Is a/b < 0? (1) a^2/b^3 > 0 (2) ab^4 < 0

The question basically asks ....

IS \(lal\) < 0 ??

or a < 0 & a > 0 ......Does the value of a >0 & a <0 .....

Statement : 1 says ...... \(\sqrt{{a}} / l{b^3}l\) > 0

or \(\sqrt{a}> 0\)

or a > 0 ... Clearly Insufficient as it doesn't tell us if a< 0 also......Therefore, Insufficient.

Statement :: 2 ... Similar to statement it just tells us one part ... i.e;

as Given ... \(ab^4\) < 0 ... or a <0 .... Clearly, Insufficient.

1+2 ...... gives us that a<0 & a > 0 ..... Therefore, Sufficient.......

Hence, C ................. Hope it Helps !!

Hi Bunuel/All ,

Why are we not considering a & b to be fractions?

Regards
Akshay

Thanks Karishma . I think sometimes it is better not to think too much and skip some possible scenarios .

Clumsy mistake.
I read st 2 as (ab)^4 <0

C is correct. Here's why:

(1) a^2/b^3 > 0

From this we know that b < 0, but we don't know whether a<0 or a>0, thus INSUFFICIENT

(2) ab^4 < 0

From this we know a < 0, but we don't know whether b>0 or b<0, thus INSUFFICIENT

(1) + (2) - We know a<0 and b>0, therefore we know a/b<0 SUFFICIENT

Prompt analysis
A and b are real numbers.
Superset
The answer will be either YES or NO.

Translation
In order to find the answer, we need:
1# exact value of a and b.
2# any equation to find the a and b
3# any equation to find the exact or the range for a/b

Statement analysis
St 1: a^2/b^3 >0. a^2 is always greater than zero. If the complete expression is positive, that means that b^3 is positive hence b is positive. But nothing can be said about a. INSUFFICIENT

St 2: ab^4<0. b^4 is always positive.nothing can be said about b though. To make the expression negative, a has to be negative.

St 1 & St 2: from st 1, we can say that b>0. From st 2, we can say that a<0. Therefore a/b <0.
Option C.

St1.
A can be + or -
B is +

St2.
A is -
B can be + or -

Together, A must be - and B must be +

C

Is a/b < 0?

We can re-write the prompt as: Do a and b have different signs?

(1) a^2/b^3 > 0

This statement tells us b is positive. No info about a. Insufficient.

(2) ab^4 < 0

This statement tells us that a is negative. No info about b. Insufficient.

(1&2) We can conclude b is positive and a is negative. Sufficient.

Answer is C.

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