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Bob purchased 18 cans of soda, some of which contained diet soda. How

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Bob purchased 18 cans of soda, some of which contained diet soda. How  [#permalink]

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New post 19 Feb 2017, 04:07
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Bob purchased 18 cans of soda, some of which contained diet soda. How many of the cans did not contain diet soda?

(1) Of the cans Bob purchased, the number containing diet soda is equal to the number not containing diet soda.
(2) Of the cans Bob purchased, the number containing diet soda is odd

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Re: Bob purchased 18 cans of soda, some of which contained diet soda. How  [#permalink]

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New post 20 Feb 2017, 08:28
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SajjadAhmad wrote:
Bob purchased 18 cans of soda, some of which contained diet soda. How many of the cans did not contain diet soda?

(1) Of the cans Bob purchased, the number containing diet soda is equal to the number not containing diet soda.
(2) Of the cans Bob purchased, the number containing diet soda is odd


Target question: How many of the cans did NOT contain diet soda?

Given: Bob purchased 18 cans of soda

Statement 1: Of the cans Bob purchased, the number containing diet soda is equal to the number not containing diet soda.
So, of the 18 cans of soda, 9 cans contained diet soda, and 9 cans did NOT contain diet soda
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Of the cans Bob purchased, the number containing diet soda is odd
There are several scenarios that satisfy statement 2. Here are two:
Case a: Bob purchased 3 (odd) cans containing diet soda and 15 cans NOT containing diet soda.
Case b: Bob purchased 5 (odd) cans containing diet soda and 13 cans NOT containing diet soda.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Re: Bob purchased 18 cans of soda, some of which contained diet soda. How  [#permalink]

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New post 20 Jul 2017, 23:04
What made me hesitate? I was looking for/asking myself if there was a trick to statement (i) specifically, I wondered if there could be an e.g. that was neither soda nor diet soda which would make information provided in (i) insufficient. This thinking cost me a little time.
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Re: Bob purchased 18 cans of soda, some of which contained diet soda. How  [#permalink]

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New post 10 Dec 2017, 13:28
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Hi All,

The wording of this question is a bit 'quirky', but the math behind it is just basic Arithmetic. We're told that there are 18 cans of soda and that some of the cans contain diet soda. In basic terms, this means:
(# of Diet Cans) + (# of Non-Diet Cans) = 18

We're asked for the number of Non-Diet Cans.

1) Of the cans Bob purchased, the number containing diet soda is equal to the number not containing diet soda.

With this Fact, we know that there are the SAME number of each soda, so since there are 18 total cans, then there must be 9 of each.
Fact 1 is SUFFICIENT

2) Of the cans Bob purchased, the number containing diet soda is odd

Since there are 18 total cans, the number of Diet Cans could be 1, 3, 5, 7, etc., which means that the number of Non-Diet Cans could be 17, 15, 13, 11, etc.
Fact 2 is INSUFFICIENT

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Re: Bob purchased 18 cans of soda, some of which contained diet soda. How &nbs [#permalink] 10 Dec 2017, 13:28
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