Divisibility by 9

Q. Question 1
If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

Q. Question 3
If 24x is a multiple of 3, where x is a digit, what is the value of x?

Q.

Question 43

If 213x27 is divisible by 9, then the value of x is 0.

Q.

Question 2
If 31z5 is a multiple of 9, where z is a digit, what is the value of z?
You will find that there are two answers for the last problem. Why is this so?

Q.

How many 5-digit numbers divisible by 11 are there containing each of the digits 2, 3, 4, 5, 6?

Q.

What is the smallest 5-digit number divisible by 11 and containing each of the digits 2, 3, 4, 5, 6?

Q.

If 5A5 is 3-digit number divisible by 9, then find the value of digit A.

1. 8

2. 9

3. 3

4. 5

Q. Sum of any two digit number and its reverse number is always divisible by 11.

1. True
2. False

Q.

Identify a number which is divisible by 5 but not by 10.

1. 60

2. 100

3. 55

4. 10

Q.

A teacher wrote a large number on a board and asked the students to tell about the divisors of the number one by one.

The 1st said, divisible by 2, the 2nd said by 3, the 3rd said by 4 and so on the 30th said the number is divisible by 31.

The teacher then commented that exactly 2 students were wrong, who spoke consecutively.

Which 2 students were wrong? Explain your answer with appropriate justification.

Q.

Take a two digit number 'ab' where a > b. When the difference between this number and the number obtained by reversing its digits is divided by 9, quotient will be equal to

1. $a-b$

2. $a+b$

3. $a^2-b^2$

4. $a^2+b^2$

Q. Test the divisibility of each of the following numbers by 11:
(i) 22222
(ii) 444444
(iii) 379654
(iv) 1057982
(v) 6543207
(vi) 818532
(vii) 900163
(viii) 7531622

Q.

The greatest four digits number which is divisible by 15, 25, 40 and 75 is:

1. 9600
2. 9800
3. 9300
4. 9500

Q. Question 1
If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

Q.

95635 is divisible by 11.

1. True

2. False

Q.

990 + 9999 is divisible by

1. 3

2. 9

3. 11

4. 7

Q.

If the number 41x is divisible by 9, then find the value of digit x.

1. 4

2. 5

3. 3

4. 6

Q.

By which of the following numbers is 392 divisible?

1. 9

2. 3
3. 2
4. 4

Q.

In the following replace * by the smallest number so that the given number is divisible by the number mentioned:
$817*67$ by$11$.

Q. is divisible by 11.

1. 585
2. 341
3. 777

Q.

If 37y4 is exactly divisible by 9, then the least value of y is

(a) 2

(b) 3

(c) 1

(d) 4

Q.

A number is divisible by $8$, by what other numbers will that number be divisible?

Q.

Using the digits 4, 5, 6, 7, 8, each once, construct a 5-digit number which is divisible by 132.

Q. Test the divisibility of each of the following numbers by 9:
(i) 327
(ii) 7524
(iii) 32022
(iv) 64302
(v) 89361
(vi) 14799
(vii) 66888
(viii) 30006
(ix) 33333

Q.

If 7x8 is exactly divisible by 9, then the least value of x is

(a) 0

(b) 2

(c) 3

(d) 5

Q.

$7x34\text{divisible by 9 ?}$

Q. 999 is divisible by ______.

1. 4
2. 7
3. 9
4. 6

Q.

68 + 86 is divisible by:

1. 11

2. 13

3. 9

4. 5

Q.

Question 2
If 31z5 is a multiple of 9, where z is a digit, what is the value of z?
You will find that there are two answers for the last problem. Why is this so?

Q.

The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by $9$ and ___________.