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The numbers a, b, c, and d are all positive, and J = a/b and

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The numbers a, b, c, and d are all positive, and J = a/b and [#permalink] New post 12 Apr 2013, 03:56
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The numbers a, b, c, and d are all positive, and J = a/b and K = c/d. Is J greater than K?

(1) a < b, c < d, and c > a
(2) a + 7 = c and b + 4 = d


please explain your answer thoroughly....
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Apr 2013, 04:20, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The numbers a, b, c, and d are all positive, and J = a/b and [#permalink] New post 12 Apr 2013, 04:39
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The numbers a, b, c, and d are all positive, and J = a/b and K = c/d. Is J greater than K?

The question asks whether \frac{a}{b}>\frac{c}{d}. Since all unknowns are positive we can safely cross-multiply: is ad>bc?

(1) a < b, c < d, and c > a. If a=1, b=2, c=2, and d=3, then ad=3<4=bc (answer NO) but if a=1, b=2, c=2, and d=5, then ad=5>4=bc. Not sufficient.

(2) a + 7 = c and b + 4 = d. The question becomes: is a(b+4)>b(a+7)? --> is ab+4a>ab+7b? --> is 4a>7b? We have no additional info to determine that. Not sufficient.

(1)+(2) The question from (2) became "is 4a>7b?" and (1) says that a<b, thus the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.
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Re: The numbers a, b, c, and d are all positive, and J = a/b and   [#permalink] 12 Apr 2013, 04:39
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The numbers a, b, c, and d are all positive, and J = a/b and

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