0
$\begingroup$

I am working with this question:

A received 1/3 more votes than B. Which of the following could have been the total number of votes cast for the two candidates? Answer options are 12, 13, 14, 15, 16.

I can see that however many votes B got, A got the same number plus 1/3 more, so the total number of votes cast is $x + \frac{4}{3}x = \frac{7}{3}x$. I can also see that x has to be an integer, and that it should be evenly divisible by three.

I got that far, then couldn't see how to get anywhere with algebra. I solved the problem by testing multiples of three (first $x = 9$, then $x = 6$) to see if $2\frac{1}{3}x$ was in the list of answers. Of course it works for $x = 6$, but I feel like this was a very haphazard way of getting the answer.

Is there some way that knowing the total number of votes is $\frac{7}{3}x$ can help me determine the correct answer directly rather than testing values? I don't feel like this was a hard question, but I do feel like I'm missing some obvious connection between the ratio and the total.

$\endgroup$
  • 2
    $\begingroup$ To find $x$ you'll have to divide by $7$. So you need an answer that is a multiple of $7$. $\endgroup$ – lhf Nov 5 '13 at 1:13
1
$\begingroup$

You have figured out that $x$ must be divisible by three. Say $x = 3y$.

Then the total number of votes is $7 y$. So we see that the total is divisible by $7$. Now all you have to do is look at the answers and see that only one of them is divisible by $7$.

$\endgroup$
  • $\begingroup$ Yes, it's obvious now. I was looking at $\frac{7}{3}x$ and thinking it didn't tell me anything useful. But it tells me that the total is a multiple of 7. Thank you. $\endgroup$ – dumb question Nov 5 '13 at 1:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.