If Carmen had 12 more tapes, she would have twice as many
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16 Jun 2023, 04:49
[quote="Bunuel"]If Carmen had 12 more tapes, she would have twice as many as Rafael. Does Carmen have fewer tapes than Rafael?
Given \(c+12=2r\), question is \(c<r\)?
(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.
(2) Carmen has fewer than 12 tapes --> \(c<12\). Max number of tapes Carol can have is 10 (if \(c=11\) then \(r=11.5\neq{integer}\), which is not possible since \(c\) and \(r\) represent # of tapes and must be integers). So, \(c_{max}=10\) and \(r=11\) (from \(c+12=2r\)), hence \(c<r\). Sufficient.
Since even for \(c_{max}\) we got that \(c<r\), then for all other possible values of \(c\), \(c<r\) will also hold true.
Answer: B.
Hi Bunuel, my take as below:
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.
My option was D. (It is shown as wrong in answer btw).
From option (1), rafael can have tapes as 6, 7, 8 and so on.
if rafael have 6 tapes, then carmen would have 0 tapes which is also a probability (Why we are assuming that everyone should have atleast a tape). And this fits in the equation too as if rafael has 6 tapes then carmen would have 0 tapes, and adding 12 to 0 would give 12 which is exactly twice of tapes that rafael has. Other no of tapes like 7, 8 and so on with rafael will give tapes no as negative with carmen which is not a possibility here. Thus in my opinion option (1) is sufficient too.
From option (2), i.e carmen has less than 12 tapes, it would be 10, 8, 6, 4, and 2 as odd no of tapes would give rafael tapes which are in fractions which is not a possibility.
From the no of tapes with carmen, i.e 10,8,6,4,and 2, with the equation c+12=2r (c=no of tapes with carmen, r=no of tapes with rafael), no of tapes with carmen will come out to be fewer than rafael. Hence option (2) is also sufficient.
Hence option D.
Any take on this.