If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael?
Its given, C + 12 = 2 R and we need to find Is C < R ?
(1) Rafael has more than 5 tapes.
Here, R >5.
Minimum possible value of R is 6 as the no of tapes should be an integer.
Case 1:
R =6
C + 12 = 2 *6
C =0
Is C < R ? => is 0 < 6 ? YES
Case 2:
R =20 as R could be any integer greater than 5
C + 12 = 2 *20
C = 40 -12 = 28
Is C < R ? => is 28 < 20 ? NO
Since we don't have a definite YES or NO for the question stem, Statement 1 alone is insufficient.
(2) Carmen has fewer than 12 tapes.
It's given C < 12.
Maximum possible value of C is 11.
Case 1: C = 11
C + 12 = 2 R
11 + 12 = 2R
R = 23/2 = 11.5 which is not possible as no of tapes should be an integer.
Case 2 :C = 10
C + 12 = 2 R
10 + 12 = 2R
R = 22/2 = 11
is C < R ? YES
Case 3:
if C = 0
C + 12 = 2 R
0 + 12 = 2R
R = 6
is C < R ? YES
Also we can conclude that C should an even integer less than 12 in-order to get a integer value for R .
6 <= R <=11
As you can see, for every possible values of C, R will be greater.
is C < R ? YESStatement 2 alone is sufficient .
Option B is the answer.
Thanks,
Clifin J Francis,
GMAT SME _________________
Crackverbal Prep Team
www.crackverbal.com