Question

If the eight-digit number 134A492B is divisible by 8 and 9, then, what is the value of (B²- A²)/13?
1. 2
2. 4
3. 3
4. 5

Answer 1

Correct Answer - Option 3 : 3

GIVEN:

The eight-digit number 134A492B is divisible by 8 and 9.

CONCEPT:

Divisibility law of 8 - A number divisible by 8 if its last three digits are divisible by 8.

Divisibility law of 9 - A number divisible by 9 if the sum of its digit is divisible by 9.

CALCULATION:

8-digit number 134A492B divisible by 8 if its last three-digit divisible by 8.

92B divisible by 8

If B = 8 or 0, so number become 134A4928 or 134A490

Case (i): when B = 0, eight-digit number 134A4920 divisible by 9 if sum of its digit divisible by 9.

⇒ 1 + 3 + 4 + A + 4 + 9 + 2 + 0

⇒ 23 + A

If we put, A = 4, then number become 27 which is divisible by 9.

So, A = 4 and B = 0

According to question -

⇒ (B²- A²)/13

⇒ (0² – 4²)/13

⇒ -16/13, it is not the answer given in the options.

Case (ii): When B = 8, 8-digit number 134A4928 divisible by 9 if the sum of its digit divisible by 9.

⇒ 1 + 3 + 4 + A + 4 + 9 + 2 + 8

⇒ 31 + A

If we put, A = 5, then number become 36 which is divisible by 9.

So, A = 5 and B = 8

According to question -

⇒ (B²- A²)/13

⇒ (8² – 5²)/13

⇒ 39/13

⇒ 3

It is the correct answer.