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Is area of triangle ABC greater than the area of triangle DE

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Is area of triangle ABC greater than the area of triangle DE

by richachampion » Fri Sep 16, 2016 5:58 pm
Is area of triangle ABC greater than the area of triangle DEF?

(1) The value of the area of ABC is less than that of the perimeter of DEF.
(2) Angles of ABC = Angles of DEF.
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Source: — Data Sufficiency |
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by GMATGuruNY » Sat Sep 17, 2016 3:02 am
Is area of triangle ABC greater than area of triangle DEF ?
1. The value of area of ABC is less than that of perimeter of DEF.
2. Angles of ABC = Angles of DEF

Test an EASY CASE.
Let ∆ABC and ∆DEF each be a 45-45-90 triangle.
The sides of a 45-45-90 triangle are in the following ratio:
1:1:√2.

Statement 1: The value of the area of ∆ABC is less than that of the perimeter of ∆DEF
Case 1: ∆ABC = 1:1:√2 (area = 1/2) and ∆DEF = 1:1:√2 (perimeter ≈ 3.4)
Here, the two areas are equal, so the answer to the question stem is NO.

Case 2: ∆ABC = 2:2:2√2 (area = 2) and ∆DEF = 1:1:√2 (perimeter ≈ 3.4)
Here, ∆ABC has a greater area, so the answer to the question stem is YES.
INSUFFICIENT.

Cases 1 and 2 satisfy BOTH STATEMENTS.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
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