If Triangle ABC Is Isosceles, What Is The Length Of Side BC? GMAT Data Sufficiency

Question: If triangle ABC is isosceles, what is the length of side BC?
(1) The length of side AB is 4
(2) The length of side AC is 4√2

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“If triangle ABC is isosceles, what is the length of side BC?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

There is only one approach to solve the problem.
Given: triangle ABC is isosceles
This tells us that the triangle has two equal sides.
Target question: What is the length of side BC?
When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……
Statements 1 and 2 combined
Here are two triangles that satisfy BOTH statements:
Case a: The triangle could look like this:

In this case, the answer to the target question is side BC has length 4
Case b: The triangle could also look like this:

In this case, the answer to the target question is side BC has length 4√2
Since we can't answer the target question with certainty, the combined statements are NOT SUFFICIENT

Correct Answer: E

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