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From the figure shown, each of N people was asked to take 12 points ou

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From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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01 Mar 2019, 07:44
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95% (hard)

Question Stats:

22% (02:45) correct 78% (02:22) wrong based on 27 sessions

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GMATH practice exercise (Quant Class 18)

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

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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01 Mar 2019, 11:22
fskilnik wrote:
GMATH practice exercise (Quant Class 18)

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

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

$$? = 15 + 1 = 16$$

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

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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02 Mar 2019, 09:47
fskilnik wrote:
fskilnik wrote:
GMATH practice exercise (Quant Class 18)

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

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

$$? = 15 + 1 = 16$$

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

Regards,
Fabio.

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From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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03 Mar 2019, 07:06
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OhsostudiousMJ wrote:

Sure, OhsostudiousMJ !

This is a trivial application of the Pigeonhole Principle.

There are 15 different possibilities, therefore if (at most) 15 people must choose one configuration each, you will still have the possibility of all 15 people choosing different configurations.

When 15+1 people are considered, at least one configuration must be chosen twice.

Regards,
Fabio.

P.S.: https://en.wikipedia.org/wiki/Pigeonhole_principle
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Re: From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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04 Mar 2019, 06:02
fskilnik Bunuel chetan2u
Hi could you please explain how are the 2 combinations (4th and 5th from left in the 2nd row of the seven diagrams) equilateral triangles?
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From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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04 Mar 2019, 06:52
Debashis Roy wrote:
fskilnik Bunuel chetan2u
Hi could you please explain how are the 2 combinations (4th and 5th from left in the 2nd row of the seven diagrams) equilateral triangles?
Hi Debashis_Roy !

Thank you for your interest in my problem and also in my solution.

In the figure above I present ONE of the diagrams you have asked about (for the other, the reasoning is the same).

Please note that I must explain to you why the purple segments (here unfortunately they appear as light grey) have the same lengths.

Reason: we have three congruent triangles (shown), by the SAS case (same two sides and intermediate angle) and the purple segments are (in all cases) opposite to the 60-degrees angle.

(We know it is a 60-degrees angle because of the one-one-one corresponding triangles... see the FIRST equilateral triangle presented in my previous solution, also the first and the last ones in the last row!)

If something is still unclear, please let me (us) know!

Regards and success in your studies,
Fabio.
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Re: From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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04 Mar 2019, 07:02
Thanks I got it!..Dint think of it though...
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Re: From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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04 Mar 2019, 07:12
Debashis Roy wrote:
Thanks I got it!..Dint think of it though...

This explanation is (as you have realized) very GMAT-related, therefore it is important to be understood throughly... I am glad you did!
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: From the figure shown, each of N people was asked to take 12 points ou  [#permalink]

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04 Mar 2019, 07:29
Debashis Roy wrote:
fskilnik Bunuel chetan2u
Hi could you please explain how are the 2 combinations (4th and 5th from left in the 2nd row of the seven diagrams) equilateral triangles?

Hi,
it might seem to you but since all triangles or dots make equilateral triangles, even 4th and 5th are equilateral triangle.
Calculate it you will get it
..draw a triangle in 4th case by joining the points and check the attachment
Attachments

IMG_20190304_195729.jpg [ 2.94 MiB | Viewed 334 times ]

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Re: From the figure shown, each of N people was asked to take 12 points ou   [#permalink] 04 Mar 2019, 07:29
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