ds#20

I think B is right. The stem gives us the equation

R = (C+12)/2

and the question is C<R? If C<R, then

C < (C+12)/2
2C < C+12
C<12

So, if we know that C < 12, then we also know that C < R.

(1) alone only gives us R > 5. If R = 6, then C = 0 and C<R. However, if R=15, then C=18 and C>R, so (1) Alone is not sufficient.

(2) alone, however, gives us C<12, which is sufficient by the logic above.

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.

From the question the equation c+12=2r can be obtained now we just have to look out for the value of c or r to solve the problem.

(1)is not sufficient because if r>5 can be any number and hence will result in many values.

(2) is sufficent because if c<12 and c+12=2r then c will have a range of values from 1-11.By substituting the value of c as 11 c becomes 23 and so the value of r can be obtained as 11.5.Since the maximum value of c can only be 11 and by substituting the values in the equation we get the value of r as 11.5 the question is answered as r>c.

I hope my way of doing this problemn helped you..