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A 4-digit number 1xy7 is divisible by 11. What is the value of x - y?
Question

A 4-digit number 1xy7 is divisible by 11. What is the value of x - y?

A.

-4

B.

-8

C.

-6

D.

-2

Correct option is C


Divisibility rule for 11: (Sum of odd positions) − (Sum of even positions) = multiple of 11.
· Sum of digits in odd places (positions 1 and 3): 1 + y.
· Sum of digits in even places (positions 2 and 4): x + 7.
This difference, (1 + y) - (x + 7) = y - x – 6, must be 0 or ±11 (or another multiple of 11) for divisibility by 11.
The valid scenario that works is y – x – 6 = 0
⇒ y – x = 6
⇒ x – y = −6.

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