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# Three positive integers a, b, and c are such that their average is 20

Author Message
Manager
Joined: 11 Dec 2013
Posts: 108
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Three positive integers a, b, and c are such that their average is 20  [#permalink]

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08 Feb 2019, 20:38
00:00

Difficulty:

(N/A)

Question Stats:

90% (02:22) correct 10% (03:54) wrong based on 10 sessions

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Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
A) 23
B) 21
C) 25
D) 26
E) 24

Source : gmatpractice

_________________

Manager
Joined: 07 Aug 2017
Posts: 60
Location: India
GPA: 4
WE: Information Technology (Consulting)
Re: Three positive integers a, b, and c are such that their average is 20  [#permalink]

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08 Feb 2019, 21:02
IMO C

From a ≤ b ≤ c and median = a + 11, it can be inferred that b is the median and b = a + 11. Also it is given that $$\frac{a+b+c}{3}=20$$. Therefore, $$2a+c=49$$
So we have,
$$b=a+11$$
$$a=\frac{49-c}{2}$$

Plugging the values,
A - c=23, a=13, b=24. Incorrect, as b≤c
B - c=21, a=14, b=25. Incorrect, as b≤c
C - c=25, a=12, b=23. Correct

-------------------------------------------------------
Math Expert
Joined: 02 Sep 2009
Posts: 52911
Re: Three positive integers a, b, and c are such that their average is 20  [#permalink]

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08 Feb 2019, 23:08
4d wrote:
Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
A) 23
B) 21
C) 25
D) 26
E) 24

Source : gmatpractice

Discussed here: https://gmatclub.com/forum/three-positi ... 12496.html
_________________
Re: Three positive integers a, b, and c are such that their average is 20   [#permalink] 08 Feb 2019, 23:08
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