Divisibility Rule for 9

Q.

If the 4-digit number x27y is exactly divisible by 9, then the least value of (x + y) is

(a) 0

(b) 3

(c) 6

(d) 9

Q.

If $x4y5z$ is exactly divisible by $9,$ then the least value of $(x+y+z)$ is

(a) $3$

(b) $6$

(c) $9$

(d) $0$

Q. If a 4-digit number 4XY2 is exactly divisible by 3, then which of the following can be the least value of (X + Y)?

1. 3
2. 5
3. 6
4. 4

Q.

If 1A2B5 is exactly divisible by 9, then the least value of (A + B) is

1. 0

2. 1

3. 2

4. 10

Q.

Given that the number $\overline{67y19}$ is divisible by 9, where y is a digit, what are the possible values of y?

Q.

Which one of the following numbers is divisible by 9?

1. 568711

2. 962497

3. 966333

4. 1257777

Q.

If 21y5 is a multiple of 9, where y is a digit, which of the numbers can take the possible value of y?

1. 1

2. 5

3. 7

4. 8

Q. If 21z4 is a multiple of 9, where z is a digit, what might be the values of z?

1. 2
2. 0
3. 5
4. All of these

Q.

If a+b+c is divisible by 9, the 3 digit number abc is divisible by 3, when a, b and c lie from 1-9.

1. True

2. False

Q.

621 is divisible by 9.

1. True

2. False

Q.

$5x555\text{a multiple of 9 ?}$

Q. Find the greatest and the smallest numbers.
$4536$, $4892$, $4370$, $4452$.

Q.

If x is a digit of the number $\overline{66784x}$ such that it is divisible by 9, find the possible values of x.

1. 6

2. 5

3. 14

4. 2

Q.

Find the value of M so that M56 is divisible by 9

1. 3

2. 7

3. 2

4. 4

Q. Which number has to be added as the last digit of 2257_ to make it divisible by 9?

1. 2
2. 5
3. 9
4. 7

Q. Which of the following numbers can perfectly divide 5763?

1. 3
2. 17
3. 27
4. 51

Q. Which smallest digit will replace ? in the number 678?74 to make it divisible by 3?

1. 2
2. 0
3. 1
4. 3

Q.

Question 2 (e)

Using divisibility test, determine whether the given number is divisible by 4; by 8:
12159

Q.

3134673 is divisible by

1. 10

2. 2 and 3

3. 6

4. 3 and 9

Q. If a number 3A98 is divisible by 11, find the value of A.
(3 marks)

Q.

Simon multiplied 4 consecutive numbers and said that, the product is always divisible by 6. Is her statement correct?

1. No, the statement is incorrect.
2. The statement is valid in some cases but not always.
3. Yes, the statement is always valid.
4. It cannot be determined and depends on the numbers taken.

Q. Which of the following numbers is divisible by 8?

(a) 87653234
(b) 78956042
(c) 64298602
(d) 98741032

Q.

Find the smallest value of 'a' if 3a9 is divisible by 9.

1. 2

2. 4

3. 6

4. 8

Q. Simplify: 57 in the form of 10a + b.

Q. What least number must be subtracted from $13601$, so that the remainder is divisible by $87$?

1. $23$
2. $31$
3. $29$
4. $49$
5. $37$

Q. If 21z4 is a multiple of 9, where z is a digit, what might be the values of z?

1. 2
2. 0
3. 5
4. All of these

Q.

3a21 is divisible by 3 and 9 , what should be the value of a

1. 5

2. 6

3. 9

4. 3

Q. How many numbers are divisible by $11$?
$121,4763,7321,7380,2475,8631,6591$

1. $4$
2. $2$
3. $5$
4. $3$

Q. Which of the following numbers is divisible by 6?

(a) 7908432
(b) 68719402
(c) 45982014
(d)

Q. Question 1
If 21y5 is a multiple of 9, where y is a digit, what is the value of y? [4 MARKS]