It is currently 14 Dec 2017, 00:35

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42599

Kudos [?]: 135579 [3], given: 12701

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

Show Tags

New post 11 Mar 2014, 02:17
3
This post received
KUDOS
Expert's post
33
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:35) correct 35% (01:39) wrong based on 709 sessions

HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
Untitled.png [ 16.3 KiB | Viewed 10783 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


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!
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135579 [3], given: 12701

Expert Post
7 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42599

Kudos [?]: 135579 [7], given: 12701

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

Show Tags

New post 11 Mar 2014, 02:17
7
This post received
KUDOS
Expert's post
17
This post was
BOOKMARKED
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).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135579 [7], given: 12701

4 KUDOS received
Manager
Manager
User avatar
Status: GMATting
Joined: 21 Mar 2011
Posts: 108

Kudos [?]: 108 [4], given: 104

Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
GMAT ToolKit User
Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink]

Show Tags

New post 11 Mar 2014, 22:39
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;

From the answer choices, 5 and 10 hold true.

Ans is (C).

Kudos [?]: 108 [4], given: 104

2 KUDOS received
Intern
Intern
avatar
Joined: 25 Mar 2012
Posts: 23

Kudos [?]: 19 [2], given: 1

Location: India
Concentration: Strategy, General Management
GMAT 1: 710 Q50 V36
GPA: 3.04
WE: Consulting (Computer Software)
Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink]

Show Tags

New post 11 Mar 2014, 02:26
2
This post received
KUDOS
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.

Kudos [?]: 19 [2], given: 1

1 KUDOS received
Intern
Intern
User avatar
Joined: 28 Jan 2014
Posts: 14

Kudos [?]: 10 [1], given: 2

Location: India
GMAT 1: 740 Q49 V41
GMAT ToolKit User
Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink]

Show Tags

New post 14 Mar 2014, 21:45
1
This post received
KUDOS
Since PQ + QR + RS + ST = 14, PT has to be < 14. Hence C

Kudos [?]: 10 [1], given: 2

Intern
Intern
avatar
Joined: 26 Sep 2012
Posts: 38

Kudos [?]: 38 [0], given: 46

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

Show Tags

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?

Kudos [?]: 38 [0], given: 46

Manager
Manager
User avatar
B
Joined: 21 Jun 2017
Posts: 71

Kudos [?]: 5 [0], given: 2

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

Show Tags

New post 09 Oct 2017, 13:52
Divide pentagon into three triangles: Triangle RST, Triangle QRT, Triangle PQT
In RST, RS = 4, ST =5; RT has to be less than their sum, and greater than their difference; therefore, RT could be 8-2; just start with 8, and if it does not work, go back and try 7-2
In QRT, QR = 2, RT = 8, and QT is unknown. QT < 10; QT >6; therefore, QT = 9-7
In PQT, PQ = 3, QT = 9, PT unknown. PT<12; PT>6; therefore, 15 cannot be PT, thus eliminating answer choices B, D, and E
Suppose QT is 8; PT<11; PT>3, so it could still be 5, or 10
Suppose QT is 7; PT<10; PT>4. 10 is eliminated here, but since if QT equals 8, 10 is still possible, as with 5. Supposing RT is 2, then QT<4; if QT is 3, then PT<6; therefore, 5 has to be the answer since we used the smallest possible outcomes. Ten could be eliminated, however, under other conditions, it is permissible.


The only answer choice that was eliminated across every possible condition is 15. The conditions showed us that it can be 5 or 10.
Therefore, the answer is (C) 5 and 10 only


A helpful general rule: questions that involve ranges, work with extremes such as biggest or smallest.

Hope this helps

Kudos [?]: 5 [0], given: 2

Manager
Manager
User avatar
B
Joined: 12 Nov 2016
Posts: 84

Kudos [?]: 2 [0], given: 40

Location: Kazakhstan
Concentration: Entrepreneurship, Finance
Schools: Sloan (S)
GMAT 1: 620 Q36 V39
GPA: 3.2
Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink]

Show Tags

New post 13 Dec 2017, 08:24
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).


I followed the same logic and eliminated 15. My concern was about 5 and 10, the official solution contains quite a long and detailed explanation but should I bother? Is there any need in a question like that and dig further - proving that 10 or 5 can be the answer?

Kudos [?]: 2 [0], given: 40

Manager
Manager
User avatar
B
Joined: 12 Nov 2016
Posts: 84

Kudos [?]: 2 [0], given: 40

Location: Kazakhstan
Concentration: Entrepreneurship, Finance
Schools: Sloan (S)
GMAT 1: 620 Q36 V39
GPA: 3.2
Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which [#permalink]

Show Tags

New post 13 Dec 2017, 22:29
Erjan_S wrote:
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).


I followed the same logic and eliminated 15. My concern was about 5 and 10, the official solution contains quite a long and detailed explanation but should I bother? Is there any need in a question like that and dig further - proving that 10 or 5 can be the answer?


Bunuel I would much appreciate your comment

Kudos [?]: 2 [0], given: 40

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which   [#permalink] 13 Dec 2017, 22:29
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.