This set of Aptitude Questions and Answers (MCQs) focuses on “Divisibility Rules for Composite Numbers”.
1. What number will replace A, if 3313A is divisible by 33?
a) 3
b) 2
c) 4
d) 6
View Answer
Explanation: For a number to be divisible by 33, it should be divisible by 3 and 11.
For a number to be divisible by 3, the sum of the digits should be divisible by 3 i.e., 3+3+1+3+A=10+A should be divisible by 3. Therefore, A can take 2, 5 or 8.
We know that, for a number to be divisible by 11, the difference between the sum of digits in odd places and the sum of digits in even places should be either 0 or a number divisible by 11.
(3+1+A) – (3+3) = A-2. Therefore, A=2.
2. Find the least perfect square which is divisible by 15, 25 and 36.
a) 1600
b) 900
c) 1800
d) 1200
View Answer
Explanation: Going with options, 1600 and 900 are the perfect square numbers.
900 is divisible by 15, 25 and 36. Therefore, least perfect square which is divisible by 15, 25 and 36 is 900.
3. What digits should come in place of A and B if the number 1456A6B is divisible by both 5 and 8?
a) 4 and 5
b) 6 and 5
c) 3 and 0
d) 8 and 0
View Answer
Explanation: For a number to be divisible by 5, last digit of the number should be either 0 or 5. So, B should be either 0 or 5.
For a number to be divisible by 8, last three digit of the number should be divisible by 8. So, B should be 0, if it has to be multiple of 8 and going with the options, A is 3, since 360 is divisible by 8.
4. What is the smallest number when increased by 7 is divisible by 9, 11 and 36?
a) 493
b) 394
c) 484
d) 389
View Answer
Explanation: LCM of 9, 11 and 36 is 396.
396 -7 = 389.
Therefore, the smallest number is 389.
5. Find the value of X and Y, if a number 77495X824Y is divisible by 8 and 9.
a) 8 and 0
b) 8 and 8
c) 6 and 8
d) 5 and 0
View Answer
Explanation: For a number to be divisible by 8, last three digits of the number should be divisible by 8.
24Y is divisible by 8, for Y = 0 or 8.
For a number to be divisible by 9, sum of all digits of the number should be divisible by 9.
7+7+4+9+5+X+8+2+4+Y = 46+X+Y.
X can take values 8 or 0.
Therefore, the value of X and Y is 8 and 0.
6. If m is an odd number greater than 1, then m(m2-1) is always divisible by which of the following number?
a) 48
b) 36
c) 24
d) 18
View Answer
Explanation: For m=3, 3*8=24
For m=5, 5*24=120
For, m=7, 7*48=36……
All the numbers are divisible by 24.
7. Find the nearest number to 6600, which is divisible by 18.
a) 6588
b) 6598
c) 6606
d) 6614
View Answer
Explanation: For a number to be divisible by 18, the number should be divisible by 2 and 9.
For a number to be divisible by 2, the number should be even.
For a number to be divisible by 9, sum of all digits of the number should be divisible by 9.
6588 and 6606 are divisible by 18. But the nearest number to 6600 is 6606.
8. Find the multiple of 22 in the following number.
a) 197175
b) 197153
c) 197131
d) 197142
View Answer
Explanation: For a number to be divisible by 22, the number should be divisible by 2 and 11.
For a number to be divisible by 2, the number should be even.
From the given options, the only even number is 197142.
Hence, 197142 is divisible by 22.
9. If m and n are two odd positive integers, then m4-n4 is divisible by which of the following number?
a) 12
b) 24
c) 8
d) 18
View Answer
Explanation: For m=3 and n=1, m4-n4 = 80, which is divisible by 8.
For m=5 and n=3, m4-n4 = 544, which is divisible by 8.
Therefore, m4-n4 is divisible by 8.
10. The difference between the square of two consecutive even integer is always divisible by which of the following number?
a) 4
b) 6
c) 8
d) 12
View Answer
Explanation: 42-22=12.
82-62=28.
222-202=84……
All the numbers are divisible by 4. Hence, the difference between the square of two consecutive even integer is always divisible by 4.
To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.
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