GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Dec 2018, 07:45

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Prep Hour

December 16, 2018

December 16, 2018

03:00 PM EST

04:00 PM EST

Strategies and techniques for approaching featured GMAT topics
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51227
If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

09 Jul 2012, 02:34
4
39
00:00

Difficulty:

35% (medium)

Question Stats:

62% (00:57) correct 38% (00:57) wrong based on 1803 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51227
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

13 Jul 2012, 01:59
7
16
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.

_________________
Current Student
Joined: 28 Mar 2012
Posts: 312
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

09 Jul 2012, 05:20
6
2
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

Regards,
##### General Discussion
Manager
Affiliations: Project Management Professional (PMP)
Joined: 30 Jun 2011
Posts: 143
Location: New Delhi, India
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

09 Jul 2012, 03:37
1
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.
_________________

Best
Vaibhav

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

Intern
Joined: 14 Nov 2012
Posts: 3
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

Updated on: 26 Nov 2012, 09:05
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, 13:50.
Last edited by morfin on 26 Nov 2012, 09:05, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 51227
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

26 Nov 2012, 01:05
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: 41
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

20 May 2014, 03:17
2
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.

Intern
Joined: 26 Jun 2014
Posts: 21
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

19 Jun 2017, 10:00
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: 51227
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

19 Jun 2017, 10:12
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
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

06 Jul 2017, 16:45
3
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
Joined: 09 Sep 2013
Posts: 9184
Re: If k is an integer and 2 < k < 7, for how many different  [#permalink]

### Show Tags

16 Jul 2018, 20:15
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 &nbs [#permalink] 16 Jul 2018, 20:15
Display posts from previous: Sort by