Question

As nine-digit number 89563x87y is divisible by 72. What is the value of $\sqrt{7x-3y}$

• A. 8
• B. 5
• C. 4
• D. 6

Answer 1

Answer:

D. 6

Solution:

Given:

89563x87y is divisible by 72

Concept used:

Divisibility rule of 8 = If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.

Divisibility rule of 9 = If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Calculation:

72 = 8 × 9

So, the number should be divisible by both 8 and 9

Now,

87y is divisible by 8

The only possible value of y is 2

Now,

8 + 9 + 5 + 6 + 3 + x + 8 + 7 + 2 = 48 + x is divisible by 9

Clossest value of (48 + x) which is divisible by 9 is 54

So, x = 6

Now,

$\sqrt{7x-3y}=\sqrt{7 \times 6-3 \times 2}$

$=\sqrt{42-6}$

$=\sqrt{36}$

$=6$

Required answer is 6.