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# In the triangle below (see attached), is x > 90? (1) a2 +

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Manager
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In the triangle below (see attached), is x > 90? (1) a2 + [#permalink]  14 Jan 2008, 08:17
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In the triangle below (see attached), is x > 90?

(1) a2 + b2 < 15
(2) c > 4

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Director
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Re: GMAT SET #16;DS; Triangle inequality [#permalink]  14 Jan 2008, 08:26

In a right triangle A^2 + B^2 = C^2

If A^2+B^2 < 15 then C^2 must be less than 15 as well. Statement 2 says that C is 4, so C^2 = 16. Since 16 is greater than 15, x is not = to 90 degrees. The legs are shorter than they would be for a right triangle, so the degree must be greater than 90 to form the triangle.
Intern
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Re: GMAT SET #16;DS; Triangle inequality [#permalink]  14 Jan 2008, 09:42
I. a2+b2 <15 Insufficient
II. c >5 Insufficient
Combining I and II together:
1. traingle is not a right ange traingle.
2. From I and II we can say that c>a and c>b.
3. for right angel traingle a2+b2=c2 and X=90
In this case c2 is greater than a2+b2 (c2>a2+b2) therefore X>90
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Re: GMAT SET #16;DS; Triangle inequality [#permalink]  14 Jan 2008, 09:50
GGUY wrote:
In the triangle below (see attached), is x > 90?

(1) a2 + b2 < 15
(2) c > 4

OA is C.

from Pith. we know that a^2 + b^2 = c^2.
1. we don't know whether a^2 + b^2 = c^2 because we don't know anything about c. it could be >< or it could equal 15. not suff
2. by itself it is clearly insuff.

C. a2 + b2 < c^2 it means that c is greater than an hypothetic hypothenuse, thus x>90
Manager
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Re: GMAT SET #16;DS; Triangle inequality [#permalink]  14 Jan 2008, 12:57
OA=C

Thanks all
Re: GMAT SET #16;DS; Triangle inequality   [#permalink] 14 Jan 2008, 12:57
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