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555-605 Level|   Geometry|      
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Bunuel
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In the triangle below, is x > 90? (1) a^2 + b^2 < 25 (2) c > 5 05 Nov 2018, 00:58
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C
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25% (medium)

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68% (01:05) correct 32% (01:22) wrong based on 136 sessions

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In the triangle below, is x > 90?



(1) a^2 + b^2 < 25

(2) c > 5


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Attachment:
2018-11-05_1157.png
2018-11-05_1157.png [ 8.33 KiB | Viewed 3243 times ]
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C
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In the triangle below, is x > 90? (1) a^2 + b^2 < 25 (2) c > 5 05 Nov 2018, 02:37
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The answer is C.
We can solve this question using the Logical approach, no need to actually answer it. to determine if x>90, we need information about the relation between a,b and c (in order to see if the relation exceeds or is less than pythagorean).
(1) and (2) are clearly insufficient, as each only provides part of the relevant data.

Combined, we know that a^2+b^2<25<c^2, giving us a direct comparison between a,b, and c. sufficient!
Answer C.

(the answer is "yes", because since c^2>a^2+b^2, this means the relation are more than pythagorean, i.e. more than a right angle.)
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In the triangle below, is x > 90? (1) a^2 + b^2 < 25 (2) c > 5 05 Nov 2018, 11:41
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(1) a^2 + b^2 < 25

(2) c > 5

From stmnt 1: we cannot determine anything as C is not given
From stmnt 2: a & b not given

Combing two eqns:
relation we get is C>25 and A^2+b^2<25 so we can say that c^2>A^2+b^2 ; which means that angle x would be obtuse angle 180>x>90
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In the triangle below, is x > 90? (1) a^2 + b^2 < 25 (2) c > 5 05 Nov 2018, 22:34
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Bunuel
In the triangle below, is x > 90?



(1) a^2 + b^2 < 25

(2) c > 5


Show Spoiler
Attachment:
2018-11-05_1157.png

\(Cos x = a^2 + b^2 - c^2/2ab\)

Each statement alone is Insufficient.

By combining two, Cos x will be negative. Hence, X > 90.
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In the triangle below, is x > 90? (1) a^2 + b^2 < 25 (2) c > 5 30 Dec 2022, 16:12
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Bunuel
In the triangle below, is x > 90?


(1) a^2 + b^2 < 25

(2) c > 5


Show Spoiler
Attachment:
The attachment 2018-11-05_1157.png is no longer available




[url]file:///C:/Users/Deeuce/Downloads/Gmatclub%20question%20for%20triangle.PNG[/url]


Hi Experts Bunuel chetan2u, Sajjad1994, walker
The following question must be a very simple thing, but I couldn't wrap my head around it, hence reaching out.
Highlighted in the image, why would angle BAC and BCA have to be equal instead of angle ABC and ACB as equal ? Same question with the inner triangle : can angle ADC and DCA be equal instead of DAC and DCA? Am I missing somethign here?
Although my final answer matched the official answer, that one part of hte explanation tricked me a bit.
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In the triangle below, is x > 90? (1) a^2 + b^2 < 25 (2) c > 5 30 Dec 2022, 21:25
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deeuce
Bunuel
In the triangle below, is x > 90?


(1) a^2 + b^2 < 25

(2) c > 5


Show Spoiler
Attachment:
2018-11-05_1157.png




[url]file:///C:/Users/Deeuce/Downloads/Gmatclub%20question%20for%20triangle.PNG[/url]


Hi Experts Bunuel chetan2u, Sajjad1994, walker
The following question must be a very simple thing, but I couldn't wrap my head around it, hence reaching out.
Highlighted in the image, why would angle BAC and BCA have to be equal instead of angle ABC and ACB as equal ? Same question with the inner triangle : can angle ADC and DCA be equal instead of DAC and DCA? Am I missing somethign here?
Although my final answer matched the official answer, that one part of hte explanation tricked me a bit.


Yes, you are correct. We cannot deduce which sides are equal from the given details.
However, we can rule out certain combinations.
For example: AC=AD and AC=AB is NOT possible because that will mean AB=AD. Finally there will 3-4 possibilities left, but we cannot be sure on exactly which sides are equal.
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