If Carmen had 12 more tapes…
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.