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# M10 #32

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Director
Joined: 25 Oct 2008
Posts: 610
Location: Kolkata,India
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M10 #32 [#permalink]  08 Oct 2009, 01:04
The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?

(C) 2008 GMAT Club - m10#32

* 179 cm and 172 cm
* 181 cm and 169 cm
* 173 cm and 178 cm
* 176 cm and 176 cm
* 174 cm and 177 cm

Denote $$X$$ as the sum of the heights of the two new people. From the stem it follows that $$\frac{(700 + X)}{6} \gt 175$$ . This reduces to $$X \gt 350$$ . Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.
The correct answer is B.

My question is that if X>350,then should'nt the two figures add up to more than 350??How is the answer which EQUAL to 350 the answer??
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Joined: 01 Jan 2009
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Schools: LBS
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Re: M10 #32 [#permalink]  08 Oct 2009, 01:11
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tejal777 wrote:
The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?

(C) 2008 GMAT Club - m10#32

* 179 cm and 172 cm
* 181 cm and 169 cm
* 173 cm and 178 cm
* 176 cm and 176 cm
* 174 cm and 177 cm

Denote $$X$$ as the sum of the heights of the two new people. From the stem it follows that $$\frac{(700 + X)}{6} \gt 175$$ . This reduces to $$X \gt 350$$ . Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.
The correct answer is B.

My question is that if X>350,then should'nt the two figures add up to more than 350??How is the answer which EQUAL to 350 the answer??

The average height of the people already is 175.

So if we add a group of people with average height more than 175 the total average will increase (as desired in the question)

But if you add a group of people with average height as 175, the total average will remain at 175 and not increase. Thus this group can not be the one added.

Hope it is clear now
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Re: M10 #32   [#permalink] 08 Oct 2009, 01:11
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# M10 #32

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