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# If you join all the vertices of a heptagon, how many quadrilaterals wi

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SVP
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If you join all the vertices of a heptagon, how many quadrilaterals wi  [#permalink]

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10 Feb 2017, 07:32
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Difficulty:

25% (medium)

Question Stats:

76% (01:05) correct 24% (02:03) wrong based on 43 sessions

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If you join all the vertices of a heptagon, how many quadrilaterals will you get?

72
36
25
35
120

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Re: If you join all the vertices of a heptagon, how many quadrilaterals wi  [#permalink]

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10 Feb 2017, 08:51
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Top Contributor
Source: http://www.testpreppractice.net

If you join all the vertices of a heptagon, how many quadrilaterals will you get?

A) 72
B) 36
C) 25
D) 35
E) 120

A heptagon is a 7-sided polygon.

ASIDE: the GMAT test-makers do not expect people to know this term.

A heptagon also has 7 vertices.
If you choose ANY 4 of the 7 vertices and connect them with lines, you will get a quadrilateral.

So, the question really becomes "In how many different ways can you select 4 of the 7 vertices?"

Since the order in which we select the 4 vertices does not matter, we can use combinations.

We can select 4 of the 7 vertices in 7C4 ways

7C4 = 7!/(4!3!)= 35

Cheers,
Brent
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Re: If you join all the vertices of a heptagon, how many quadrilaterals wi  [#permalink]

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10 Feb 2017, 09:15
As noted by the other poster, this problem will need to define "heptagon" for students. It also needs to specify "convex" or "regular," because actually it is possible to have three or even four collinear vertices of a non-convex heptagon, which would of course reduce the correct answer.
Re: If you join all the vertices of a heptagon, how many quadrilaterals wi &nbs [#permalink] 10 Feb 2017, 09:15
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