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# If a, b, c, d, and x are all nonzero integers, is the product ax • (bx

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If a, b, c, d, and x are all nonzero integers, is the product ax • (bx  [#permalink]

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21 Feb 2019, 11:16
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Difficulty:

55% (hard)

Question Stats:

69% (01:26) correct 31% (01:39) wrong based on 35 sessions

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If a, b, c, d, and x are all nonzero integers, is the product $$ax • (bx)^2 • (cx)^3 • (dx)^4$$ negative?

(1) a < c < x < 0

(2) b < d < x < 0

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Re: If a, b, c, d, and x are all nonzero integers, is the product ax • (bx  [#permalink]

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21 Feb 2019, 11:53
As a,b,c,d, and x are non zero integers, the product $$(bx)^2$$ and $$(dx)^4$$ will always remain positive as the powers are positive.
The question reduces to whether $$ax*(cx)^3$$ is negative, or $$a*c^3$$ is negative? as $$x^4$$ will always be positive.

From S1:

both a and c are negative, then $$a*c^3$$ will be positive.
Hence S1 is sufficient.

From S2:

No info about a and c.
Insufficient.

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If a, b, c, d, and x are all nonzero integers, is the product ax • (bx  [#permalink]

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21 Feb 2019, 15:33
If a, b, c, d, and x are all nonzero integers, is the product $$ax • (bx)^2 • (cx)^3 • (dx)^4$$ negative?

(1) a < c < x < 0

(2) b < d < x < 0

Statement 1:

a<c<x<0.

a, c, x, all are negative.

ax = positive.

$$(bx)^2$$ = positive all time.

cx = positive as both c and x are negative.

$$(cx)^3$$ = positive.

$$(dx)^4$$ = positive all time.

So, all are positive . Product will be positive.

Statement A is sufficient.

Statement 2:

b < d < x < 0

b, d, x are negative.

*** No information about a and c.

$$( bx)^2$$ = positive all time.

$$(dx)^4$$ = positive all time.

ax = positive if a is negative

ax = negative if a is positive.

$$(cx)^3$$ = negative if c is positive.

$$(cx)^3$$ = positive if c is negative.

Therefore different combination is possible.

Here ax and $$(cx)^3$$ are the keys to answer this question but we have 4 different choices that make the statement Insufficient to answer this question

NOT sufficient.

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Re: If a, b, c, d, and x are all nonzero integers, is the product ax • (bx  [#permalink]

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21 Feb 2019, 16:08
Statement #1 suff as we only care about signs of odd powered terms.
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Re: If a, b, c, d, and x are all nonzero integers, is the product ax • (bx  [#permalink]

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22 Feb 2019, 01:54
If a, b, c, d, and x are all nonzero integers, is the product $$ax • (bx)^2 • (cx)^3 • (dx)^4$$ negative?

(1) a < c < x < 0

(2) b < d < x < 0

GIVEN:
$$ax • (bx)^2 • (cx)^3 • (dx)^4$$

#1
a < c < x < 0
means all integers here are -ve, irrespective of their value ...

so
$$ax • (bx)^2 • (cx)^3 • (dx)^4$$
+*+*+*+ = +ve value
sufficient

#2 b < d < x < 0
so now since value of a and c are not given ,
$$ax • (bx)^2 • (cx)^3 • (dx)^4$$
can be +ve or -ve
Insufficient

IMO A
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Re: If a, b, c, d, and x are all nonzero integers, is the product ax • (bx   [#permalink] 22 Feb 2019, 01:54
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