wastedyouth wrote:

Eighteen tokens, each of which is either a subway token or a bus token, are distributed between a glass and a mug. If the mug contains a total of 3 tokens and at least one of each type of token, what is the total ratio of subway tokens to bus tokens?

(1) Exactly one of the 3 tokens in the mug is a bus token.

(2) The ratio of subway tokens to bus tokens in the mug is twice the total ratio of subway tokens to bus tokens.

Dear

wastedyouth,

I'm happy to help with this.

You may find this blog helpful:

http://magoosh.com/gmat/2013/gmat-quant ... oportions/Statement #1 tells us only what's in the mug, not what's in the glass, so it is obviously not sufficient.

Statement #2 is very interesting. There are two possible cases to consider

Case I: mug contains {S, S, B}

In this case, the ratio in the mug is S:B = 2/1. The ratio in the total collection would be half of this, S:B = 1/1. Therefore, there could be 9 S tokens and 9 B tokens altogether. This is a possible scenario.

Case II: mug contains {S, B, B}

In this case, the ratio in the mug is S:B = 1/2. The ratio in the total collection would be half of this, S:B = 1/4. Thus, the ratio if S to the whole would be 1/5, and the whole would have to be divisible by 5. But the total number of tokens, 18, is not divisible by 5. Therefore, this is not possible.

According to this statement, the only case possible is {S, S, B}, which makes the total ratio 1/1. This statement allows us to give a definitive answer to the prompt question, so this statement, alone and by itself, is

sufficient.

Answer =

(B)Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)