GMAT Data Sufficiency-The Length of the Median BD in a Triangle ABC is 12 Centimeters, What is the Length of the Side AC?

Question: The length of the median BD in a triangle ABC is 12 centimeters, what is the length of the side AC?

1. ABC is an isosceles triangle
2. \(AC^2=AB^2+BC^2\)

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.

“The length of the median BD in a triangle ABC is 12 centimeters, what is the length of the side AC?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative 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.

Answer:

Approach Solution 1

Firstly consider S(1), it is given that ABC is an isosceles triangle. Hence this statement is clearly insufficient.
Now consider S(2), we have \(AC^2=AB^2+BC^2\)

The statement implies that ABC is a right triangle and AC is its hypotenuse.
Important Property: Median from the right triangle is half of the hypotenuse.

Hence, BD = 12 = \(\frac{AC}{2}\) , from which we have AC = 24

Hence this statement is sufficient in itself.

Correct option: B

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