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

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

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New post 08 Feb 2019, 20:38
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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

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Re: Three positive integers a, b, and c are such that their average is 20  [#permalink]

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New post 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

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Re: Three positive integers a, b, and c are such that their average is 20  [#permalink]

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New post 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


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

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