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## Sequence and Series

tagged by: Roland2rule

### Top Member

Roland2rule Legendary Member
Joined
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#### Sequence and Series

Fri Dec 29, 2017 9:07 am
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

OA is B
Should we use the G.P or A.P formula to solve this? An Expert contribution is needed pls.Thanks

### Top Member

elias.latour.apex Master | Next Rank: 500 Posts
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Posted:
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GMAT Score:
770
Fri Jan 05, 2018 5:54 am
Meaning no disrespect to the Economist GMAT Tutor, but any of a number of answers is possible. It depends entirely on one's understanding of the question. The question states: "... the difference among the first 3 men was 2 [inches]...," a statement that EGT has taken to mean that man 1 is the shortest, man 2 is 2 inches taller, and man 3 is 2 inches taller than that. But is this the only interpretation? Couldn't one suppose that man 1 was the shortest, man 2 was 1 inch taller, and man 3 was 2 inches taller than the first? This would result in a 2 inch difference "among them." If that is the case, then the correct answer would be 79Â¼.

But even this assumes that man 1 is the shortest. Isn't it equally possible that man 3 was the shortest, at 71 inches, man 2 at 73 inches, and man 1 at 75 inches, leaving man 4 at 77 inches, 6 inches taller than the third man?

Or perhaps the 3rd man is the middle of the three heights. The problem doesn't say. In my opinion, the language should be cleaned up to eliminate not only the grammatical errors but also the ambiguity.

_________________
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### GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
Joined
04 Oct 2017
Posted:
551 messages
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Fri Jan 05, 2018 5:23 am
Hello Roland2rule.

Let's take a look at your question.

First of all, there is a mistake. B is NOT the correct answer. Let's see which one is the correct option.

We have 4 men with different heights. We can set the following sequence with the height of each man: $$m_1,\ \ m_1+2\ ,\ \ m_1\ +\ 4\ ,\ m_1\ +\ 10.$$ On the other hand, we know that the average is 74. It implies that $$\frac{m_1+m_1+2+m_1+4+m_1+10}{4}=74\ \Leftrightarrow\ \ \frac{4m_1+16}{4}=\ 74$$ $$\frac{4\left(m_1+4\right)}{4}=\ 74\ \Leftrightarrow\ \ m_1+4=74\ \Leftrightarrow\ m_1=\ 70.$$ It implies that the height of the fourth man is $$m_1+10=\ 70+10=80.$$ Therefore, the correct answer is the option D=80.

Feel free to ask me again if you have a doubt.

Regards.

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