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If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0

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If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   04 Sep 2020, 00:15
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If \(a^{5}b^{6}c^{7} > 0\), is \(ab^{3}c^{5} <0\) ?


(1) b < 0

(2) c > 0


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Re: If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   04 Sep 2020, 00:33
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Question states ac>0 as b with an even power is always positive
So for ab^3c^5<0 we just need to find whether b is positive
1) states what is required i.e b <0 sufficient
2) no info about b only states c >0 and eventually a>0
Ans A

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Re: If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   04 Sep 2020, 01:03
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we know that even powers is always positive - so b^6 is positive.
since the whole number is positive, a^5 and c^7 are also positive, implying that a and c are of same sign. i.e. ac>0

(1) b < 0

In our required number, the number changed to odd power of b, if this is the case ab^3c^5 will be negative
so statement 1 is enough

(2) c > 0

If c is greater than 0, then a is greater than 0. but we don't know anything about the sign of b.
so Statement 2 is insufficient.

IMO A
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Re: If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   04 Sep 2020, 01:20
From given data it is clear that a and c should be either positive or negative. Means both have same sign. So there product is always positive. Hence to get our answer we only need to know sign of b.

(1) b < 0
Now we know b is negative and product is less than 0.

Sufficient

(2) c > 0
We don't know value of b.

Insufficient.

IMO Answer is A.
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If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   04 Sep 2020, 02:24
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If \(a^{5}b^{6}c^{7} > 0\), is \(ab^{3}c^{5} <0\) ?

let us split LHS term in terms of what we want \(a^{5}b^{6}c^{7} > 0\),
~(\(ab^{3}c^{5}\))*(\(a^{4}b^{3}c^{2})>0\)
now if the part from what is asked is taken in to consideration a & c have even powers so result will be positive but need sign of b

(1)\( b < 0\) this makes it clear that (\(a^{4}b^{3}c^{2})<0\)
so as product is positive \(ab^{3}c^{5} <0\) SUFFICIENT

(2) \(c > 0\)
if we place this in \(a^{5}b^{6}c^{7} > 0\) we can conclude \(a>0\)
now with \(a,c>0\) we still need b sign
so this doesn't help
INSUFFICIENT

A is the answer
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Re: If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   04 Sep 2020, 11:38
a^5*b^6*c^7>0

b^6 will always be positive. This means a and c both are positive or both are negative. Either ways a*c > 0.

So, to determine if a*b^3*c^5 < 0, all we need to know is if b<0. because a*c^5 will always be positive.

1. b<0. Sufficient.
2. c> 0. This only tells us a is also >0. But, no mention of b. Insufficient.

Answer: A
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Re: If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   05 Sep 2020, 01:33
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If a^5*b^6*c^7 > 0
That means a,c +ve and b is +ve or -ve. --- (A)
OR
That means a,c -ve and b is +ve or -ve. --- (B)

Is a*b^3*c^5< 0? --- (C)
To find we need to find b or both a and c together.

Statements:

(1) b<0
For either (A) or (B), the expression (C) would depend on b.
Since b<0, (C) would be negative.
Sufficient.

(2) c>0
We don't know b. If c>0 that means a>0 but depending on b the value of (C) would change.
Insufficient.

Hence, the answer is Option (A).
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Re: If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   05 Sep 2020, 04:57
Kindly see the attachment. Just go with the statement at hand. Then see the options.
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Re: If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink] New post   21 Oct 2021, 09:17
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Re: If a^5*b^6*c^7 > 0, is a*b^3*c^5 <0 ? (1) b < 0 (2) c > 0 [#permalink]
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