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Eighteen tokens, each of which is either a subway token

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Intern
Joined: 16 Jun 2011
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Eighteen tokens, each of which is either a subway token [#permalink]

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09 Dec 2013, 10:20
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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.
[Reveal] Spoiler: OA
Magoosh GMAT Instructor
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Re: Eighteen tokens, each of which is either a subway token [#permalink]

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09 Dec 2013, 14:08
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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.

Does all this make sense?
Mike
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Joined: 05 Jun 2014
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Location: India
GMAT 1: 610 Q44 V34
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Re: Eighteen tokens, each of which is either a subway token [#permalink]

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31 Jan 2015, 23:39
This makes a lot of sense. I went with (C) because I stopped after realizing that there were 2 ratios. But you went one step further and found out that the second ratio is not possible.

How did you know that you have to actually test the obtained ratio and just not choose (C) after getting 2 ratios ?
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Re: Eighteen tokens, each of which is either a subway token [#permalink]

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01 Feb 2015, 14:30
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Hi saleem1992,

DS questions are designed to test a variety of skills, including organization, accuracy, attention-to-detail, the ability to PROVE that you're right, etc. DS questions are a great way to assess the 'thoroughness' of your thinking, which is why there are so many of them in the Quant section. If you're not very thorough, then your Quant Scaled Score will suffer.

It's also worth noting that the correct answer is only "C" about 20% of the time, so if you find yourself picking that answer often, chances are that you're missing little things (or not doing enough work to prove what the actual answer is). You should come in to each DS question with a bit of cynicism and a purpose - do the necessary work to PROVE what the correct answer is. Theories and instincts are 'nice', but you're not going to score at a high level without doing actual work.

GMAT assassins aren't born, they're made,
Rich
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Re: Eighteen tokens, each of which is either a subway token [#permalink]

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21 May 2016, 06:07
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Re: Eighteen tokens, each of which is either a subway token [#permalink]

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24 Aug 2017, 09:06
Be alert when dealing with value based DS question. The value should be unique
Statement 1 :clearly is not sufficient to answer as we have no information for tokens in glass.
Statement 2 :Two cases can be there,
Case1: in mug number of Subway tickets is 2 and number of bus tickets is 1(from information)
$$\frac{S_m}{B_m}$$ = $$\frac{2}{1}$$ = 2*$$\frac{S_t}{B_t}$$
Thus $$\frac{S_t}{B_t}$$ = $$\frac{1}{1}$$, and we can find a unique answer

Case2:in mug number of Subway tickets is 1 and number of bus tickets is 2(from information)
$$\frac{S_m}{B_m}$$ = $$\frac{1}{2}$$ = 2*$$\frac{S_t}{B_t}$$
Thus $$\frac{S_t}{B_t}$$ = $$\frac{1}{4}$$,
this is going to divide tickets in fractions which is not possible. Thus this case is not possible.
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Re: Eighteen tokens, each of which is either a subway token   [#permalink] 24 Aug 2017, 09:06
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