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Isosceles trick

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by lkcr » Tue Apr 03, 2012 11:38 pm
Not sure if I'm missing something here but...

If triangle RST is an isosceles, what is angle R?
1) angle T = 100
2) angle S = 40

I thought for an isosceles, if you knew the middle angle; [180-middle angle] /2 would be each remaining angle no?

Apparently the answer is NOT choice D....

Sorry I know it sounds like a silly question and it was from the gmatprep as well..
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Source: — Data Sufficiency |
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by Pharo » Tue Apr 03, 2012 11:49 pm
Statement 1 : If one angle is 100; that means in an isosceles triangle the other angles are 40 each. ;Sufficient

Statement 2 : One angle is 40. Now this is the trick. Since we do not know which sides are equal, we cannot say which angles are equal. If one angle is 40 it might mean:
a. 40-40-100;
b. 40-70-70;
;Hence not sufficient.

--> Answer is A :)
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by Anurag@Gurome » Tue Apr 03, 2012 11:54 pm
lkcr wrote:Not sure if I'm missing something here but...

If triangle RST is an isosceles, what is angle R?
1) angle T = 100
2) angle S = 40

I thought for an isosceles, if you knew the middle angle; [180-middle angle] /2 would be each remaining angle no?

Apparently the answer is NOT choice D....

Sorry I know it sounds like a silly question and it was from the gmatprep as well..
Triangle RST is an isosceles triangle implies that its two angles are equal.

(1) angle T = 100 implies no other angle can be 100 degrees because the sum of 3 angles in a triangles cannot be more than 180 degrees. This means other two angles, R and S are equal.
So, angle R = (180 - 100)/2 = 80/2 = 40 degrees; SUFFICIENT.

(2) angle S = 40
If angle S = angle R = 40 degrees and angle T = 100 degrees, here angle R = 40 degrees
If angle S = 40 degrees and angle R = angle T = 70 degrees, here angle R = 70 degrees
No definite answer; NOT sufficient.

The correct answer is A.
Anurag Mairal, Ph.D., MBA
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by neelgandham » Wed Apr 04, 2012 12:01 am
If triangle RST is an isosceles, what is angle R?
1) angle T = 100
Angle R + Angle S + Angle T = 180
Case 1: Angle R = Angle T, then
Angle R + Angle T = 200 > 180 (Sum of Angles R,S and T).
Not possible
Case 2: Angle R = Angle S, then
Angle S + Angle S + Angle T = 180
Angle R = Angle S = 40, Angle T = 100
Angle R = Angle S = 40.
Sufficient
2) angle S = 40
Angle R + Angle S + Angle T = 180
Case 1: Angle R = Angle T, then
Angle R + Angle S + Angle R = 180
Angle R = Angle T = 70, Angle S = 40
Case 2: Angle R = Angle S, then
Angle S + Angle S + Angle T = 180
Angle R = Angle S = 40, Angle T = 100
Two different cases, Oops Insufficient!

IMO A
Anil Gandham
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