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If k is an integer and 2 < k < 7, for how many different
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09 Jul 2012, 03:34
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Re: If k is an integer and 2 < k < 7, for how many different
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13 Jul 2012, 02:59
SOLUTIONIf 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: \((72)<k<(7+2)\) > \(5<k<9\). 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.
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Re: If k is an integer and 2 < k < 7, for how many different
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09 Jul 2012, 06:20
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 72 < k < 7+2 or 5 < k < 9 thus k = 6, 7, 8, but 2 < k < 7 therefore, k = 6 Answer (A), Regards,




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Re: If k is an integer and 2 < k < 7, for how many different
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09 Jul 2012, 04:37
Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectIf 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 ProjectEach 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.
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Re: If k is an integer and 2 < k < 7, for how many different
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Updated on: 26 Nov 2012, 10:05
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, 14:50.
Last edited by morfin on 26 Nov 2012, 10:05, edited 1 time in total.



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Re: If k is an integer and 2 < k < 7, for how many different
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26 Nov 2012, 02:05



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Re: If k is an integer and 2 < k < 7, for how many different
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20 May 2014, 04:17
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.
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Re: If k is an integer and 2 < k < 7, for how many different
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19 Jun 2017, 11:00
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?



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Re: If k is an integer and 2 < k < 7, for how many different
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19 Jun 2017, 11:12



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Re: If k is an integer and 2 < k < 7, for how many different
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06 Jul 2017, 17:45
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. Answer: A
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Re: If k is an integer and 2 < k < 7, for how many different
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