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# If the average height of three people is 68 inches, is the shortest pe

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Math Expert
Joined: 02 Sep 2009
Posts: 43792
If the average height of three people is 68 inches, is the shortest pe [#permalink]

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06 Feb 2018, 04:40
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If the average height of three people is 68 inches, is the shortest person more than 60 inches tall?

(1) The height of the tallest person is 72 inches.

(2) One of the persons is 70 inches tall.
[Reveal] Spoiler: OA

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Re: If the average height of three people is 68 inches, is the shortest pe [#permalink]

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07 Feb 2018, 05:01
Bunuel wrote:
If the average height of three people is 68 inches, is the shortest person more than 60 inches tall?

(1) The height of the tallest person is 72 inches.

(2) One of the persons is 70 inches tall.

Let the heights of three be denoted by a, b, c respectively such that a <= b <= c
Given: a+b+c = 3*68 = 204. We have to determine whether a > 60 or not.
Now if a=60, then b+c = 204-60 = 144. This means if (b+c) < 144, then definitely a > 60 otherwise not.

(1) Given c=72, this means (a+b) = 204-72 = 132.
We could have b=72, then a=60. We could also have b=71 ,then a=61. (b could be 72 but not more than 72, since tallest person is 72 inches only)
So 'a' may or may not be greater than 60. Not sufficient.

(2) One person is 70. Sum of heights of other two = 204-70 = 134. Its possible that out of that 134, one of them is 60 and other is 74. But its also possible that one of them is 61 and other is 73. So 'a' may or may not be greater than 60. Not sufficient.

Combining the two statements, one of them (tallest) is 72, other is 70. Their sum = 72+70 = 142. this is < 144, so definitely a will be > 60. (actually a = 204-142 = 62)
So sufficient.

Re: If the average height of three people is 68 inches, is the shortest pe   [#permalink] 07 Feb 2018, 05:01
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