GMAT OFFICIAL GUIDE DS – If Carmen had 12 more tapes…

Solution:

We are given that if Carmen had 12 more tapes she would have twice as many tapes as Rafael. If we let C = the number of tapes that Carmen has and R = the number of tapes that Rafael has, we can create the following equation:

C + 12 = 2R

We need to determine whether Carmen has fewer tapes than Rafael has.

Is C < R?

Using our given equation, C + 12 = 2R, we can get variable C in terms of R.

C = 2R – 12.

Since C = 2R – 12, we can substitute 2R – 12 for C in our inequality C < R.  So our new question looks like:

Is 2R – 12 <R ?

Is R < 12?

We must determine whether Rafael has fewer than 12 tapes.

Statement One Alone:

Rafael has more than 5 tapes.

Using the information from statement one we cannot determine whether Rafael has fewer than 12 tapes. We can eliminate answer choices A and D.

Statement Two Alone:

Carmen has fewer than 12 tapes.

We can express the information in statement two in the form of an inequality.

C < 12

Since C = 2R – 12, we can substitute 2R – 12 for C in the inequality C < 12.

2R – 12 < 12

2R < 24

R < 12

We see that Rafael has fewer than 12 tapes. Statement two is sufficient to answer the question.