Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50042

In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
11 Mar 2014, 03:17
Question Stats:
66% (02:00) correct 34% (02:04) wrong based on 1109 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIn 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 ProjectEach 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! Attachment:
Untitled.png [ 16.3 KiB  Viewed 15840 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Math Expert
Joined: 02 Sep 2009
Posts: 50042

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
11 Mar 2014, 03:17
SOLUTIONIn 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? Extrahard Quant Tests with Brilliant Analytics




Manager
Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
11 Mar 2014, 23:39
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).




Intern
Joined: 25 Mar 2012
Posts: 17
Location: India
Concentration: Strategy, General Management
GPA: 3.04
WE: Consulting (Computer Software)

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
11 Mar 2014, 03:26
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.



Intern
Joined: 28 Jan 2014
Posts: 13
Location: India

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
14 Mar 2014, 22:45
Since PQ + QR + RS + ST = 14, PT has to be < 14. Hence C



Intern
Joined: 26 Sep 2012
Posts: 30

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
14 Aug 2014, 02:23
Bunuel wrote: SOLUTIONIn 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?



Manager
Joined: 21 Jun 2017
Posts: 83

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
09 Oct 2017, 14:52
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 82; just start with 8, and if it does not work, go back and try 72 In QRT, QR = 2, RT = 8, and QT is unknown. QT < 10; QT >6; therefore, QT = 97 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



Manager
Joined: 12 Nov 2016
Posts: 139
Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39 GMAT 2: 650 Q47 V33

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
13 Dec 2017, 09:24
Bunuel wrote: SOLUTIONIn 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?



Manager
Joined: 12 Nov 2016
Posts: 139
Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39 GMAT 2: 650 Q47 V33

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
13 Dec 2017, 23:29
Erjan_S wrote: Bunuel wrote: SOLUTIONIn 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



Intern
Joined: 11 Sep 2017
Posts: 19

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
09 Jan 2018, 10:47
Erjan_S wrote: Bunuel wrote: SOLUTIONIn 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? Hi Erjan, Please find a picture attached for easy understanding. Divide the pentagon PQRST into three triangles triangle PQR, triangle PRS and triangle PST. The range for the lengths of PR, PS and PT comes from one of the properties of triangles that the length of the third side will be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides. I hope this helps. Aiena.
Attachments
Pentagon PQRST.jpg [ 681.92 KiB  Viewed 3985 times ]



Intern
Joined: 15 Aug 2017
Posts: 14

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
10 Jan 2018, 01:30
PQ + QR + RS + ST = 14, PT has to be < 14. SoC



Intern
Joined: 14 Jan 2018
Posts: 2

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
14 Jan 2018, 13:09
Would you not say this is a 700 question? I find it quite tedious



Math Expert
Joined: 02 Sep 2009
Posts: 50042

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
14 Jan 2018, 20:36



Director
Joined: 09 Mar 2016
Posts: 951

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
28 Mar 2018, 13:48
Bunuel wrote: SOLUTIONIn 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 there is typo in your sentence The length of any side of a triangle must be smaller than the sum of the other two sides. "BE" is missing



Intern
Joined: 26 Jan 2016
Posts: 35

Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which
[#permalink]
Show Tags
13 Jul 2018, 15:40
Hi Bunuel Can we derive a general rule: length of any side of a polygon (including regular polygons) must be < sum (n1) sides. Also, can we derive a rule for the minimum? Say > difference of two smallest lengths? Thanks.




Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which &nbs
[#permalink]
13 Jul 2018, 15:40






