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# If a, b, c, and d are integers and ab2c3d4 > 0, which of the

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If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

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27 Jul 2012, 09:10
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If a, b, c, and d are integers and $$ab^2c^3d^4 > 0$$, which of the following must be positive?

I. $$a^2cd$$
II. $$bc^4d$$
III. $$a^3c^3d^2$$

A) I only
B) II only
C) III only
D) I and III
E) I, II, and III
[Reveal] Spoiler: OA
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Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

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27 Jul 2012, 09:29
superpus07 wrote:
If a, b, c, and d are integers and $$ab^2c^3d^4 > 0$$, which of the following must be positive?

I. $$a^2cd$$
II. $$bc^4d$$
III. $$a^3c^3d^2$$

A) I only
B) II only
C) III only
D) I and III
E) I, II, and III

Since given that $$a*b^2*c^3*d^4 > 0$$, then we know that none of the unknowns is zero. Therefore, $$b^2>0$$ and $$d^4>0$$, which means that we can safely reduce by them to get $$a*c^3>0$$ (so, the given expression does not depend on the value of $$b$$ or $$d$$: they can be positive as well as negative).

Next, $$a*c^3>0$$ means that $$a$$ and $$c$$ must have the same sign: they are either both positive or both negative.

Evaluate each option:

I. $$a^2cd$$. Since $$d$$ can positive as well as negative then this option is not necessarily positive.

II. $$bc^4d$$. Since $$d$$ can positive as well as negative then this option is not necessarily positive.

III. $$a^3c^3d^2$$. Since $$a*c^3>0$$, then $$a^3*c^3>0$$ and as $$d^2>0$$, then their product, $$(a^3*c^3)*d^2$$ must be positive too.

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Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

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31 Jul 2014, 18:32
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Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

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31 Jul 2014, 21:32
a*(b^2)*(c^3)*(d^4) > 0,

since b^2 and d^4 are always positive..

a*(c^3) is positive .. so 'a' and 'c' are of the same sign, eithr positive or negative. we have no information about 'b' and 'd' , so they could b negative..

so the first 2 statements ( I and II ) have 'd' in them, which could be negative.. so we can eliminate them then and there.

in statement III, 'd' is squared, so thats positive and since 'a' and 'c' are of the same sign, a^3 * c^3 must be positive.

so III only , that option C.
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Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

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11 Nov 2015, 20:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the   [#permalink] 11 Nov 2015, 20:28
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