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If x and y are positive integers such that (3x 7y)is a multiple of 11,then which of the following will be divisible by 11? A)4x 6y B)x y 4 C)9x 4y D)4x-9y?
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Most Upvoted Answer
If x and y are positive integers such that (3x 7y)is a multiple of 11,...
Given:
- x and y are positive integers
- (3x + 7y) is a multiple of 11

To find:
Which of the following expressions is divisible by 11?

Approach:
We can use the divisibility rule for 11 to determine which expression is divisible by 11. According to the rule, a number is divisible by 11 if the difference between the sum of its alternate digits (from left to right) is divisible by 11.

Solution:
Let's apply the divisibility rule for 11 to each expression:

A) 4x + 6y
- Sum of alternate digits: 4 + 6 = 10
- Since 10 is not divisible by 11, A) is not divisible by 11.

B) xy + 4
- Sum of alternate digits: x + 4
- We cannot determine the divisibility by 11 without knowing the specific values of x and y. Therefore, we cannot conclude if B) is divisible by 11.

C) 9x + 4y
- Sum of alternate digits: 9 + 4 = 13
- Since 13 is not divisible by 11, C) is not divisible by 11.

D) 4x - 9y
- Sum of alternate digits: 4 - 9 = -5
- Since -5 is not divisible by 11, D) is not divisible by 11.

Conclusion:
None of the given expressions (A, B, C, or D) is guaranteed to be divisible by 11. The divisibility by 11 depends on the specific values of x and y.
Community Answer
If x and y are positive integers such that (3x 7y)is a multiple of 11,...
Option c
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If x and y are positive integers such that (3x 7y)is a multiple of 11,then which of the following will be divisible by 11? A)4x 6y B)x y 4 C)9x 4y D)4x-9y?
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