Data Sufficiency

If Carmen had 12 more tapes, she would have twice Rafael's. Does Carmen have fewer tapes than rafael.

1. rafael has more than 5 tapes
2. carmen has fewer than 12 tapes

oa : b

my analysis

c+12=2r ?c<r ??

1. r>5
2r >10
c+12=2r>10
c>-2>0 is true

so sufficient ??

2. c<12
c+12 <24
i.e. 2r<24
i.e. r<12
so C<12 ==> r<12
==> C and R have both less than 12. How do I conclude ??

Of course there is some mistake in my logic for 1 also

Need the right way to solve such questions also !!

C + 12 = 2R

(1) R > 5
2R > 10
C + 12 > 10
C > -2
Since C is number of tapes, C > 0
So, we have C > 0, R > 5
That doesn't tell us anything.

For e.g if you plug in numbers,
if C = 10, R = 11
C = 12, R = 12
C = 14, R = 13

Not sufficient.


(2) C < 12
C + 12 < 24
2R < 24
R < 12
Now plug in numbers. Since numbers of tapes can't be fractional
C = 0, R = 6
C = 2, R = 7
C = 4, R = 8
C = 6, R = 9
C = 8, R = 10
C = 10, R 11
Carmen has fewer tapes than Rafael does in each of this case.

Sufficient.


Answer is (B)

Here's How I aprroached the problem....
It's easier if you resolve the question stem...

Its given that C+12=2R
So,Simplify this to C = 2(R-6)

Looking at this expression its easy to observe that R should be atleast 6 to have a valid value of C..Isn't it ?

Now,lets look at each statement.

(1) says R > 5
So,R can take values 6,7,8 ..... (assuming that they are positive integers - tapes cannot be real numbers )

It can be observed by plugging numbers that C is less than R so long as
5 < R < 12 but the trend reverses as soon as the value of R exceeds 12.
C=R when R=12.

So,with statement 1,it is possible that C can be less than,equal or greater than R.Hence,not sufficient.

(2) Looking at the above explanation,its clear - what we need for C to be always less than R.Statement 2 give this exact information that R < 12.

Hence,Sufficient.

So,B

Its always easier if you simplify the question stem before proceeding with the choices...