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tricky challenge question - Is CB || ED?

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by Brent@GMATPrepNow » Sun Jun 10, 2018 5:12 am

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00:00

Answers

A

B

C

D

E

Stats

Difficulty—

Image

Is CB || ED?

(1) ∆ABC and ∆AED are both isosceles triangles
(2) ∠C = ∠E
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tricky challenge question - Is CB || ED?

by GMATGuruNY » Tue Jun 12, 2018 2:48 am
Brent@GMATPrepNow wrote:Image

Is CB || ED?

(1) ∆ABC and ∆AED are both isosceles triangles
(2) ∠C = ∠E
Statements combined:
Case 1:
Image
In this case, ∠B = ∠E and ∠C = ∠D, so CB || ED.

Case 2:
Image
In this case, ∠B ≠ ∠E and ∠C ≠ ∠D, so CB ∦ ED.

Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Tue Jun 12, 2018 4:14 am
Brent@GMATPrepNow wrote:Image

Is CB || ED?

(1) ∆ABC and ∆AED are both isosceles triangles
(2) ∠C = ∠E
Target question: Is CB || ED?

Let's jump straight to....

Statements 1 and 2 combined
Statement 1 tells us that ∆ABC and ∆AED are both isosceles triangles
Statement 2 tells us that ∠C = ∠E

Let's start with 2 identical isosceles triangles:
Image

If we arrange the triangles this way....
Image
....we can see that the answer to the target question is YES, side CB IS parallel to side ED

HOWEVER, if we arrange the triangles this way....
Image
....we can see that the answer to the target question is NO, side CB is NOT parallel to side ED

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Brent
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