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# If a is a positive number less than 10, is c greater than the average

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Math Expert
Joined: 02 Sep 2009
Posts: 43917
If a is a positive number less than 10, is c greater than the average [#permalink]

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08 Jan 2018, 22:39
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Difficulty:

55% (hard)

Question Stats:

55% (01:07) correct 45% (01:13) wrong based on 22 sessions

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If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.
[Reveal] Spoiler: OA

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If a is a positive number less than 10, is c greater than the average [#permalink]

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09 Jan 2018, 07:45
Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?

(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.

Given $$a<10$$ and to find is $$c>$$mid point of $$a$$ & $$10$$ i.e. $$c>\frac{a+10}{2}=>2c>a+10$$

Statement 1: This implies $$c$$ is more than the mid-point of $$a$$ & $$10$$ because mid-point will be equidistant from both $$a$$ & $$10$$ and given $$c$$ is closer to $$10$$ than $$a$$. Sufficient

Statement 2: implies $$2c-10>a=>2c>a+10$$. Sufficient

Option D
If a is a positive number less than 10, is c greater than the average   [#permalink] 09 Jan 2018, 07:45
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