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a^3b^4c^7>0

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a^3b^4c^7>0 [#permalink] New post 18 Jul 2018, 17:00
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\(a^3b^4c^7>0\)

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] New post 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] New post 29 Aug 2018, 07:38
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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


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] New post 16 Nov 2018, 18:20
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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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Re: a^3b^4c^7>0 [#permalink] New post 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] New post 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 \(ac>0\)

Answer: C

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



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] New post 01 Sep 2019, 23:44
how come B isn't an answer?
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Re: a^3b^4c^7>0 [#permalink] New post 02 Sep 2019, 06:08
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shadowmr20 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
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Re: a^3b^4c^7>0 [#permalink] New post 04 Sep 2019, 06:28
GreenlightTestPrep wrote:
shadowmr20 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] New post 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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