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If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the followings is also a multiple of 11 ?
Answer & Solution
Correct Answer:
Option
A
Let 3x + 7y = 11k
Then, y = $$\frac{(11k - 3x)}{7}$$
Then,
$$\eqalign{ & = 5x - 3y \cr & = 5x - \frac{{3(11k - 3x)}}{7} \cr & = \frac{{35x - 33k + 9x}}{7} \cr & = \frac{{44x - 33k}}{7} \cr & = \frac{{11(4x - 3k)}}{7} \cr} $$
Which is divisible by 11
Then, y = $$\frac{(11k - 3x)}{7}$$
Then,
$$\eqalign{ & = 5x - 3y \cr & = 5x - \frac{{3(11k - 3x)}}{7} \cr & = \frac{{35x - 33k + 9x}}{7} \cr & = \frac{{44x - 33k}}{7} \cr & = \frac{{11(4x - 3k)}}{7} \cr} $$
Which is divisible by 11
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