This is quite tricky
From the question we have that C+12 = 2R which can be rewritten as R = C/2 + 6. Before even start thinking about this you should already be aware that C has to be even and multiple of 2 since number of tapes has to be integer.
(i) R>5: Resolve the equation to [b]C = 2 ( R - 6) [/b]
Here start plugging numbers so you have
R = 6 gives C =0
R = 7 gives C = 2
etc etc
R = 12 gives C =12 (btw this is not a option as we allready know that one of the two has more)
R = 13 gives C =14
So as you can see
R > C for 6<= R <12 AND
R < C for R >=13 hence insufficient. It would be sufficient if and only if we could see that R>C for R>5.
(ii) C>12: Use the original equation [b]R = C/2 + 6 (for the more "mathy" people this can be seen as y = 0.5x+6) [/b]. Again start plugging numbers BUT the twist is that you care only for the even values defined by the space 0 < R <12
Start plugging numbers again
C = 10 gives R = 11
C = 8 gives R =10
C = 6 gives R = 9
C = 4 gives R = 8
C = 2 gives R = 6
Notice that for all values of C the variable R IS ALWAYS GREATER THAN C therefore sufficient
On a side note:
Bunuel wrote:
(1) Rafael has more than 5 tapes --> \(r>5\). If \(r=6>5\) then \(c=0\) and \(c<r\) BUT if \(r=14>5\) then \(c=16\) and \(c>r\). Two different answers. Not sufficient.
imho the take away msg from this question is to be able to understand the trend of equation for all values of x given by the question. Essentially boils down to the point to be able to undestand that in (i) the equation changes while in (ii) constantly y < x.
I am pretty sure people with solid math background just by looking the two equations could figure out the right answer rather than plug in number etc.