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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink]

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11 Mar 2014, 23:39

4

This post received KUDOS

The pentagon can be split in to 3 triangles: PQR, PRS and PST Consider Triangle PQR: Since PQ= 3, QR = 2; we can say that 1<PR<5 - Based on the property of triangles: The length of any side of a triangle must be smaller than the sum of the other 2 sides and greater than the difference of the other 2 sides.

Consider Triangle PRS: We can say that 1<PS<9;

Consider Triangle PST: We can say that PT is definitely less than 15. So, eliminate B, D and E. 4<PT<14;

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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Isn't this a question of geometry rather than arithmetic percents ?

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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Isn't this a question of geometry rather than arithmetic percents ?

Yes, of course. Edited the typo. Thank you.
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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink]

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14 Aug 2014, 02:23

Bunuel wrote:

SOLUTION

In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which of the lengths 5, 10, and 15 could be the value of PT ?

(A) 5 only (B) 15 only (C) 5 and 10 only (D) 10 and 15 only (E) 5, 10, and 15

The length of any side of a triangle must smaller than the sum of the other two sides.

The same for pentagon: the length of any side of a pentagon must be smaller than the sum of the other four sides.

PQ + QR + RS + ST = 3 + 2 + 4 + 5 = 14, so the length of the fifths side can not be more than 14.

Answer: C (5 and 10 only).

Bunuel, thanks for your explanation! I understand the solution and I agree, but I have one concern.

On the figure drawn we can see that 1) the direction of lines PQ, QR and RS is to the right from the point P. The sum of of these lines is only 9. 2) the direction of line ST is opposite (or to the left / back to point P).

So, if taking into account this fact, it appears that the line TP is <=9.

Is this reasoning incorrect only because it is written that the figure is drawn to scale?

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink]

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03 Oct 2016, 02:13

how do we prove the sides of pentagon can be 5 and 10 both? Also, is there any property which says that the length of any side of a pentagon must be smaller than the sum of the other four sides??

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