RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If m and n are both odd prime numbers andm < n, then how many different positive integer factors does2mnhave?
A. 3
B. 8
C. 6
D. 4
Answer: B. 8
Explanation: m and n are both odd prime numbers- It means either m or n is not 2
and since prime numbers have only two factors - 1 and the number itself
m and n each will have (1+1)= 2 factors
Hence 2mn will have (1+1)(1+1)(1+1)= 8 factors
B is the answer
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
A.46%
B.57%
C.74%
D.63%
Answer: B.57%
Explanation: B
57%
Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage =(11628x100/20400)% = 57%.
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.3500 and B Rs.1500, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
A.1978
B.2707
C.7728
D.7008
Answer: D.7008
Explanation: 35:15 => 7:3
9600*10/100 = 960
9600 - 960 = 8640
8640*7/10 = 6048 + 960
= 7008
Answer: D
Question: if p/q=3/4
then3p+7q=?
A.37/4
B.25/2
C.20/4
D.35/4
Answer: A.37/4
Explanation: 3p+7q=?
Divided by q,
3(p/q)+7=x
3*(3/4)+7=37/4
ANSWER:A
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
A.99
B.277
C.48
D.99
Answer: C.48
Explanation: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer:C
Question: If (x^2 + x - 8) ≤ x + 1, then x could be represented by which of the following?
A.− 4 ≤ x ≤ − 3
B.− 4 ≤ x ≤ 3
C.− 3 ≤ x ≤ 3
D.− 3 ≤ x ≤ 4
Answer: C.− 3 ≤ x ≤ 3
Explanation: IMO C is correct answer
solving through eqautions
x^2 +x-8<= x+1
(x+3)(x-3)<=0
Question: If r and h are two positive integers and r/h = 1.60, then r can equal which one of the following?
A. 9
B. 24
C. 20
D. 22
Answer: B. 24
Explanation: r/h = 1.60 = 160/100 = 8/5
So, r COULD equal 24
Answer: B
Question: A bag contains 8 red, 7 blue and 6 green dress. If one dress is picked up randomly then ewhat is the probability that it is neither red nor green?
A.1/3
B.2/3
C.2/5
D.3/7
Answer: A.1/3
Explanation: Total number of dress = (8 + 7 + 6) = 21.
Let E	= event that the dress drawn is neither red nor green
= event that the dress drawn is blue.
n(E) = 7.
P(E) =	n(E)	=	7	=	1/3
n(S) 21
A
Question: A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 3 new workers. How many different ways can she assign the new workers?
A.2430
B.2640
C.3300
D.4860
Answer: B.2640
Explanation: whatever : my take selecting team of 3 out of 12 to assign to the shifts = 12C3 = 220 ways.
now 3 out of 12 means total of 4 group possible.
so putting them in shifts = counting methode: first, second, third, alt , alt
= 4*3*2*1 = 24
here alt and alt are the same: so 24/2 = 12 ways.
total ways of selecting = (selecting 3 out of 12)*arranging those teams in shifts
= 220*24 = 2640
Ans: B
Question: In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
A.8m/s
B.9m/s
C.6m/s
D.4m/s
Answer: A.8m/s
Explanation: Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25 = 8 m/s.
Answer: A
Question: Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 55% of Mary and John’s combined income?
A.$3,000
B.$4,000
C.$7,000
D.$11,000
Answer: C.$7,000
Explanation: Let Mary's income increase by x, then the equation will be
15,000 + x= (55/100)* (15,000 + x + 18000 )
15,000 + x = (11/20) * (33,000 + x)
300,000 + 20x = 11x + 363,000
9 x = 63,000
x = 7,000
So, Answer will be C
Question: If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is?
A.Rs. 850
B.Rs. 900
C.Rs. 800
D.Rs. 910
Answer: A.Rs. 850
Explanation: Sol We have, A : Rs.1U2D
Let the pr xnpal be R5 x
Then mterest u — 12 : wzo — x
Therefore, by u xglurmula.
_umxx
’ Rx’: (
, _ma>< 1nzn—xv
\4Ve|\a\e,Jc— 5“
:> ~(:51DD—S*(or6x:51UU
or, J: : w 350
. The sum of money burrowed : Rs. 850
A)
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
A.187 min
B.177 min
C.144 min
D.189 min
Answer: C.144 min
Explanation: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.
Answer:C
Question: If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?
A.x + y
B.y – z
C.xy + 1
D.xyz + 1
Answer: D.xyz + 1
Explanation: xyz and xyx+1 are are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Since xyz is a multiple of each x, y, and z, then xyx+1 cannot be a multiple of any of them.
Answer: D.
Question: The average of first five prime numbers greater than 61 is?
A.32.2
B.32.98
C.74.6
D.32.8
Answer: C.74.6
Explanation: 67 + 71 + 73 + 79 + 83
= 373/5
= 74.6
Answer: C
Question: Three partners A,B,C start a business.Twice A’s capital is equal to thirce B’s capital and B’s capital is four times C’s capital.Out of a total profit of Rs.16,500 at the end of the year,B’s share is :
A.Rs.4000
B.Rs.6000
C.Rs.7500
D.Rs.6600
Answer: B.Rs.6000
Explanation: Solution
Let C = x.Then,B = 4x and 2A = 3 4x = 12 x or A = 6x.
∴ A : B : C = 6x : 4x : x = 6 : 4 : 1 .
So, B’s capital = Rs. (16500x4/11) = Rs. 6000. Answer B
Question: if N is a prime number bigger than 5. Which of the following expressions must be even?
A.(a) (N+2)^2
B.(b) N^2+2.
C.(c) N(N+2).
D.(d) (N+1)(N+2)
Answer: B.(b) N^2+2.
Explanation: N=11
a. 169
b. 123
c. 143
d. 180
e. 81
B
Question: Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four pink stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?
A.120
B.350
C.700
D.1,960
Answer: D.1,960
Explanation: Number of ways to choose 2 colors among 8 - 8c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))
Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]
Total number of combinations -8c2 * 2* 7c4 = 1960
D
Question: If x > 1, which of the following decreases as x decreases?
I. x + x^2
II. 2x^2 − x
III. (x + 1)
A.I only
B.II only
C.III only
D.I , II and III
Answer: D.I , II and III
Explanation: let x= 4 and 3 b old and new values
ST1: x= 4 -> 4+16 = 20
x=3-> 3+9 = 12 ...decreased
ST2:x= 4-> 2*16-4 = 28
x=3->2*9-3 = 15
decreased
St3: x=4-> 5
x=3->1/3 4
Ans: D
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A.2 years
B.4 years
C.6years
D.12 years
Answer: C.6years
Explanation: Solution
Mother's age when Ayesha's brother was born	= 36 years.
Father's age when Ayesha's brother was born
= (38+4) years.
= 42 years.
Required difference	= (42-36)
= 6 years.
Answer C
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
A.6 days
B.10 days
C.15 days
D.20 days
Answer: B.10 days
Explanation: Explanation:
Work done by X in 4 days = (1/20 * 4) = 1/5
Remaining work = (1 - 1/5) = 4/5
(X + Y)'s 1 day work = (1/20 + 1/12) = 2/15
Now, 2/15 work is done by X and Y in 1 day.
So, 4/5 work will be done by X and Y in (15/2 * 4/5) = 6 days.
Hence, total time taken = (6 + 4) = 10 days.
ANSWER IS B
Question: There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(46)-A(45)?
A.2^22+1
B.2^45
C.2^23+1
D.2^24
Answer: B.2^45
Explanation: A1= 3
A2= 2*3-1= 5
A3= 2*5-1= 9
A4= 2*9-1= 17
We can notice that there is a squence
A2-A1= 2^1
A3-A2= 2^2
A4-A3= 2^3
Hence A46-A45= 2^45
B is the answer
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
A.230
B.997
C.266
D.289
Answer: A.230
Explanation: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Question: Question: What is the remainder when Q=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
A. 0
B. 25
C. 49
D. 81
Answer: D. 81
Explanation: 144 =12 *12
(1!)^3=1
2!=2, therefore (2!)^3=2*2*2=8
3!=6, therefore (3!)^3=6*6*6=216
4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144
thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0
now the remainder when Q=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144
now remainder when 225 is divided by 144 is 81. hence answer should be D
Question: Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.Rs. 15
B.Rs. 15.70
C.Rs. 19.70
D.Rs. 20
Answer: C.Rs. 19.70
Explanation: Let the amount taxable purchases be Rs. x.
65 of x =30/100
X = (30/100)x(100/6)
= 5
Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70
answer : C
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
A.6.09%
B.6.08%
C.6.1%
D.6.07%
Answer: A.6.09%
Explanation: Amount of Rs. 100 for 1 year when compounded half-yearly
=100 x (1 + 3/100)^2 = 106.09
Therefore Effective rate = (106.09 - 100)% = 6.09%
Answer A) 6.09%
Question: Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
5 ~ 2 ~ 7 ~ 4 = ____
A.2410
B.2910
C.2940
D.3749
Answer: A.2410
Explanation: A
2410
2410
The rule that is being followed here is
P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]
Using the same rule in the incomplete equation,
5 ~ 2 ~ 7 ~ 4 = [first digit of (5 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (5 * 4)]
= 2410
Thus 2410 is the missing number.
Question: An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters Q long?
A.0.5
B.1
C.1.5
D.2
Answer: B.1
Explanation: Let x be the number of desks and bookcases that are placed along the library wall.
2x + 1.5x < 15
3.5x < 15
Since x is a non negative integer, the largest number x can be is 4.
When x is 4, the desks and bookcases take up 3.5 * 4 = 14m=Q, leaving 1m of empty space.
Thus, I believe the answer is B) 1
Question: E=(429)^2 * 237 * (1243)^3 is thrice of ?
A.33605 * 31960 * (1243)^2
B.33654 * 538219 * (1243)^2
C.33891 * 533247 * (1243)^2
D.34122 * 532004 * (1243)^2
Answer: C.33891 * 533247 * (1243)^2
Explanation: E=(429)^2*237*(1243)^3 is an odd number.
Among answer choices only C is an odd number, (so thrice C also will be an odd number).
Answer: C.
Question: Set A consists of the integers from 4 to 15, inclusive, while set B consists of the integers from 7 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?
A.5
B.7
C.8
D.9
Answer: D.9
Explanation: A={4,5,6,7,8,9,10,11,12}
B={6,7,8,9,10,11,12...}
Thus we see that there are 9 distinct integers that are common to both. D is the correct answer.
Question: If the average (arithmetic mean) of the four numbers 5, 15, 30, and (N + 1) is 30, then N =
A. 19
B. 20
C. 69
D. 78
Answer: C. 69
Explanation: 5+15+30+N+1= 30x 4 = 120
=>N +51 = 120
=>N=69
Answer C
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
A.3:4
B.2:5
C.6:7
D.4:6
Answer: A.3:4
Explanation: Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y = 80
Ratio of speeds = 60:80 = 3:4
ANSWER A
Question: The present population of a town is 10000. Population increase rate is 10% p.a. Find the population of town after 2 years?
A.10000
B.11100
C.15000
D.12100
Answer: D.12100
Explanation: P = 10000
R = 10%
Required population of town = P(1 + R/100)^T
= 10000(1 + 10/100)^2
= 10000(11/10)^2
= 12100
Answer is D
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 35
A.1
B.3
C.5
D.7
Answer: B.3
Explanation: P Ã· 44 = 432
=> P = 432 * 44 = 19008
P / 35 = 19008 / 35 = 543, remainder = 3
B
Question: Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid?
A.D + 40
B.D + H – 1
C.D + 2H
D.6.93H
Answer: D.6.93H
Explanation: before Discount price was: 1.4D+1.5H
After Discount: 1.4D +1.5H-.42D-.45H
substitute D=6H
final value: 6.93H
Ans Is D
Question: Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 15 kmph and 25 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
A.144
B.36
C.124
D.32
Answer: B.36
Explanation: Time taken to meet the first time = length of track/relative speed
= 400/ (15 +25) (5/18)
= 400/40 *(18/5) = 36 sec.
Answer : B
Question: The product of digit is a Factor of a two digit number.No of such digit are:
A.3
B.5
C.9
D.27
Answer: B.5
Explanation: 11, 1*1=1
12 , 1*2=2
15 ,1*5=5
24 ,2*4=8
36 , 3*6=18
so Ans is 5
ANSWER:B
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent R of thatbeforeJuly 1 last year?
A.90%
B.99%
C.100%
D.101%
Answer: B.99%
Explanation: the total number of employees = n
the average salary = x
total salary to all emplyoees = xn
after
the total number of employees = n - 0.1n = 0.9n
the average salary = x + 10% of x = 1.1x
total salary to all emplyoees = 0.9n (1.1x)
total salary after as a % of total salary before R= [0.9n (1.1x)]/xn= 0.99 or 99%.B
Question: A vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the lengths OP and AB respectively. Suppose ∠APB = 60°, then the relationship between h and b can be expressed as :
A.2b^2 = h^2
B.2h^2 = b^2
C.3b^2 = 2h^2
D.3h^2 = 2b^2
Answer: B.2h^2 = b^2
Explanation: Explanation :
As OP is at centre of square so clearly PA = PB.
so, angle ∠PAB = ∠ PBA.
and as ∠APB = 60,so we can see that in ∆ APB, ∠ PAB = ∠ PBA = 60.
Hence, its an equilateral triangle thus making AP = PB = AB = b.
Now lets see ∆ AOB ,
O is centre of square so angle AOB=900​.
giving us AO = OB = AB/√2.
so AO= b/√2
Now in triangle AOP right angled at O,
=> AO2 + OP2 = PA2 .
=> b2/2 + h2 = b2 .
=> h2 = b2/2
Answer : B
Question: If x is an odd integer, which of the following is an odd integer?
A.2x
B.3x-1
C.5x+6
D.x+x^2
Answer: C.5x+6
Explanation: Plug in an odd integer; in this case 3
(2*3) = 6 Even
(3*3)-1 = 8 Even
(5*3)+6 = 15 + 6 = 21 Odd
3+3^2 = 3 + 9 = 12 Even
(6*3)-6 = 18 - 6 = 12 Even
Answer: C
Question: The least perfect square, which is divisible by each of 21, 36 and 66 is:
A.213444
B.214344
C.214434
D.231444
Answer: A.213444
Explanation: L.C.M. of 21, 36, 66 = 2772.
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 22 x 32 x 72 x 112 = 213444
Answer: Option A
Question: The average of first 15 natural numbers is?
A.6
B.5.5
C.5.1
D.8
Answer: D.8
Explanation: Sum of 15 natural no.
= 240/2 = 120
Average =120/15
= 8
Answer:D
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
A.Rs.480
B.Rs.420
C.Rs.430
D.Rs.440
Answer: A.Rs.480
Explanation: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer:A
Question: If the average (arithmetic mean) of a and b is 110, and the average of b and c is 170, what is the value of a − c?
A.−120
B.−100
C.100
D.135
Answer: A.−120
Explanation: a+b = 220
b+c = 340
a-c = -120.
IMO option A.
Question: 3 candidates in an election and received 3000, 5000 and 15000 votes respectively. What % of the total votes did the winningcandidate got in that election?
A.65.21%
B.50.16%
C.57%
D.60%
Answer: A.65.21%
Explanation: Total number of votes polled = (3000 + 5000 + 15000) = 23000
So, Required percentage = 15000/23000 * 100 = 65.21%
A
Question: A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)?
A.0
B.20
C.75
D.5
Answer: A.0
Explanation: Explanation :
Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0
Answer : A
Question: If 15 toys cost Rs, 234, what do 35 toys cost?
A.645
B.564
C.546
D.654
Answer: C.546
Explanation: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
.	15 : 35 : : 234 : x = (15 x x) = (35 x 234) = x=(35 X 234)/15 =546
Hence, the cost of 35 toys is Rs. 546.
Answer is C
Question: The duplicate ratio of 1:4 is?
A.1:2
B.1:4
C.1:8
D.1:18
Answer: C.1:8
Explanation: 1^2: 4^2 = 2:16=1:8
ANSWER:C
Question: Two men A and B start from place X walking at 4 Â½ kmph and 5 Â¾ kmph respectively. How many km apart they are at the end of 3 Â½ hours if they are walking in the same direction ?
A.1 3/8 km
B.3 3/8 km
C.5 3/8 km
D.4 3/8 km
Answer: D.4 3/8 km
Explanation: Explanation:
Relative Speed = 5 Â¾ - 4 Â½ = 1 Â¼
Time = 3 Â½ h.
Distance = 5/4 x 7/2 = 35/8 = 4 3/8 km.
Answer: D
Question: What proximate value should come in place of the question mark (?) in the following question?
6.595 × 1084 + 2568.34 – 1708.34 = ?
A.6,000
B.12,000
C.10,000
D.8,000
Answer: D.8,000
Explanation: ? ≈ 6.6 × 1080 + 2560 – 1700 ≈ 7128 + 860 ≈ 8000
Answer D
Question: A man wants to sell his scooter.There are two offers,one at Rs.12,000 cash and the other at a credit of Rs. 12,880 to be paid after 8 months,money being at 18% per annum. Which is the better offer ?
A.Rs. 12,000 in cash
B.Rs. 12,880 at credit
C.Both are equally good
D.none of these
Answer: A.Rs. 12,000 in cash
Explanation: Solution
P.W. of Rs. 12,880 due 8 months hence
= Rs. [12880 x100/100 +( 18x8/12) ] = Rs. ( 12880x100/112)= Rs.11500.
Clearly, Rs.12,000 in cash is a better offer.
Answer A
Question: Noelle walks from point A to point B at an average speed of 3 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 4 kilometers per hour?
A.5.75
B.6
C.7.25
D.7.5
Answer: B.6
Explanation: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
4= 2*3*x/3+x
x= 6
B is the answer
Question: c is the product of each integer from 1 to 50, inclusive and d=100^k, where k is an integer . What is the greatest value of k for which y is a factor of c?
A.7
B.6
C.5
D.4
Answer: B.6
Explanation: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*50 = 50!
No. of trailing zeros in 50! = 50/5 + 50/5^2 = 10+2 = 12
100^k = 10^2k → k = 12/2 = 6
B
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is?
A.1
B.2
C.6
D.8
Answer: B.2
Explanation: Let the ten's and unit digit be x and 8 respectively.
x
Then, 10x + 8 + 18 = 10 x 8 + x
x x
10x2 + 8 + 18x = 80 + x2
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
Option B
Question: What could be the range of a set consisting of odd multiples of (6+1)?
A.70
B.24
C.35
D.62
Answer: A.70
Explanation: Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 7*(2n+1) where n is any positive integer.
Range = 7*(2m + 1) - 7*(2n + 1) = 7*2*(m-n) = 14 * (m-n).
m, n - any positive integers
The answer must be divisible by 14, which is only 70.
The correct answer is A.
Question: In a 120 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
A.22 seconds
B.12 seconds
C.10 seconds
D.8 seconds
Answer: D.8 seconds
Explanation: B runs 56 m in 7 sec.
=> B runs 120 m in 7/56*120 = 15 seconds
Since A beats B by 7 seconds, A runs 120 m in (15-7) = 8 seconds
Hence, A's time over the course = 8 seconds
ANSWER:D
Question: The triplicate ratio of 1:3 is?
A.1:64
B.1:62
C.1:27
D.3:64
Answer: C.1:27
Explanation: 1^3: 3^3 = 1:27
ANSWER:C
Question: A straight pipe 5 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
A. 1/6 and 1/4 only
B. 1/4 and 1/3 only
C. 1/6, 1/4, and 1/3
D. 1/12, 1/6 and 1/4
Answer: A. 1/6 and 1/4 only
Explanation: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/4, 6-4=2=2/12=1/6meters long pieces.
Answer: A.
Question: A rectangular block 10cm by 20cm by 35cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
A.6
B.56
C.15
D.40
Answer: B.56
Explanation: Volume of the block = 10*20*35 = 7000 cm^3
Side of the largest cube = H.C.F of 10,20,35 = 5cm
Volume of the cube = 5*5*5= 125 cm^3
Number of cubes = 7000/125 = 56
Answer is B
Question: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 500 feet. What is its area, in square feet?
A.12,000
B.19,600
C.20,000
D.20,400
Answer: A.12,000
Explanation: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.
diagonal = 200
2x + 2y = 560, or x + y = 280
a^2 + b^2 = c^2 for each the sides of the triangle
using the ratio 3:4:5 for sides, and knowing c = 500, you can deduce the following
a=300
b=400
300x400=120,000
A is the answer.