[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 37: Undefined array key "last_recommended_questions_epoch"
[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 41: Undefined array key "last_recommended_questions_epoch"
If k is an integer and 2 < k < 7, for how many different : Problem Solving (PS)
 Last visit was: 20 Jul 2024, 03:16 It is currently 20 Jul 2024, 03:16
Toolkit
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

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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94428
Own Kudos [?]: 642456 [157]
Given Kudos: 86335
Math Expert
Joined: 02 Sep 2009
Posts: 94428
Own Kudos [?]: 642456 [72]
Given Kudos: 86335
Senior Manager
Joined: 29 Mar 2012
Posts: 266
Own Kudos [?]: 1529 [11]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30839 [3]
Given Kudos: 799
If k is an integer and 2 < k < 7, for how many different [#permalink]
2
Kudos
1
Bookmarks
Top Contributor
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

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B

So, if a triangle has sides 2, 7 and k, we can write: 7 - 2 < k < 7 + 2
Simplify to get: 5 < k < 9

We're told that k is an INTEGER, and that 2 < k < 7.
So, the only possible value of k that satisfies the inequality 5 < k < 9 is k = 6

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 12 Mar 2019, 15:53.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:19, edited 1 time in total.
General Discussion
Manager
Joined: 30 Jun 2011
Affiliations: Project Management Professional (PMP)
Posts: 98
Own Kudos [?]: 155 [2]
Given Kudos: 12
Location: New Delhi, India
Concentration: Marketing
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
1
Kudos
1
Bookmarks
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:
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.
Intern
Joined: 14 Nov 2012
Posts: 3
Own Kudos [?]: 1 [1]
Given Kudos: 0
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
1
Kudos
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.

Originally posted by morfin on 25 Nov 2012, 14:50.
Last edited by morfin on 26 Nov 2012, 10:05, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 94428
Own Kudos [?]: 642456 [1]
Given Kudos: 86335
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
1
Kudos
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
Intern
Joined: 14 May 2014
Posts: 35
Own Kudos [?]: 160 [3]
Given Kudos: 1
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
3
Kudos
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.
Intern
Joined: 26 Jun 2014
Posts: 17
Own Kudos [?]: 5 [0]
Given Kudos: 217
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
Bunuel wrote:
SOLUTION

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.

Then I take it that the GMAT ignores the degenerate triangle, in which the sum of the two shorter sides can equal the longer side?
Math Expert
Joined: 02 Sep 2009
Posts: 94428
Own Kudos [?]: 642456 [0]
Given Kudos: 86335
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
Chakolate wrote:
Bunuel wrote:
SOLUTION

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.

Then I take it that the GMAT ignores the degenerate triangle, in which the sum of the two shorter sides can equal the longer side?

Yes, degenerate "triangle" with three collinear points is obviously not a part of GMAT quant. You should refer to OG to know what is tested on the GMAT.
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6597 [6]
Given Kudos: 1646
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
5
Kudos
1
Bookmarks
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

We can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle (in this case, the sides are 2 and k) must be greater than the length of its third side (in this case, 7).

Thus, we see that:

2 + k > 7

k > 5

Since k < 7, the only integer value of k that is greater than 5 but less than 7 is 6.

Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 959
Own Kudos [?]: 5017 [0]
Given Kudos: 690
Concentration: Accounting
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
Top Contributor
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

The other two sides of the triangle can be $$5<S<9$$
So k can be only 6.

Non-Human User
Joined: 09 Sep 2013
Posts: 34039
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
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.
Re: If k is an integer and 2 < k < 7, for how many different [#permalink]
Moderator:
Math Expert
94421 posts