phoenix9801 wrote:A class contains only juniors and seniors in a ratio of p:q. How many seniors are there if there are only r juniors?

p juniors --> q seniors
1 junior ---> q/p senior
r juniors --> (q/p)*r seniors

The correct answer is D.

phoenix9801 wrote:For every x executives there are 2y directors. If there are z executives, how many total executives and directors are there?

x executives --> 2y directors
1 executive ---> (2y/x) directors
z executives --> (2y/x)*z directors

Hence, total executives and directors = [z + z*(2y/x)] = [xz + 2yz]/x

Check your options.

phoenix9801 wrote:Can you plug in number to make my life easier??

To solve this by plugging numbers you have to determine the expression qr/p. Without determining that we cannot plug numbers. Hence, the approach I made is more easier and less time consuming than plugging numbers.

But this problem can be solved efficiently by plugging the options.
We know that, ratio of number of juniors to number of seniors is p:q.

Let's check each of the options for which r/(option) = p/q

• A) r/[q(r+p)] ≠ p/q
  B) r/[pq/p] ≠ p/q
  C) r/[pr/q] ≠ p/q
  D) r/[qr/p] = p/q ---> CORRECT OPTION
  E) r/[qp/r] ≠ p/q

The correct answer is D.