December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL. December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51121

Let q represent the integer length of a side of a triangle. If r repre
[#permalink]
Show Tags
15 Jul 2015, 02:21
Question Stats:
61% (01:29) correct 39% (01:44) wrong based on 137 sessions
HideShow timer Statistics



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2711
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: Let q represent the integer length of a side of a triangle. If r repre
[#permalink]
Show Tags
15 Jul 2015, 03:36
Bunuel wrote: Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 9, and 13, what is the value of r?
A. 5 B. 17 C. 18 D. 22 E. 29
Kudos for a correct solution. Sides of triangle are q, 9 and 13 for a triangle to exist Sum of the two sides > third sidei.e. For Smallest value of q q + 9 > 13 i.e. q > 4 i.e. For Largest value of q 13 + 9 > q i.e. q < 22 i.e. q can be any Integer from 5 to 21 Total Possible values of q = r = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21} i.e. r = 17 Answer: Option B
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Let q represent the integer length of a side of a triangle. If r repre
[#permalink]
Show Tags
15 Jul 2015, 03:51
Bunuel wrote: Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 9, and 13, what is the value of r?
A. 5 B. 17 C. 18 D. 22 E. 29
Kudos for a correct solution. The trick here is to know that for a given traingle with sides a,b,c , for any side the following relation holds: ab < c < a+b (for ALL triangles). Thus, per the given question, 139< q < 13+9 > 4 <q < 22 > This gives us 17 integer values for q and thus r= 17. B is the correct answer.



Intern
Joined: 11 Sep 2013
Posts: 7

Re: Let q represent the integer length of a side of a triangle. If r repre
[#permalink]
Show Tags
15 Jul 2015, 21:32
As per triangle inequality, length of q will be greater than the difference of 2 sides and less than the sum of 2 sides. So 4<q<22
The number of distinct values or r will then be 215/1 + 1 = 17 (coz 4 and 22 will not be included)
Option B



Manager
Joined: 20 Jul 2011
Posts: 80

Re: Let q represent the integer length of a side of a triangle. If r repre
[#permalink]
Show Tags
17 Jul 2015, 21:22
Bunuel wrote: Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 9, and 13, what is the value of r?
A. 5 B. 17 C. 18 D. 22 E. 29
Kudos for a correct solution. We know that, the sum of any two sides of a triangle should be greater than the third side (a+b > c) and the difference between any two sides should be less than the third side (ab<c) 9+13 < q < 139 22 < q < 4 q ranges from 5 to 21. No of items in this range = 215+1 = 17. Option B



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: Let q represent the integer length of a side of a triangle. If r repre
[#permalink]
Show Tags
19 Jul 2015, 12:11
Bunuel wrote: Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 9, and 13, what is the value of r?
A. 5 B. 17 C. 18 D. 22 E. 29
Kudos for a correct solution. 800score Official Solution:From the triangle inequality rule, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the three inequalities are q + 9 > 13, 9 + 13 > q, and q + 13 > 9. The third equation holds for any positive value of q. So solve the first two inequalities for q, so q > 4 and 22 > q. So the value of q is 4 < q < 22. Since the lengths of the sides of the triangle are of integer value, the lowest possible integer/side can be 5 and the highest possible integer/side can be 21 (q = 5, 6, 7, 8, 9 ..., 19, 20, or 21). So, r, the number of numbers in this set, must equal 21 – (5 – 1) = 17. The correct answer is B.
_________________
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



NonHuman User
Joined: 09 Sep 2013
Posts: 9138

Re: Let q represent the integer length of a side of a triangle. If r repre
[#permalink]
Show Tags
20 Feb 2017, 02:24
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Let q represent the integer length of a side of a triangle. If r repre &nbs
[#permalink]
20 Feb 2017, 02:24






