Divisibilty
Type 1: BASIC DIVISIBILITY
1. 7386038 is divisible by: [CDS 2001, 02]
(a) 3
(b) 4
(c) 9
(d) 11
Answer: (d)
Explanation:
The given number is 7386038.
The sum of the digits at even places is = 3+ 6+ 3=12.
The sum of the digits at odd places is = 7+ 8+ 0+ 8 = 23.
The difference is given by 23-12 = 1
2. Which one of the following is divisible by 9? [CDS 1999]
(a) 23, 50, 821
(b) 28, 70, 052
(c) 42, 13, 533
(d) 64, 000, 80
Answer: (d)
Explanation:
(a) 2350821 = 2+3+5+0+8+2+1 = 21, not divisible by 9
(b) 2870052 = 2+8+7+5+2 = 24, not divisible by 9.
(c) 4213533 = 4+2+1+3+5+3+3 = 19, not divisible by 9.
(d) 6400080 = 6+4+8 = 18, divisible by 9.
So, the answer is (d) 64000
3. Which one of the following numbers is divisible by 11? [CDS 2001]
(a) 4823718
(b) 8423718
(c) 8432718
(d) 4832718
Answer: (d)
Explanation:
4832718 = (4+3+7+8) – (8+2+1) = 11
So, the given number is divisible by 11
4. Which one of the following numbers is divisible by 99? [CDS 2002, 01]
(a) 3572404
(b) 135792
(c) 913464
(d) 114345
Answer: (d)
Explanation:
The sum of all the digits of 114345 is 18.
The sum of all digits at even places and odd places are 9 and 9 respectively.
The difference between the sums is 0.
So, the number is divisible by both 9 and 11 and hence by 99.
Type 2: DIVISIBILITY WITH ADDITION AND SUBTRACTION
5. The sum of three consecutive natural numbers each divisible by 3 is 72. What is the largest among them? [SSC Grad. 1999]
(a) 21
(b) 24
(c) 27
(d) 30
Answer: (c)
Explanation:
Let us take three consecutive numbers which are divisible by 3 are, 3x, 3x+3 and 3x+6.
Consider x as 7,
The largest of them= 27.
6. In a six digit number, the sum of the digits in the even places is 9 and the sum of the digits in the odd places is 20. All such numbers are divisible by:
(a) 7
(b) 9
(c) 6
(d) 11
Answer: (d)
Explanation:
Given that the sum of the digits at even places is 9 and that of at odd places is 20.
The difference between the two sums is 20-9=11.
So, all such numbers are divisible by 11
7. If the number 7×86038 is exactly divisible by 11, then the smallest whole number in place of x?
(a) 2
(b) 3
(c) 1
(d) 4
Answer: (b)
Explanation:
The given number =7×86038
Sum of the odd places =8+0+8+7=23
Sum of the even places = 3+6+x
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(9+x) = divisible by 11
14 – x = divisible by 11.
X must be 3, to make given number divisible by 11.
8. Which one of the following numbers will completely divide by 
?
(a) 7
(b) 11
(c) 9
(d) 13
Answer: (b)
Explanation:
9. The total number of two digit positive integer < than 100, which are not divisible by 2, 3 and 5 is
(a) 23
(b) 24
(c) 25
(d) 26
Answer: (b)
Explanation:
Numbers less than 100 divisible by 2 are 10, 12, 14, 16,… 98
Total numbers divisible by 2 are 45
Remaining numbers are 11, 13, 15, 17, 19, … 99 = 45 integers
Numbers divisible by 3 in the above numbers
15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93 and 99
Total numbers divisible by 3 are = 15
Remaining integers = 45 – 15 = 30
Numbers divisible by 5 in the remaining numbers = 25, 35, 55, 65, 85, 95
Total numbers = 6
Remaining 30–6 = 24 numbers are not divisible by 2, 3 and 5
10. 
When n is an integer > 0 is divisible by
(a) 120
(b) 127
(c) 130
(d) 137
Answer: (b)