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# If a, b, and c are positive, is a > (b + c)/2 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 60555
If a, b, and c are positive, is a > (b + c)/2 ?  [#permalink]

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15 Nov 2019, 02:27
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Difficulty:

45% (medium)

Question Stats:

68% (01:54) correct 32% (02:02) wrong based on 34 sessions

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If a, b, and c are positive, is $$a > \frac{b + c}{2}$$ ?

(1) On the number line, a is closer to b than it is to c.
(2) b > c

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Math Expert
Joined: 02 Aug 2009
Posts: 8340
Re: If a, b, and c are positive, is a > (b + c)/2 ?  [#permalink]

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15 Nov 2019, 06:08
If a, b, and c are positive, is $$a > \frac{b + c}{2}$$ ?

The question is asking us whether a is greater than the average of b and c.

(1) On the number line, a is closer to b than it is to c.
The answer will be depend on the relative values of b and c.
0...a..b...|...c -------- NO
0...b..a.|.....c --------NO
0...c.|.b..a -----YES
0...c.....|...a..b ---YES
Insuff

(2) b > c
Insuff

Combined
c is closer to 0, and a is more than midpoint of b and c, so answer is YES
0...c.|.b..a -----YES
0...c....|....a..b ---YES
Suff

C
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Re: If a, b, and c are positive, is a > (b + c)/2 ?   [#permalink] 15 Nov 2019, 06:08
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