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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]

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12 Apr 2013, 04:56
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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

[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Apr 2013, 05:20, 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]

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12 Apr 2013, 05:39
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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.

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, 05:39
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