EC is the diameter of the semicircle shown above. Is the

Question

EC is the diameter of the semicircle shown above. Is the area of the right isosceles triangle ABC greater than 80 square units?

(1) The area of the semicircle is greater than 40 square units
(2) |BE| is greater than 2 units

prashrash · Answer

if stmt (2) says |BE| instead of BC, then answer is (C).
Else answer is (E).

gmatornot · Answer

Would you please explain the steps ? I also get E earlier but am not sure how you can be certain of C after the correction.

gk3.14 · Answer

1. The area of the semicircle = 1/2 * pi * (EC/2)^2 > 40
EC > 8 * sqrt (5/pi)

Area of the triangle = 1/2 * AC * BC = 1/2 BC^2 ( isoceles triangle)

BC = EC + ? say 1
then area of the triangle = 1/2 * (8* sqrt(5/pi) + 1)^2 < 80
if BC = EC + 3 then area of triangle > 80 INSUFF

1. BE is > 2 . by itself INSUFF

combined: SUFF so C

Kevincan, is there an easier way to approach the math?
It took me more than 2 minutes to do the calculation..

haas_mba07 · Answer

Answer: A
Q: Area of ABC > 80

As isosceles triangle :
AC= BC = a

1/2 x a x a > 80

or a^2 > 160

S1: Given Area of semicircle > 40

pi x r x r > 2 x 40
or r x r > 2 x 40 x 7/22 (approx) (pi = 22/7)

r^2 > 280/11

or d^2 > 1120/11

or EC^2 > 1120/11

We know BC = a > EC

For area to be greater than 80, 
=> a^2 > EC^2
=> 160 > 1120/11
=> 1760 > 1120 True... 

Sufficient. 

S2: |BE| > 2 

Not sufficient to determine.

Answer: A

Futuristic · Answer

I think the answer is E.

ABC = 45, OD is a tangent, so ODB=90, so BOD=45
OD=R, so BD=R, so BO=R sqrt(2)

Area of triangle ABC

=1/2AC.BC
=0.5(R+Rsqrt(2))^2
=0.5R^2(2.414)^2 =2.9R^2

From 1:
Area of Â½ circle = 0.5pi R^2>40
or R^2>80/3.14 ...(1)

Now, we are looking for ABC > 80
or 2.9R^2 > 80
or R^2>80/2.9 (2)

As we can see 1 does not prove 2. INSUFF

From 2:
0.414R>2
R>4.8
R^2 > 23.04
2.9R^2 > 69 max, not 80 hence insuff.

Of course, I may be totally off here, everyone else has a different answer

prashrash · Answer

Can u pls explain what u are doing in this step ? IMO this step takes 80 > 40 and then writes this in terms of a and EC and then converts back to numbers to try and prove the assumption. Pls let me know if this is not the case. IMO that becomes a circular fallacy!!

I have tried by a lengthy geometric analysis to see if area of triangle is greater than 80 based on the first statement and I am not getting a satisfactory answer, i.e. what I am getting is that it may or may not be greater than 80. In conjunction with st (2) it will become greater than 80.

EC is the diameter of the semicircle shown above. Is the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards