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# If a,b,c,d and x are all non zero integers, is the product

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Joined: 16 Apr 2007
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If a,b,c,d and x are all non zero integers, is the product [#permalink]

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11 Oct 2007, 23:56
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If a,b,c,d and x are all non zero integers, is the product ax*(bx)^2*(cx)^3*(dx)^4 positive or negative?
(1) a < c < x < 0
(2) b < d < x < 0

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Director
Joined: 11 Jun 2007
Posts: 910

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12 Oct 2007, 00:06
mohansb wrote:
If a,b,c,d and x are all non zero integers, is the product ax*(bx)^2*(cx)^3*(dx)^4 positive or negative?
(1) a < c < x < 0
(2) b < d < x < 0

i get A

we just need to know the signs for a, c, and x because regardless of what b and d are, their expressions will always be positive since they are raised to an even power

stmt 1 clearly tells us that a, c, and x are all negative
so the expression ax*(bx)^2*(cx)^3*(dx)^4 ends up positive
suff

stmt 2 only tells us that x is neg
not suff

Last edited by beckee529 on 12 Oct 2007, 00:08, edited 1 time in total.

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SVP
Joined: 01 May 2006
Posts: 1794

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12 Oct 2007, 02:14
(A) too for me

Sign(ax*(bx)^2*(cx)^3*(dx)^4) = Sign(a*x) * Sign(c*x) as (bx)^2 > 0 and (dx)^4 > 0

So, we have to know the sign of a*x and of b*x. Let see the statments now

Stat 1
a < c < x < 0

Implies that:
o a*x > 0
o c*x > 0

SUFF.

Stat 2
b < d < x < 0

INSUFF.

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Intern
Joined: 09 Oct 2007
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12 Oct 2007, 02:43
mohansb wrote:
If a,b,c,d and x are all non zero integers, is the product ax*(bx)^2*(cx)^3*(dx)^4 positive or negative?
(1) a < c < x < 0
(2) b < d < x < 0

Agree, it is A. We should examine only those products that may be positive or negative. Those with powers 2 and 4 may be neglected.

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Re: DS   [#permalink] 12 Oct 2007, 02:43
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