Fast method of Solving 8767 Q25

Forum for the GRE subject test in mathematics.
yoyobarn
Posts: 80
Joined: Sun Dec 19, 2010 7:01 am

Fast method of Solving 8767 Q25

Postby yoyobarn » Thu Dec 29, 2011 4:21 am

q25: Let x and y be positive integers such that 3x+7y is divisible by 11. 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

Is there a fast method for solving this type of question?

Slower method:
3x+7y=0 (mod 11)
Multiplying by 5,
15x+35y=0 (mod 11)
4x+2y=0 (mod 11)
4x-9y=0 (mod 11)

The problem is that it takes a while to guess that we need to multiply by 5 (so this problem might end up taking more than 2 minutes)

Thanks a lot.

apap
Posts: 14
Joined: Wed Oct 26, 2011 11:22 pm

Re: Fast method of Solving 8767 Q25

Postby apap » Thu Dec 29, 2011 4:50 am

How about substitution?

It's pretty easy to come with a solution. x=4 and y=3 works. Plugging this into the equations in the answers you'll see that only one of the choices is divisible by 11. These calculations shouldn't take more than 2 minutes but you might not be able to eliminate all answers in one go.




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