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If 3x + 7y is a multiple of 11, then which of the following is divisible by 11?
A4x + 6y
B4x − 9y
C9x + 4y
Dx + y + 4
Answer & Solution
Correct answer: B. 4x − 9y
1. Given 3x + 7y ≡ 0 (mod 11).
2. Multiply both sides by 4: 12x + 28y ≡ 0 → x + 6y ≡ 0 → 4x + 24y ≡ 0 → 4x + 2y ≡ 0 (mod 11). Also 4x − 9y has 4x ≡ -2y so 4x − 9y ≡ -2y − 9y = -11y ≡ 0.
3. Therefore 4x − 9y is divisible by 11.
_Source: KMAT Karnataka 2021 PYQ Q.34_