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If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a +

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Bunuel
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If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   25 Nov 2014, 08:24
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If a, b, and c are distinct nonzero numbers, is \(\frac{(a - b)^3(b - c)}{(a + b)^2(b + c)^2} < 0\) ?

(1) a > b
(2) b > c


Source: Chili Hot GMAT­
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C
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Ankur9
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   25 Nov 2014, 10:04
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Bunuel wrote:

Tough and Tricky questions: Inequalities.



If a, b, and c are distinct nonzero numbers, is \(\frac{(a - b)^3(b - c)}{(a + b)^2(b + c)^2} < 0\) ?

(1) a > b
(2) b > c

Kudos for a correct solution.

Source: Chili Hot GMAT


\(\frac{(a - b)^3(b - c)}{(a + b)^2(b + c)^2} < 0\)
(a + b)^2 and (b + c)^2 will always be positive
(1) a > b
a-b>0 thus (a - b)^3 is positive but we have no information about (b-c) thus not sufficient
(2) b > c
b-c>0 but no info about a and b. Not sufficient
combining 1 and 2
a-b>0 and b-c>0 then
\(\frac{(a - b)^3(b - c)}{(a + b)^2(b + c)^2}\) will always be greater then 0.
Sufficient. [C]
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   25 Nov 2014, 10:15
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I will go with (C) again not sure though

Denominator will always be +ve since the numbers are distinct and non zero (i think this assumption is incorrect because if a=2, b=-2 & c=-3 then the denominator is 0 and the fraction is undefined, but anyways)

1. (a-b)^3 will be +ve if a>b and then (b-c) has to be -ve meaning b<c
2. (b-c) will be +ve if b>c and then (a-b)^3 has to be -ve meaning a<b

Combining the two 1 & 2 we will always get greater than 0

Not convinced with the question because of the assumption above.
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   25 Nov 2014, 17:51
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The premise is asking whether that expression is greater than 0. The denominator has the square of a product times the square of a different product. These two values are always greater than or equal to 0. So, we must determine the sign of the two expressions on top.

Statement 1 says that a>b, meaning that a-b > 0 (pos). Insufficient as we don't know how b relates to c.
Statement 2 says that b>c, meaning that b-c > 0 (pos). Insufficient as we don't know how a relates to b.
Combining them we know that the numerator is positive. Choose C as we know the expression is not negative.
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   25 Nov 2014, 20:59
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The value of (a-b)^3 and the value of (b-c) will be instrumental to determine whether the fraction is less than zero or not, since the denominator has squares which will either be positive or zero.

1. a > b. Insufficient since we don't know the relationship between b and C
2. b > c. Insufficient since we don't know the relationship between a and b

Combining both , we can (a-b)^3 * (b-c) is positive. Hence the fraction is also positive. Sufficient.

C) should be the answer
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   26 Nov 2014, 01:04
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Bunuel wrote:

Tough and Tricky questions: Inequalities.



If a, b, and c are distinct nonzero numbers, is \(\frac{(a - b)^3(b - c)}{(a + b)^2(b + c)^2} < 0\) ?

(1) a > b
(2) b > c

Kudos for a correct solution.

Source: Chili Hot GMAT


I will also got with C.
Clearly denominator is always positive and does not determine the sign.
1) a>b but no information about b-c.
2) b>c no information about a-b.
Both INSUFFICIENT.

Combining we know a-b and b-c are positive so numerator is positive.
Answer = C/
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   26 Nov 2014, 07:23
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The correct answer is C.
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   22 Sep 2015, 11:47
To make the value of the fraction,its enough if we have any one set of numbers with brackets to be -ve .ie either (a-b)^3 or (b-c)

we need not worry about the squares as they would become +ve anyway

option1: a>b .It confirms that (a-b)^3 is +ve but if (b-c) is -ve then the result will be -ve and option 2 says b>c

So (b-c) is also +ve and hence the whole fraction is +ve

The answer is C as we need both the inputs to confirm that the fraction is +ve
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink] New post   29 Jun 2017, 12:13
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Re: If a, b, and c are distinct nonzero numbers, is (a b)^3(b c)/(a + [#permalink]
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