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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which

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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 11 Mar 2014, 02:17
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A
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C
D
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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Untitled.png
Untitled.png [ 16.3 KiB | Viewed 1651 times ]
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

Problem Solving
Question: 150
Category: Geometry
Page: 82
Difficulty: 600


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[Reveal] Spoiler: OA

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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 11 Mar 2014, 22:39
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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;

From the answer choices, 5 and 10 hold true.

Ans is (C).
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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 11 Mar 2014, 02:17
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SOLUTION

Image
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).
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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 11 Mar 2014, 02:26
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Bunuel wrote:
RESERVED FOR A SOLUTION.


Divide the pentagon into triangles:

From triangle PQR, PQ+QR > PR,
or, PR < 5 ---(1)

From triangle PRS, PR + RS > PS
or, PR + 4 > PS ---(2)
from (1) and (2), PS < 9 ---(3)

From triangle PST, PS + ST > PT
or, PS + 5 > PT ---(4)
from (3) and (4), PT < 14

So, PT can not be 15. So, C is the answer.
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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 14 Mar 2014, 21:45
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Since PQ + QR + RS + ST = 14, PT has to be < 14. Hence C
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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 21 May 2014, 04:57
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
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

Problem Solving
Question: 150
Category: Arithmetic Percents
Page: 82
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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.

Thank you!



Isn't this a question of geometry rather than arithmetic percents ?
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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 15 Mar 2014, 09:28
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SOLUTION

Image
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).
_________________

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 21 May 2014, 05:44
Expert's post
himanshujovi wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
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

Problem Solving
Question: 150
Category: Arithmetic Percents
Page: 82
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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.

Thank you!



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


Yes, of course. Edited the typo. Thank you.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink] New post 14 Aug 2014, 01:23
Bunuel wrote:
SOLUTION

Image
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] 14 Aug 2014, 01:23
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