Solution given in OG is complicated
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Statement 1: (c-a) / (d-b) > 0If 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)
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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- faraz_jeddah
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GMATGuruNY wrote:Statement 1: (c-a) / (d-b) > 0If 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)
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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The reasoning for statement 2 holds true as along as the values are POSITIVE.faraz_jeddah wrote:Hi MitchGMATGuruNY wrote:Statement 2: (ad/bc)² < (ad)/(bc)If a, b, c, and d, are positive numbers, is a/b < c/d?
(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.
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.
Whether a, b, c and d are fractions or integers is irrelevant.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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].
Student Review #1
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