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# a^3b^4c^7>0

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a^3b^4c^7>0 [#permalink]  18 Jul 2018, 17:00
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37% (00:50) correct 62% (00:40) wrong based on 185 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]  18 Jul 2018, 19:53
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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]  29 Aug 2018, 07:38
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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 $$ac>0$$

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: a^3b^4c^7>0 [#permalink]  16 Nov 2018, 18:20
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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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Re: a^3b^4c^7>0 [#permalink]  15 Jul 2019, 08:13
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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]  15 Jul 2019, 08:15
GreenlightTestPrep wrote:
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 $$ac>0$$

Cheers,
Brent
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Re: a^3b^4c^7>0 [#permalink]  01 Sep 2019, 18:56
Fatemeh wrote:
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.

I'm confused with this question-answer at this point, why is B not a "must be true" statement?

nvm got it, got tricked

abc: - - + -> +
347: - + + -> -
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Re: a^3b^4c^7>0 [#permalink]  01 Sep 2019, 23:44
how come B isn't an answer?
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Re: a^3b^4c^7>0 [#permalink]  02 Sep 2019, 06:08
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Expert's post
how come B isn't an answer?

We're told that $$a^3b^4c^7>0$$
So, it COULD be the case that $$a=1$$, $$b=-1$$ and $$c=1$$

Statement B says $$abc$$ must be positive
However, if $$a=1$$, $$b=-1$$ and $$c=1$$ then $$abc$$ is negative

So, we can eliminate B

Cheers,
Brent
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Re: a^3b^4c^7>0 [#permalink]  04 Sep 2019, 06:28
GreenlightTestPrep wrote:
how come B isn't an answer?

We're told that $$a^3b^4c^7>0$$
So, it COULD be the case that $$a=1$$, $$b=-1$$ and $$c=1$$

Statement B says $$abc$$ must be positive
However, if $$a=1$$, $$b=-1$$ and $$c=1$$ then $$abc$$ is negative

So, we can eliminate B

Cheers,
Brent

if b is equal -1 then it must be positive as rules coz $$b^4$$. If a or c is equal -1 not the b then we can easily eliminate the answer choice B.
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Re: a^3b^4c^7>0 [#permalink]  30 May 2020, 18:13
Brent's answer is a really clever one, and a reminder that when you see inequalities like this on the GRE, you should look to manipulate it so that it's still true. You'll likely find a cool shortcut.
Re: a^3b^4c^7>0   [#permalink] 30 May 2020, 18:13
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