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# If the average height of three people with different heights is 68 inc

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If the average height of three people with different heights is 68 inc  [#permalink]

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06 Feb 2018, 05:40
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If the average height of three people with different heights 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.

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Re: If the average height of three people with different heights is 68 inc  [#permalink]

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07 Feb 2018, 06:01
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.

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Re: If the average height of three people with different heights is 68 inc  [#permalink]

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09 Mar 2018, 00:52
Hi Bunuel,

Statement 1:
I have one question, can we assume there can be only one tallest person?
if thats the case, Statement 1 is clearly sufficient.
72 + (<72) + small = 204
small > 60

On the other hand, if we assume there are two people with tallest height.
then 72 + 72 + small = 204

small = 60 which is not sufficient

thanks
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Re: If the average height of three people with different heights is 68 inc  [#permalink]

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09 Mar 2018, 01:02
hellosanthosh2k2 wrote:
Hi Bunuel,

Statement 1:
I have one question, can we assume there can be only one tallest person?
if thats the case, Statement 1 is clearly sufficient.
72 + (<72) + small = 204
small > 60

On the other hand, if we assume there are two people with tallest height.
then 72 + 72 + small = 204

small = 60 which is not sufficient

thanks

Edited the question to avoid this issue.
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Re: If the average height of three people with different heights is 68 inc  [#permalink]

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09 Mar 2018, 01:50
Bunuel wrote:
If the average height of three people with different heights 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 Heights of three people are A, B and C such that A < B < C
i.e. A+B+C = 68*3 = 204

Question: Is A > 60?

Statement 1: C = 72

i.e. A+B = 204-72 = 132

But now maximum value of B must be less than 72 as Tallest has height 72
60+72 = 132
therefore if B < 72 then A > 60, Hence

SUFFICIENT

Statement 2: One of the persons is 70 inches tall.

Case 1: C = 70, B = 69, A = 65 i.e. A > 60
Case 2: C = 80, B = 70, A = 54 i.e. A < 60
NOT SUFFICIENT

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Re: If the average height of three people with different heights is 68 inc  [#permalink]

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09 Mar 2018, 01:51
Bunuel wrote:
If the average height of three people with different heights 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.

Since we're asked about the height of the shortest person, we'll look at the extremes of the range.
This is a Logical approach.

(1) If the tallest is 72, we'll try making the second tallest as tall as possible (so that the shortest will be as short as possible).
Then the second tallest is 71.
Since the tallest is 72-68=4 more than average and the second tallest is 71-68=3 more than average,
the shortest needs to balance them out by being 4+3=7 less than average, which is 68 - 7 = 61.
Sufficient.

(2) Again let's try looking at the extremes. First, say the heights are very different from each other.
Say our tallest is 90 or even 100. Then clearly the shortest must be much less than 60 (we won't bother calculating this!)
Now, let's look at the other extreme - where the heights are very close to each other.
If the tallest is 70, the middle is exactly average, then the shortest needs to be 'opposite' to 70, that is, at 66.
Insufficient.

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Re: If the average height of three people with different heights is 68 inc  [#permalink]

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09 Mar 2018, 06:30
Bunuel wrote:
hellosanthosh2k2 wrote:
Hi Bunuel,

Statement 1:
I have one question, can we assume there can be only one tallest person?
if thats the case, Statement 1 is clearly sufficient.
72 + (<72) + small = 204
small > 60

On the other hand, if we assume there are two people with tallest height.
then 72 + 72 + small = 204

small = 60 which is not sufficient

thanks

Edited the question to avoid this issue.

Thanks Bunuel, now clear A
Re: If the average height of three people with different heights is 68 inc   [#permalink] 09 Mar 2018, 06:30
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