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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # GRE Math Challenge #6-If x>0, and two sides of a certain  Question banks Downloads My Bookmarks Reviews Important topics
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Director  Joined: 16 May 2014
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GRE Math Challenge #6-If x>0, and two sides of a certain [#permalink]
Expert's post 00:00

Question Stats: 0% (00:00) correct 100% (01:05) wrong based on 8 sessions
If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?

Indicate all possible lengths.

A) $$4x+5$$
B) $$x+2$$
C) $$6x+1$$
D) $$5x+6$$
E) $$2x+17$$

[Reveal] Spoiler: OA
A,C,E
[Reveal] Spoiler: OA

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If you find this post helpful, please press the kudos button to let me know ! Intern Joined: 02 Feb 2019
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Re: GRE Math Challenge #6-If x>0, and two sides of a certain [#permalink]
soumya1989 wrote:
If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?

Indicate all possible lengths.

A) $$4x+5$$
B) $$x+2$$
C) $$6x+1$$
D) $$5x+6$$
E) $$2x+17$$

[Reveal] Spoiler: OA
A,C,E

Are you sure answer E is ok?
Manager Joined: 04 Feb 2019
Posts: 204
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Re: GRE Math Challenge #6-If x>0, and two sides of a certain [#permalink]
Expert's post
Malbash212 wrote:
soumya1989 wrote:
If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?

Indicate all possible lengths.

A) $$4x+5$$
B) $$x+2$$
C) $$6x+1$$
D) $$5x+6$$
E) $$2x+17$$

[Reveal] Spoiler: OA
A,C,E

Are you sure answer E is ok?

Yes. Note that choice E is always bigger than 2x + 1. However, it is not always bigger than 3x + 4. When 2x + 17 and 2x + 1 are combined, though, they equal 4x + 18, which is always bigger than 3x + 4. This means that there are times when 3x + 4 is the hypotenuse, and the sum of both legs is greater than it.

For example, take x = 10. When that is the case, the triangle has side lengths 21, 27, and 34. This is totally fine, as the sum of the two smaller sides is greater than the length of the third side. Re: GRE Math Challenge #6-If x>0, and two sides of a certain   [#permalink] 21 Feb 2019, 15:06
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