Practice Questions

Solution:
Given:

Given number is 785x3678y

The number is divisible by 72

Concept used:

If a number is divisible by 72 then the number will be divisible by 8 and 9

A number is divisible by 8 if the last three digits are divisible by 8.

A number is divisible by 9 if the sum of its digits is divisible by 9.

Calculation:

As, the number 785x3678y is divisible by 8

⇒ 78y is divisible by 8

For y = 4, the number is divisible by 8

As, the number 785x3678y is divisible by 9

⇒ 7 + 8 + 5 + x + 3 + 6 + 7 + 8 + y is divisible by 9

⇒ 44 + x + y is divisible by 9

⇒ 44 + x + 4 is divisible by 9

⇒ 48 + x is divisible by 9

Nearest integer to 48 is 54 which is divisible by 9

48 + x = 54

⇒ x = 6

x – y = 6 – 4

⇒ 2

∴ The value of (x – y) is 2

If a nine-digit number 785x3678y is divisible by 72, then the value of (x - y) is :

Solution: Divisibility rule of 11 is, (x + 4 + 1) – (4 + 4) is divisible by 11, ⇒ For (x – 3) to be divisible by 11, x = 3 ∴ Value of x = 3

If the number x4441 is divisible by 11, what is the face value of x?

$(2^{89}/9) $$⇒ \frac{(2^3)^29 × 2^2}{9}$ $⇒ \frac{(8)^29 \times{4}}{9}$ $⇒\frac{(-1)^29 × 4}{9}$$ ⇒ \frac{(-1\times{4})}{9}$ $⇒\frac{ - 4}{9}$ ⇒ Remainder = - 4 + 9 = 5

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If a nine-digit number 785x3678y is divisible by 72, then the value of (x - y) is :

If the number x4441 is divisible by 11, what is the face value of x?