Question

If the nine-digit number 7p5964q28 is completely divisible by 88, what is the value of (p² - q), for the largest value of q, where p and q are natural numbers?

Answer 1

Correct Answer - Option 3 : 72

Given:

Number = 7p5964q28 

Calculation:

Number should be divisible by 88 then number should be divisible by 8 and 11 both.

Largest possible value of q to be divisible by 8 is = 9

⇒ 928/8 = 116

For q = 9, then

Number should be divisible by 11 -

= (7 + 5 + 6 + 9 + 8) - (p + 9 + 4 + 2) 

= 20 - p

(20 - p) should be divisible by 11 then for p = 9 this condition will satisfy.

So, possible value of p = 9

Then,

∴ p² - q = 81 - 9 = 72