If the 8-digit number 43x259y2 is divisible by 88, then which of the following expressions is not true?

Correct option is C

Given :

8-digit number = 43x259y2
It is divisible by 88.
Options given for x, y, and we have to find which is NOT true.

Concept Used:

Divisibility by 11

Rule:
(Sum of digits at odd places) - (Sum of digits at even places) = 0 or multiple of 11

Solution :

Divisibility by 8

A number is divisible by 8 if its last 3 digits are divisible by 8.

Last 3 digits = 9y2

Check for given options:

y = 1 $$\implies 912 \div 8 = 114$$​​

y = 9$$\implies 992 \div 8 = 124$$​​

y = 5$$\implies 952 \div 8 = 119$$​​

All options satisfy divisibility by 8.

Number: 4 3 x 2 5 9 y 2

Odd places: 4 + x + 5 + y = 9 + x + y

Even places: 3 + 2 + 9 + 2 = 16

Difference:
(9 + x + y) - 16 = x + y - 7

For divisibility by 11:
x + y - 7 = 0$$\text{ or } \pm 11$$​​

Check options:

Answer :

Option (c): x = 4 and y = 1 is NOT true.