ds#20

[dunkin77]

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.




Hi,
I thought the answer was E) but the text says B) -- Can anyone confirm?

[mschling52]

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.

[moneyman]

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..