Home › CAT › Quantitative Aptitude › Number Theory › If 3x + 7y is a multiple of 11, then which of th…
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_
Related questions
The side opposite one acute angle of a right triangle is, for the other angle, the:Cosecant, secant and cotangent are described as the reciprocals of the:Tangent is the ratio of the opposite side to which side?Positive reference angles have terminal sides lying in which quadrant?A reference angle is the smallest positive acute angle formed with which axis?One radian is the central angle intercepting an arc equal in length to the:Cosine is the ratio of the hypotenuse and which side?How many coterminal angles does any angle have?