Find the value of x. (1) The length of B C is 2 \sqrt{3} (2) The length of A C is 4 .

Correct Answer is : The problem can be solved using EITHER statement (1) only or statement (2) only.

Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.

Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.

The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).

The problem can be solved using EITHER statement (1) only or statement (2) only.

The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

GMAT Quantitative Reasoning Practice Test 6

Question : 11 of 100

Marks: +1, -0

Find the value of x.

(1) The length of

B C

2 {√{3}}

(2) The length of

A C

is 4 .

Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.
Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.
The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).
The problem can be solved using EITHER statement (1) only or statement (2) only.
The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

Validate

Solution:

From the diagram, if the measure of angle C is 30 degrees and angle B is a right angle, then ΔABC is a 30-60-90 right triangle. Using statement (1), if the measure of BC is 2 square root of 3 , then the shortest side x must be

\;{2 × 2 {√{3}}}/{2 {√{3}}}

which reduces to 2. Using statement (2), if the length of AC is 4 and AC is the hypotenuse of the triangle, then the shortest side of the triangle x is equal to

4/2 = 2

. Either statement is sufficient

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