Is ab

Question

Is ab < 0?

(1)  a^4b^9c^2 < 0

(2)  a(bc)^6 > 0

jedit · Answer

It should be C.

Statement 1: Since a and c have even powers, expression is less than 0 only because b is negative. However, we do not know the sign of a as a^4 would be +ive in all cases. 
Statement 2: we can know a is positive since  (bc)^6  can only be positive. However, we do not know if b is positive.

Combined.
From 1, we know b is negative and from 2 we know a is positive, so combined the two expressions are sufficient to answer the question. An important aspect to note is both expressions result in values greater or less than 0 which suggests none of these numbers is zero.

carnab31 · Answer

Should be C :
From first option we can conclude that just b is negative , no information about A
From second option we can conclude that a definitely must be positive
Combining statement A & B , we can conclude that ab <0 - Sufficient

jyotipes21@gmail.com · Answer

A.

statement 1:for equation to be less than zero, b has to be -ve (as a and c are even power thus does not effect the equ.)
thus stat 1 alone sufficient.
stat 2:a has to be +ve for the equ to be true. b and c can be +ve or -ve (since even power; we can't say much).thus stat 2 insuff.

ans A

gps5441 · Answer

For ab<O ie be negative either a or b has to be negative. If both are negative than ab will be >0
In short we need to know the sign of a and b. 
statement 1. The expression is less than 0. Any negative no raised to an even power will be +ve. In the expression only b is raised to an odd power and is negative. we are not sure about a. Insufficient 
Statement 2. The expression is +ve only possible if a is positive Since other part of the expression is raised to an even power. This statement does not give any information on B. Insufficient. 
combine both the statements. b is negative and a is positive. hence above is negative or <0. Answer C.

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gps5441 · Answer

For ab<O ie be negative either a or b has to be negative. If both are negative than ab will be >0
In short we need to know the sign of a and b. 
statement 1. The expression is less than 0. Any negative no raised to an even power will be +ve. In the expression only b is raised to an odd power and is negative. we are not sure about a. Insufficient 
Statement 2. The expression is +ve only possible if a is positive Since other part of the expression is raised to an even power. This statement does not give any information on B. Insufficient. 
combine both the statements. b is negative and a is positive. hence above is negative or <0. Answer C.

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hiranmay · Answer

Is ab < 0? (1) a^4b^9c^2 < 0 --> insuff: b < 0, we don't whether a is +/- (2) a(bc)^6 > 0 --> insuff: a > 0, we don't whether b is +/- Combining (1) & (2)=> a>0 & b<0, so ab<0 --> suff Answer: C

Goncalo13072001 · Answer

Is ab < 0?

When one is asked if the product of two variables (i.e.: a and b) is negative one is asked whether the variables display contrary signs (that is (a > 0 and b < 0) or (a < 0 and b > 0)).

From (1), a^4 and c^2 must be greater than zero regardless of their absolute value since their power is even whereas b has an odd exponent yielding a negative value => b < 0!

However, it is not really interesting as we cannot still infer anything about the sign of a.
Hence, S1 is INSUFFICIENT.

From (2), since (bc)^6 must be positive it comes that a is also positive => a > 0.
Again, the rationale behind is the same (bc)^6 is positive but we cannot infer anything about the direction of B.
Hence, S2 is INSUFFICIENT.

Combining S1(b<0) and S2 (a>0) together, it follows that:
(-) * (+) < 0 - TRUE proposition.

Hence S1 and S2 together are sufficient to answer if ab < 0!

Hope it helps,

Gonçalo

Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0

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