If a 9 - digit number 29x4957y4 is divisible by 88, then which of the following is NOT true?

Correct option is B

Given:

A 9-digit number 29x4957y4 is divisible by 88. 

Formula Used:

For divisibility by 8, check if the last three digits are divisible by 8.

For divisibility by 11, check if the difference between the sum of the odd-position digits and the sum of the even-position digits is divisible by 11.

Solution: 

For Divisibility by 11 

Odd-position digits:  Sum = 2 + x + 9 + 7 + 4 = x + 22

Even-position digits: Sum = 9 + 4 + 5 + y = 18 + y 

Difference  = (x + 22) - (18 + y) = x + 4 - y

For Divisibility by 8

We need to check whether 7y4 is divisible by 8 for each option:

Option A: x = 7, y = 0:

Last three digits = 704

704 ÷ 8 = 88, so it is divisible by 8.

now,  difference = 7 + 4 - 0 = 11 (satisfies divisibility by 11)

Option B: x = 7, y = 1:

Last three digits = 714

714 ÷ 8 = 89.25, so it is not divisible by 8.

Option C: x = 0, y = 4:

Last three digits = 744

744 ÷ 8 = 93, so it is divisible by 8.

Difference = 0 + 4 - 4 = 0 (satisfies divisibility by 11)

Option D: x = 4, y = 8:

Last three digits = 784

784 ÷ 8 = 98, so it is divisible by 8. 

difference = 4 + 4 - 8 = 0(satisfies divisibility by 11)

Option B does not satisfy both the divisibility rules for 8 and 11, so the correct answer is: option(B)