*3!
=[(4*3*2*1)*(5*4*3*2*1)*(3*2*1)]
=17280 ways
Option C
Question: M is the set of all consecutive odd integers between A and B. If B>A>1, and both A and B are even integers, what is the average (arithmetic mean) of M?
A.(A−B)/2
B.(A−B)/2 + 1
C.(A+B−1)/2
D.(A+B)/2
Answer: D.(A+B)/2
Explanation: Let A be 2 and B be 6...as per condition..A and B have to be even...
2,3,4,5 and 6...then M is avg of odd integers...in our case 3+5/2 = 4..
We need to check which option is going to yield 4 and only option D does..
6+2/2 = 4...
Answer option D.
Question: If x represents the sum of the interior angles of a square and y represents the sum of the interior angles of a regular pentagon, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?
A.Triangle
B.Square
C.Rhombus
D.Trapezoid
Answer: A.Triangle
Explanation: Sum of angles of square = 180*(4-2) = 360 => using formula sum of angles of polygon = 180*(n-2) where n is the number of sides in a polygon
Sum of angles in Pentagon = 180*(5-2) =540
Difference = 540 - 360 = 180 => Triangle
hence (A).