Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Aug 2015, 09:20
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If k is an integer and 2 < k < 7, for how many different

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49636 [0], given: 7400

If k is an integer and 2 < k < 7, for how many different [#permalink] New post 09 Jul 2012, 02:34
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

58% (01:35) correct 42% (00:35) wrong based on 470 sessions
If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

(A) one
(B) two
(C) three
(D) four
(E) five

Diagnostic Test
Question: 19
Page: 22
Difficulty: 600
[Reveal] Spoiler: OA

_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Affiliations: Project Management Professional (PMP)
Joined: 30 Jun 2011
Posts: 213
Location: New Delhi, India
Followers: 3

Kudos [?]: 39 [0], given: 12

Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 09 Jul 2012, 03:37
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

(A) one
(B) two
(C) three
(D) four
(E) five

Diagnostic Test
Question: 19
Page: 22
Difficulty: 650


GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th 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!

Believe ans is A as k can be 3,4,5 or 6. for all cases except k=6, sum of teo sides can be less than equal to third side which should not be true

As as per triangle property sum of two sides is greater than third side.
_________________

Best
Vaibhav

If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks

Senior Manager
Senior Manager
User avatar
Joined: 28 Mar 2012
Posts: 287
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 21

Kudos [?]: 240 [0], given: 23

GMAT ToolKit User
Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 09 Jul 2012, 05:20
1
This post was
BOOKMARKED
Bunuel wrote:
If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

(A) one
(B) two
(C) three
(D) four
(E) five

Hi,

Difficulty level: 600

|7-2| < k < |7+2|
or 5 < k < 9
thus k = 6, 7, 8, but 2 < k < 7
therefore, k = 6

Answer (A),

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49636 [0], given: 7400

Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 13 Jul 2012, 01:59
Expert's post
SOLUTION

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

(A) one
(B) two
(C) three
(D) four
(E) five

Relationship of the Sides of a Triangle: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

According to the above the following must be true: \((7-2)<k<(7+2)\) --> \(5<k<9\). So, \(k\) could be 6, 7 or 8. Since also given that \(2 < k < 7\), then \(k=6\). Hence \(k\) can take only one value: 6.

Answer: A.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 14 Nov 2012
Posts: 3
Followers: 0

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

Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 25 Nov 2012, 13:50
Why is it only one value?
What if 2 is the smallest side and 7 is the largest? Then, k can be 6, 7 or 8. since:

2 + 7 = 9
7 - 2 = 5
So 5 < k < 9

The problem does not specify that 2 and 7are the smaller two sides.

Last edited by morfin on 26 Nov 2012, 09:05, edited 1 time in total.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49636 [0], given: 7400

Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 26 Nov 2012, 01:05
Expert's post
morfin wrote:
What if 2 is the smallest side and 7 is the largest? Then, the answer is B (two) since:

2 + 7 = 9
7 - 2 = 6
So 6 < k < 9

The problem does not specify that 2 and 7are the smaller two sides.


Not sure I understand your question.

First of all: 7-2=5, not 6.

Next, obviously since the lengths of the sides are 2, 7 and k, where 2<k<7, then the length of the smallest side is 2 and the length of the largest side is 7. Check here for complete solution: if-k-is-an-integer-and-2-k-7-for-how-many-different-135543.html#p1104032
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Manager
Manager
avatar
Joined: 29 Oct 2013
Posts: 171
Concentration: Finance
GMAT 1: 750 Q48 V46
GMAT 2: Q V0
GRE 1: 327 Q161 V166
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 7

Kudos [?]: 198 [1] , given: 116

GMAT ToolKit User
Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 19 May 2014, 22:39
1
This post received
KUDOS
Hi Bunuel, 39% got it wrong. Do u wanna tag it 600-700 instead of sub600? thanks
_________________

Please consider giving 'kudos' if you like my post and want to thank :)

Read about my journey to 750 here - a-non-native-speakers-journey-to-99-le-on-verbal-750overall-171722.html#p1367876

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49636 [0], given: 7400

Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 19 May 2014, 22:43
Expert's post
Manager
Manager
avatar
Joined: 29 Oct 2013
Posts: 171
Concentration: Finance
GMAT 1: 750 Q48 V46
GMAT 2: Q V0
GRE 1: 327 Q161 V166
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 7

Kudos [?]: 198 [0], given: 116

GMAT ToolKit User
Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 19 May 2014, 22:49
Bunuel wrote:
MensaNumber wrote:
Hi Bunuel, 39% got it wrong. Do u wanna tag it 600-700 instead of sub600? thanks

____________
Done. Thank you.


Great ! Thanks for a quick reply.
_________________

Please consider giving 'kudos' if you like my post and want to thank :)

Read about my journey to 750 here - a-non-native-speakers-journey-to-99-le-on-verbal-750overall-171722.html#p1367876

Intern
Intern
User avatar
Joined: 14 May 2014
Posts: 45
Followers: 0

Kudos [?]: 25 [0], given: 1

Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 20 May 2014, 03:17
Relationship of the Sides of a Triangle: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Above relationship is in the core of this solution. Many times I have found students having difficulty is assimilating this concept.

Best way to get this concept is trying to actually draw triangles which contradict this. For example, try to draw a triangle with following sides (actual scale)

4, 3, 8

Once you failed, you will realize that The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
_________________

Help me with Kudos if it helped you "

Mathematics is a thought process.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6093
Followers: 340

Kudos [?]: 68 [0], given: 0

Premium Member
Re: If k is an integer and 2 < k < 7, for how many different [#permalink] New post 09 Aug 2015, 13:35
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: If k is an integer and 2 < k < 7, for how many different   [#permalink] 09 Aug 2015, 13:35
    Similar topics Author Replies Last post
Similar
Topics:
16 Experts publish their posts in the topic How many different pairs of integers (a, b) exist such that 2 <= a <= Bunuel 4 04 May 2015, 05:05
5 Experts publish their posts in the topic If k is an integer and 121 < k^2 < 225, then k can have at most how Bunuel 10 27 Mar 2015, 04:28
6 Experts publish their posts in the topic How many even integers n ; 13<=n<=313 are of the form 3k+4, honchos 9 13 Sep 2013, 23:01
The sum of all the integers k such that -26<k<24 is Baten80 4 03 Jan 2012, 08:16
5 Experts publish their posts in the topic For how many integers k is k^2 = 2^k ? metallicafan 9 03 Jan 2012, 05:35
Display posts from previous: Sort by

If k is an integer and 2 < k < 7, for how many different

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.