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Is a^7b^2c^3 > 0? (1) bc < 0 (2) ac > 0

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Stanindaw
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Is a^7b^2c^3 > 0? (1) bc < 0 (2) ac > 0 [#permalink] New post   23 Aug 2022, 21:47
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Is a^7∗b^2∗c^3 > 0?

(1) bc < 0
(2) ac > 0

M11-26

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Bunuel
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Re: Is a^7b^2c^3 > 0? (1) bc < 0 (2) ac > 0 [#permalink] New post   24 Aug 2022, 01:10
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Stanindaw wrote:
Is a^7∗b^2∗c^3 > 0?

(1) bc < 0
(2) ac > 0

M11-26


Is \(a^7*b^2*c^3 \gt 0\)?

Inequality \(a^7*b^2*c^3 \gt 0\) to be true two conditions must be met:

    (i) \(a\) and \(c\) must be either both positive or both negative: in this case \(a^7*c^3\) will be positive;

    (ii) \(b\) must not be zero: if \(b = 0\), then the entire expression (\(a^7*b^2*c^3\)), irrespective \(a\) and \(c\), will be 0, not more than 0.

(1) \(bc \lt 0\). Hence, \(b \ne 0\). Don't know about \(a\) and \(c\). Not sufficient.

(2) \(ac \gt 0\). Hence, \(a\) and \(c\) are either both positive or both negative. Don't know about \(b\): if \(b=0\), then the expression will be equal 0. Not sufficient.

(1)+(2) Sufficient.


Answer: C
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VineelSurya
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Re: Is a^7b^2c^3 > 0? (1) bc < 0 (2) ac > 0 [#permalink] New post   23 Aug 2022, 22:34
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\(a^{7}\)*\(b^{2}\)*
\(c^{3}\)>0

From the question, we can conclude that bis always a
Statement 1 says bc>0

With this we can't say much because, for any sign, the whole equation depends on "a" as well.
Insufficient.

Statement 2 says that ac>0

Means either a & c has to be positive or negative.

In any way, \(a^{7}\)*\(c^{3}\) will be greater that zero and also \(b^{2}\) is always positive.
Sufficient.

So the answer has to be Option B

I wonder why it is C. Can someone explain?

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Re: Is a^7b^2c^3 > 0? (1) bc < 0 (2) ac > 0 [#permalink] New post   23 Aug 2022, 22:53
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VineelSurya wrote:
Statement 2 says that ac>0

Means either a & c has to be positive or negative.

In any way, \(a^{7}\)*\(c^{3}\) will be greater that zero and also \(b^{2}\) is always positive.
Sufficient.

So the answer has to be Option B

I wonder why it is C. Can someone explain?

With Statement 2 alone,
If b=0 then a^7 * b^2 * c^3 = 0, even if ac>0

Statement 1 tells us that b cannot be 0.

So we need both statements

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Re: Is a^7b^2c^3 > 0? (1) bc < 0 (2) ac > 0 [#permalink] New post   17 Nov 2023, 07:44
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Re: Is a^7b^2c^3 > 0? (1) bc < 0 (2) ac > 0 [#permalink]
17 Nov 2023, 07:44
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