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Which is greater x or 90

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Which is greater x or 90 [#permalink] New post 13 Mar 2019, 12:06
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Question Stats:

81% (00:25) correct 18% (01:16) wrong based on 11 sessions
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Quantity A
Quantity B
x
90


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: Which is greater x or 90 [#permalink] New post 13 Mar 2019, 13:24
Hi can you please explain how you got this?
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Re: Which is greater x or 90 [#permalink] New post 14 Mar 2019, 01:13
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This is a good question.

If the three sides of a triangle are specified, then there can only be one triangle shape that has those three sides. This is what is called congruence in geometry.

Moreover, the 3 sides are in a similar fashion of the triplets geometry : 3,4,5; 6,8,10 and so on (you should memorize for the test at very least the first 5 triplets)

3,4,5 means that the triangle has 90°,60°,30° angles.

If in our case the triplet is 6,8,11 and x must be the greatest angle because it corresponds to the greatest side ( 11 )

Therefore, if the triplet term 10 = 90° then 11 must be > 90°

A is the answer
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Re: Which is greater x or 90 [#permalink] New post 15 Mar 2019, 12:11
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Answer: A

If x was 90, then the triangle would be the right one and since we have 6 and 8 on the sides, the other side would be:

\(\sqrt{(6^2 + 8^2)} = 10\). But now it is 11, so x should be bigger than 90
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Last edited by Carcass on 15 Mar 2019, 12:16, edited 2 times in total.
Edited by Carcass
Re: Which is greater x or 90   [#permalink] 15 Mar 2019, 12:11
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