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23 Aug 2022, 21:47
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
31% (01:07) correct
69%
(01:04)
wrong
based on 105
sessions
History
Date
Time
Result
Not Attempted Yet
Is a^7∗b^2∗c^3 > 0?
(1) bc < 0
(2) ac > 0
M11-26
(1) bc < 0
(2) ac > 0
M11-26
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24 Aug 2022, 01:10
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Stanindaw
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
General Discussion
VineelSurya
Joined: 24 May 2021
Last visit: 12 Mar 2023
Posts: 11
Given Kudos: 48
Location: India
Schools: Scheller '25
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?
Posted from my mobile device
\(c^{3}\)>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?
Posted from my mobile device
