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a^3b^4c^7>0 [#permalink]
Expert's post 00:00

Question Stats: 37% (00:40) correct 62% (00:47) wrong based on 58 sessions
$$a^3b^4c^7>0$$

Which of the following statements must be true?

Indicate all such statements.

A. $$ab$$ is negative

B. $$abc$$ is positive

C. $$ac$$ is positive
[Reveal] Spoiler: OA

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Re: a^3b^4c^7>0 [#permalink]
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Carcass wrote:
$$a^3b^4c^7>0$$

Which of the following statements must be true?

Indicate all such statements.

A. $$ab$$ is negative

B. $$abc$$ is positive

C. $$ac$$ is positive

the above statement will be true if any of the following statement are true,

1. a , b , c are all positive numbers

2. if a is +ve, b is -ve and c is +ve

3. if a is -ve, b is +ve and c is -ve

Therefore only option C is always true
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Re: a^3b^4c^7>0 [#permalink]
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Expert's post
Carcass wrote:
$$a^3b^4c^7>0$$

Which of the following statements must be true?

Indicate all such statements.

A. $$ab$$ is negative

B. $$abc$$ is positive

C. $$ac$$ is positive

Key Concept: (any number)^(EVEN INTEGER) ≥ 0

First, since $$a^3b^4c^7>0$$, we know that a ≠ 0, b ≠ 0, and c ≠ 0

Next, since $$b^4$$ must be POSITIVE, we can safely divide both sides of the inequality by $$b^4$$ to get: $$a^3c^7>0$$
Also, since $$c^6$$ must be POSITIVE, we can safely divide both sides of the inequality by $$c^6$$ to get: $$a^3c>0$$
Finally, since $$a^2$$ must be POSITIVE, we can safely divide both sides of the inequality by $$a^2$$ to get: $$ac>0$$

So, the ONLY relevant conclusion we can make is that $$ac>0$$

Answer: C

Cheers,
Brent
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Re: a^3b^4c^7>0 [#permalink]
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Answer: C
A: if ab <0 then:
a<0 and b>0 : then c should be negative to have a^3*b^4*c^7 >0
a>0 and b<0 : then it’s ok because b’s power is even.
So A is possible but not obligatory.

B: it’s possible, But it’s not obligatory.

C: ac is positive: True
Because power of a and c are odd, they both should have same sign, both negative or positibve to have the whole expression positive.
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Follow your heart Re: a^3b^4c^7>0   [#permalink] 16 Nov 2018, 18:20
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