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 number?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 72
Given :
Number (N) = 7p5964q28
N is divisible by 8 and 11
Concept used :
Divisibility rule of 8 and 11
Calculations :
Largest possible value of q to be divisible by 8 = 9
⇒ 928/8 = 116
For, value of q = 9,
N is divisible by 11 when
⇒ (7 + 5 + 6 + 9 + 8) - (p + 9 + 4 + 2)
⇒ 20 - p
If (20 - p) is divisible by 11 then p = 9
Put the value of p and q in the given equation below
⇒ p2 - q
⇒ 81 - 9
⇒ 72