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M04-34

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Math Expert
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Joined: 02 Sep 2009
Posts: 57193
M04-34  [#permalink]

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New post 16 Sep 2014, 00:24
2
7
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (00:53) correct 33% (01:01) wrong based on 148 sessions

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Math Expert
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Joined: 02 Sep 2009
Posts: 57193
Re M04-34  [#permalink]

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New post 16 Sep 2014, 00:24
2
1
Official Solution:

There is a certain triangle with sides 7, 10, and \(x\). If it is known that \(x\) is an integer, how many different values are there of \(x\)?

A. 8
B. 10
C. 13
D. 14
E. 16


Important property: 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.

Hence, \(10-7 \lt x \lt 10+7\) \(\rightarrow\) \(3 \lt x \lt 17\). Since given that \(x\) is an integer then it can take 13 values, from 4 to 16, inclusive.


Answer: C
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Re: M04-34  [#permalink]

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New post 02 Aug 2019, 08:21
Bunuel wrote:
There is a certain triangle with sides 7, 10, and \(x\). If it is known that \(x\) is an integer, how many different values are there of \(x\)?

A. 8
B. 10
C. 13
D. 14
E. 16


For those who may be more visual in their approach to geometry problems, I am uploading a Google Doc I created to illustrate the rule. It may not be as fast as the official solution, but it can get the job done in a pinch. Happy studies.

- Andrew
>> !!!

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GMAT Club Bot
Re: M04-34   [#permalink] 02 Aug 2019, 08:21
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