Data Sufficiency

BTGmoderatorDC wrote:If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael?

(1) Rafael has more than 5 tapes.
(2) Carmen has fewer than 12 tapes.

OA B

Source: Official Guide

Say Carmen has C number of tapes and Rafael has R number of tapes. Thus, from the given condition, we have

C + 12 = 2R

We have to determine whether C < R.

Let's take each statement one by one.

(1) Rafael has more than 5 tapes.

Case 1: Say R = 6 (Minimum possible value of R)

Thus, as per C + 12 = 2R, we have C = 0, an invalid value since C ≥ 1.

Case 2: Say R = 7 (Qualified minimum possible value of R)

Thus, as per C + 12 = 2R, we have C = 2 and C < R. The answer is Yes.

Case 3: Say R = 20 (A bigger value of R)

Thus, as per C + 12 = 2R, we have C = 28 and C > R. The answer is No.

No unique answer. Insufficient.

(2) Carmen has fewer than 12 tapes.

=> C < 12

Case 1: Say C = 10 (Qualified maximum possible value of C; C must be even for R to be an integer; thus, C cannot be 11)

Thus, as per C + 12 = 2R, we have R = 11 and C < R. The answer is Yes.

Case 2: Say C = 2 (Qualified minimum possible value of C; C must be even for R to be an integer; thus, C cannot be 1)

Thus, as per C + 12 = 2R, we have R = 7 and C < R. The answer is Yes.

Unique answer. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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