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From the figure shown, each of N people was asked to take 7

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by fskilnik@GMATH » Fri Mar 01, 2019 6:33 am

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GMATH practice exercise (Quant Class 18)

Image

From the figure shown, each of N people will be asked to take 7 points out, so that the 3 points left form vertices of an equilateral triangle. If all of them proceed correctly, what is the minimum value of N to guarantee that at least two people will take out exactly the same 7 points?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17

Answer: [spoiler]____(D)__[/spoiler]
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by fskilnik@GMATH » Fri Mar 01, 2019 10:09 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 18)

Image

From the figure shown, each of N people will be asked to take 7 points out, so that the 3 points left form vertices of an equilateral triangle. If all of them proceed correctly, what is the minimum value of N to guarantee that at least two people will take out exactly the same 7 points?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Image

$$?\,\, = \,\,\left( {\# \,\,{\rm{possible}}\,\,\Delta \,\,{\rm{equilateral}}\,\,{\rm{configurations}}} \right)\,\,{\rm{ + }}\,\,{\rm{1}}$$
$$? = 15 + 1 = 16$$


The correct answer is (D).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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