GMAT question - In a rectangle ABCD, P is at the midpoint of AB and ... - Review

In a rectangle ABCD, P is at the midpoint of AB and Q is at the midpoint of BC. What is the area of triangle PBQ?

1. Area of triangle ABD is 20
2. The length of AB is 10

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

Explanation

We will approach this question step by step.

Draw a diagram

You are given a great deal of information in the question and unless you draw a diagram on your noteboard you will find this question very difficult.

The diagram above shows you rectangle ABCD with point P marked at the midpoint of AB and Q marked at the midpoint of BC. The triangle PBQ, that the question asks for the area of, is shaded in green.

It should be clear that this triangle PBQ is 1/8 of the total area of the rectangle ABCD and so if we knew the area of the whole rectangle we would know the area of the triangle.

Is statement (1) sufficient?

This tells us the area of triangle ABD which is clearly half of the area of the rectangle ABCD. And if we know the area of the rectangle ABCD we can find the area of PBQ.

Therefore statement (1) is sufficient to work out the answer.

Is statement (2) sufficient?

Knowing the length of AB is not sufficient to find the area of the rectangle ABCD and therefore is not sufficient to find the area of PBQ.

Choose an answer

Statement (1) is sufficient and statement (2) is not sufficient which means that the answer is A (1 only).