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# There are 4 men of different heights. If the difference amon

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Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
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There are 4 men of different heights. If the difference amon [#permalink]

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04 Aug 2010, 07:03
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Question Stats:

17% (00:00) correct 83% (00:45) wrong based on 12 sessions

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There are 4 men of different heights. If the difference among the first 3 men was 2 inch and the difference between the third and fourth was 6 inch and average height was 74. How tall was the 4th man ?

A 70
B 78
C 74
D 80
E 84
[Reveal] Spoiler: OA

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Re: PS - Need definite solution ! [#permalink]

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04 Aug 2010, 07:49
nusmavrik wrote:
Sorry I marked this by POE.

There are 4 men of different heights. If the difference among the first 3 men was 2 inch and the difference between the third and fourth was 6 inch and average height was 74. How tall was the 4th man ?

A 70
B 78
C 74
D 80
E 84

The wording of this question is poor but I think it means the following:

Let the first be $$x$$ inches tall, then the second would be $$x+2$$ inches tall, the third $$x+2+2=x+4$$ inches tall and the fourth $$x+4+6=x+10$$ inches tall.

As the average height is 74 inches then the sum of their heights is 74*4, so $$x+(x+2)+(x+4)+(x+10)=74*4$$ --> $$4x=280$$ --> $$x=70$$ --> the fourth men is $$x+10=80$$ inches tall.

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Re: PS - Need definite solution ! [#permalink]

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04 Aug 2010, 10:59
I arrived to the same result for it D

My approach was slightly different

The average of an even number of a items arranged in an ascending way is in the middle of two in the center

___ ____ 74 _____ ____

From the question stem we get the differences among each of the men, difference that totals 10 from the smallest to the biggest

___ +2 ____ +2_____ +6 ___

So we get that the first man's height is 70 +10 = 80

D

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Re: PS - Need definite solution ! [#permalink]

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04 Aug 2010, 11:10
Quote:
There are 4 men of different heights. If the difference among the first 3 men was 2 inch and the difference between the third and fourth was 6 inch and average height was 74. How tall was the 4th man ?

Are you sure you're not paraphrasing the question? If you are, kindly post the actual wording of the question henceforth. It helps users answer your queries more efficiently instead of having to second guess the nature of the question. The problem with the wording of the question is that it mentions a "difference in height". However, this can be interpreted in two ways, with either person being taller and hence can lead to different results.

Assuming you meant that the difference in height between the first and second, and the second and third were respectively 2 inches each, the problem can be solved as follows.

Let the first man's height be $$X$$

Second man's height $$= X + 2$$

Third man's height$$= (X+2)+2 = X+4$$

Fourth man's height $$= X+4+6 = X+10$$

Average = (Total height of all men)/Number of men$$= \frac{X+X+2+X+4+X+10}{4} = \frac{4X + 16}{4} = X+4 = 74$$ Hence, height of the fourth man$$= X+10 = 80$$

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Re: PS - Need definite solution ! [#permalink]

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07 Aug 2010, 04:25
i got the answer but took the long route ...I mark D

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Re: PS - Need definite solution ! [#permalink]

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20 Dec 2012, 22:28
nusmavrik wrote:
Sorry I marked this by POE.

There are 4 men of different heights. If the difference among the first 3 men was 2 inch and the difference between the third and fourth was 6 inch and average height was 74. How tall was the 4th man ?

A 70
B 78
C 74
D 80
E 84

If I solved it with the others' assumption, I get 80 as well. But, yeah the wording of the question is poor. "difference among the first 3 men was 2 inch" - yeah perhaps the three are progressing by 2 inch..
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Re: PS - Need definite solution !   [#permalink] 20 Dec 2012, 22:28
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