# GMAT OFFICIAL GUIDE DS – If Sara’s age is exactly twice…

## Solution:

We are given that Sara’s age is twice Bill’s age. If we let Sara’s current age = S and Bill’s current age = B, we can create the following equation:

S = 2B

We need to determine Sara’s current age.

Statement One Alone:

Four years ago, Sara’s age was exactly 3 times Bill’s age.

Using the information in statement one we can create the following equation, noting that we must subtract 4 from both Sara’s current age and Bill’s current age to determine their respective ages 4 years ago:

S – 4 = 3(B – 4)

Since we have the equation S = 2B, from the given information we see that we have enough information to determine Sara’s age. Let’s complete the problem, even though it is not necessary.

2B – 4 = 3(B – 4)

2B – 4 = 3B – 12

B = 8 and thus S = 2B = 16

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

Eight years from now, Sara’s age will be exactly 1.5 times Bill’s age.

Using the information in statement two we can create the following equation, noting that we must add 8 to both Sara’s current age and Bill’s current age to determine their respective ages in 8 years:

S + 8 = 1.5(B + 8)

Since we have the equation S = 2B, from the given information we see that we have enough information to determine Sara’s age. Statement two alone is sufficient to answer the question.