Hello,

Option E: Both alone are in sufficient and both together are insufficient too.

Consider 1)

A>0 from this alone we cannot say anything.

1. Do not know if they are integers or fractions.

2. Do not know if B is positive or negative.

If fraction then consider and even if both positive:

A= 1/2 and B = 1/3

(A/B)^3 = ((1/2)/(1/3))^3 = (3/2)^3 = 27/8

(AB)^3 = (1/6)^3 = 1/216

Please note that since the power on both sides in ODD. Since ODD powers do not alter the sign we have

In sufficient.

Consider 2)

AB>0

1. Both are positive or both are negative.

2. Do not know if they are integers or fractions.

If fraction then consider:

A= 1/2 and B = 1/3

(A/B)^3 = ((1/2)/(1/3))^3 = (3/2)^3 = 27/8

(AB)^3 = (1/6)^3 = 1/216

In sufficient.

Consider both 1 and 2 :

1. A is positive hence B is also positive

2. Do not know if they are integers or fractions.

If integers

then the equation is true

If fraction then consider:

A= 1/2 and B = 1/3

(A/B)^3 = ((1/2)/(1/3))^3 = (3/2)^3 = 27/8

(AB)^3 = (1/6)^3 = 1/216

Hence both together are insufficient.

Regards

Raghav.V

Consider Kudos if you find my posts helpful: