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# If Carmen had 12 more tapes, she would have twice as many

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SVP
Joined: 30 Mar 2006
Posts: 1737
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If Carmen had 12 more tapes, she would have twice as many [#permalink]  18 Jun 2006, 02:51
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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
Manager
Joined: 01 Jun 2006
Posts: 141
Followers: 1

Kudos [?]: 2 [0], given: 0

B it is.
(1) is insufficient because if C+12=2R so it is obvious that R>6
(2) C<12 so if C+12=2R. We must have C<R<12
Director
Joined: 07 Jun 2006
Posts: 513
Followers: 10

Kudos [?]: 91 [0], given: 0

Another approach

since C+12 = 2R, R = (c + 12)/2

R has to be an integer, so let's take the greatest possible tapes C could have given condition (B),

Plugging in 11 for C, is ruled out since R = 23/2 (not an integer)
Plugging in 10 for C, R = 11;

So the greatest possibililty of C is lesser than what it would result for R. So (B) is sufficient.
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