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# If a, b, c are positive numbers such that c = 10a + 12b and a + b = 1,

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Joined: 02 Sep 2009
Posts: 58340
If a, b, c are positive numbers such that c = 10a + 12b and a + b = 1,  [#permalink]

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26 Sep 2018, 05:31
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Difficulty:

55% (hard)

Question Stats:

63% (02:10) correct 37% (01:44) wrong based on 31 sessions

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If a, b, c are positive numbers such that c = 10a + 12b and a + b = 1, is c > 11?

(1) a > 1/2
(2) a > b

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Re: If a, b, c are positive numbers such that c = 10a + 12b and a + b = 1,  [#permalink]

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26 Sep 2018, 07:03
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Top Contributor
Bunuel wrote:
If a, b, c are positive numbers such that c = 10a + 12b and a + b = 1, is c > 11?

(1) a > 1/2
(2) a > b

Given: c = 10a + 12b and a + b = 1

Target question: Is c > 11?
This is a good candidate for rephrasing the target question.

See the video below for tips on rephrasing the target question

Given: c = 10a + 12b
Rewrite as: c = 10a + 10b + 2b
Rewrite as: c = 10(a + b) + 2b
This means: c = 10(1) + 2b [since we're also told that a+b = 1]
Simplify: This means: c = 10 + 2b

The target question asks Is c > 11?
Replace c with 10+2b to get: Is 10+2b > 11?
Subtract 10 from both sides to get: Is 2b > 1?
Divide both sides by 2 to get: Is b > 1/2?
So.....
REPHRASED target question: Is b > 1/2?

Statement 1: a > 1/2
First, we already know that a+b = 1 and that a and b are both POSITIVE.
So, if a > 1/2 then it must be the case that b < 1/2
So, the answer to the REPHRASED target question is NO, b is NOT greater than 1/2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a > b
Once again, we already know that a+b = 1 and that a and b are both POSITIVE.
So, if a > b, then we know that a > 1/2 and b < 1/2
So, the answer to the REPHRASED target question is NO, b is NOT greater than 1/2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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If a, b, c are positive numbers such that c = 10a + 12b and a + b = 1,  [#permalink]

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26 Sep 2018, 07:09
Wow. I got the same answer but knew there could be a better way of getting it done faster. GMATPrepNow
If a, b, c are positive numbers such that c = 10a + 12b and a + b = 1,   [#permalink] 26 Sep 2018, 07:09
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