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# If the average of a and 15 is b, is b > a? (1) 14 < b < 15 (2) a + b

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
If the average of a and 15 is b, is b > a? (1) 14 < b < 15 (2) a + b  [#permalink]

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07 Jan 2018, 23:15
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Difficulty:

35% (medium)

Question Stats:

68% (02:05) correct 32% (02:02) wrong based on 34 sessions

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If the average of a and 15 is b, is b > a?

(1) 14 < b < 15
(2) a + b = 28.5

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Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: If the average of a and 15 is b, is b > a? (1) 14 < b < 15 (2) a + b  [#permalink]

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08 Jan 2018, 11:29
Bunuel wrote:
If the average of a and 15 is b, is b > a?

(1) 14 < b < 15
(2) a + b = 28.5

Given that (a+15)/2 = b or a+15 = 2b. We are asked whether b > a.
Now a = 2b - 15. We want to know whether b > 2b - 15 OR whether 15 > 2b-b OR whether 15 > b. Thus all we need to know is whether b is less than 15 or not.

(1) 14 < b < 15. So b < 15. Sufficient.

(2) a + b = 28.5. Replacing a with 2b - 15, we get 2b - 15 + b = 28.5 OR 3b = 43.5 Or b = 14.5. Thus b < 15. Sufficient.

Hence D answer
Re: If the average of a and 15 is b, is b > a? (1) 14 < b < 15 (2) a + b   [#permalink] 08 Jan 2018, 11:29
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# If the average of a and 15 is b, is b > a? (1) 14 < b < 15 (2) a + b

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