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Solution given in OG is complicated

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Jul 26, 2013 7:30 am
If a, b, c, and d, are positive numbers, is a/b < c/d?

(1) 0 < (c-a) / (d-b)

(2) (ad/bc)^2 < (ad)/(bc)
Statement 1: (c-a) / (d-b) > 0
Make c and d both greater than a and b.
Try two cases:
c > d, so that c/d > 1.
c < d, so that c/d < 1.

Case 1: a=1, b=1, c=3, and d=2.
In this case, a/b = 1 and c/d = 3/2, so a/b < c/d.

Case 2: a=1, b=1, c=2, and d=3.
In this case, a/b = 1 and c/d = 2/3, so a/b > c/d.
INSUFFICIENT.

Statement 2: (ad/bc)² < (ad)/(bc)
Since all of the values are positive, we can rephrase the question stem by cross-multiplying:
a/b < c/d
ad < bc.
Question stem rephrased: Is ad < bc?

Since all of the values are positive, we can divide each side of statement 2 -- (ad/bc)² < (ad)/(bc) -- by ad/bc, yielding the following:
ad/bc < 1
ad < bc.
SUFFICIENT.

The correct answer is B.
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by faraz_jeddah » Thu Aug 01, 2013 4:37 am
GMATGuruNY wrote:
If a, b, c, and d, are positive numbers, is a/b < c/d?

(1) 0 < (c-a) / (d-b)

(2) (ad/bc)^2 < (ad)/(bc)
Statement 1: (c-a) / (d-b) > 0
Make c and d both greater than a and b.
Try two cases:
c > d, so that c/d > 1.
c < d, so that c/d < 1.

Case 1: a=1, b=1, c=3, and d=2.
In this case, a/b = 1 and c/d = 3/2, so a/b < c/d.

Case 2: a=1, b=1, c=2, and d=3.
In this case, a/b = 1 and c/d = 2/3, so a/b > c/d.
INSUFFICIENT.

Statement 2: (ad/bc)² < (ad)/(bc)
Since all of the values are positive, we can rephrase the question stem by cross-multiplying:
a/b < c/d
ad < bc.
Question stem rephrased: Is ad < bc?

Since all of the values are positive, we can divide each side of statement 2 -- (ad/bc)² < (ad)/(bc) -- by ad/bc, yielding the following:
ad/bc < 1
ad < bc.
SUFFICIENT.

The correct answer is B.

Hi Mitch

In statement 2 dont we consider the possibility that a b c d could be fractions (< 1)? The question does not mention that they are integers.
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by GMATGuruNY » Thu Aug 01, 2013 6:29 am
faraz_jeddah wrote:
GMATGuruNY wrote:
If a, b, c, and d, are positive numbers, is a/b < c/d?

(2) (ad/bc)^2 < (ad)/(bc)
Statement 2: (ad/bc)² < (ad)/(bc)
Since all of the values are positive, we can rephrase the question stem by cross-multiplying:
a/b < c/d
ad < bc.
Question stem rephrased: Is ad < bc?

Since all of the values are positive, we can divide each side of statement 2 -- (ad/bc)² < (ad)/(bc) -- by ad/bc, yielding the following:
ad/bc < 1
ad < bc.
SUFFICIENT.
Hi Mitch

In statement 2 dont we consider the possibility that a b c d could be fractions (< 1)? The question does not mention that they are integers.
The reasoning for statement 2 holds true as along as the values are POSITIVE.
Whether a, b, c and d are fractions or integers is irrelevant.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by topspin20 » Thu Aug 01, 2013 5:25 pm
Also for statement 2, you know that since (ad/bc)^2 < (ad)/(bc), then (ad)/(bc)<1, and ad<bc.
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