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

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If Carmen had 12 more tapes, she would have twice as many [#permalink] New post 25 Feb 2012, 08:33
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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.
[Reveal] Spoiler: OA
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Re: stumped over DS problem, please help [#permalink] New post 25 Feb 2012, 08:42
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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.

Hope it's clear.
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Re: If Carmen had 12 more tapes, she would have twice as many [#permalink] New post 26 Feb 2012, 09:53
yes, definitely....

thanks Bunuel :D :D
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Re: If Carmen had 12 more tapes, she would have twice as many [#permalink] New post 20 Aug 2013, 01:33
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Re: If Carmen had 12 more tapes, she would have twice as many [#permalink] New post 10 Jan 2014, 09:39
nina11 wrote:
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.



The time pressure is killing me..

We're given: C + 12 = 2R


1), we don't know anything about how many tapes carmen has, she could have more or less than Rafael, so insufficient.

2) Here's why so many of us get this wrong: We forget that the number of tapes Carmen has cannot be odd, it HAS to be a multiple of 2 otherwise we get fractions, and tapes have to be integer values.

So, she has, at most 10 tapes and then Rafael has 24/2 = 11 tapes.. So he always has more tapes than her, for all even values from 2-10... So, B is sufficient..
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Re: If Carmen had 12 more tapes, she would have twice as many [#permalink] New post 28 May 2014, 22:46
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I think algebraic approach works the best here. 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?

Lets simplify the question. First lets put c in terms of r in the inequality: c<r --> 2r-12<r --> r<12?
Second, lets put r in terms of c in the inequality: c<r --> c<(c/2+6) --> c<12?
Thus we will have sufficient info if we know either r<12 or c<12.

St1) r>5: r could be greater, equal, or less than 12. Not Suff
St2) c<12: Suff

Answer: B
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Re: If Carmen had 12 more tapes, she would have twice as many   [#permalink] 28 May 2014, 22:46
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