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# M04-34

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Math Expert
Joined: 02 Sep 2009
Posts: 57193

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16 Sep 2014, 00:24
2
7
00:00

Difficulty:

25% (medium)

Question Stats:

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

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 57193

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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.

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Joined: 16 May 2019
Posts: 41

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

Moderators: chetan2u, Bunuel