http://www.wmich.edu/mathclub/files/GR8767.pdf

How do I solve number 25?

The question is:

x and y are positive integers such that

Which of the following must also be divisible by 11?

A: 4x + 6y

B: x + y + 5

C: 9x + 4y

D: 4x - 9y

E: x + y - 1

## General Strategy for GR8767 #25

### General Strategy for GR8767 #25

Last edited by markisus on Tue Mar 12, 2013 12:21 am, edited 2 times in total.

### Re: General Strategy for GR8767 #25

Probably the quickest way is to just multiply the original expression modulo 11 and check each of the answers.

If

3x + 7y = 0 (mod 11),

then by multiplying by 4 we find that

x + 6y = 0 (mod 11),

so adding both together shows that

4x + 2y = 0 (mod 11).

This is the same as

4x - 9y (mod 11),

so the answer is D.

If

3x + 7y = 0 (mod 11),

then by multiplying by 4 we find that

x + 6y = 0 (mod 11),

so adding both together shows that

4x + 2y = 0 (mod 11).

This is the same as

4x - 9y (mod 11),

so the answer is D.

### Re: General Strategy for GR8767 #25

Oh nice! Thanks.