If |ab| ≠ ab, is a > b? (1) |a| > b^3 (2) a^2 < b

a<0 or b<0

Statement 1: a=1; b=-1
a=-2; b=1

Statement 2: a^2>0; thus b>0; thus b>a
Sufficient

Answer B

The question itself contains some extra info. That info is:

|ab|≠ab

Think through what that info actually means. The only situation where a number isn't equal to its own absolute value, is where that number is negative. So, this really just says 'ab is negative'. And if the product of two numbers is negative, exactly one of those numbers is negative. You know for sure that either a is negative, or b is negative, but not both.

You want to know whether a is greater than b. Since one of them is definitely negative and the other is definitely positive, the positive one will definitely always be bigger. Really, all you need to figure out is whether a is the positive number or not.

Statement 1: This doesn't tell you for sure whether a is positive and b is negative, or whether it's the other way around. It can actually go either way. If a = -100 and b = 1, then \(|a|>b^3\). If a = 100 and b = -1, then \(|a|>b^3\). So, we don't know for sure which one is the positive number, so it's insufficient.

Statement 2: This does tell you that b has to be positive. \(a^2\) is a perfect square, which means it can't be any smaller than 0. A perfect square will never be negative. So, it can't be smaller than a negative number! That tells you that b is definitely positive. And since we already know that one of the numbers is positive and the other is negative, we know that a is negative.

Knowing that a is negative and b is positive is enough info to answer the question: a is definitely not greater. So, statement 2 is sufficient.

From the question stem |ab| does not equal ab means a or b is minus.

Try a = 2 and b = -1
a > b yes

Try a = -2 and b = 1
a > b no.

Insufficient.

Statement 2)

a^2 < b

This means b is positive.

a > b no.

Answer choice B

Posted from my mobile device

|ab| ≠ ab
means either of a or b is -ve
#1
|a| > b^3
means a can be -ve or b -ve
not sufficient
#2
a^2 < b
a being -ve , b has to be +ve
IMO B

labl ≠ ab IMPLIES, a and b have different signs.

From statement (1), it is not possible to find whether a is +ve or -ve, but it becomes clear that b is +ve. So, either a > b if a is +ve or a < b, if a is -ve. Hence, (1) is not sufficient.

From (2), it is clear that ====> a^2 < b, for sure, b is +ve and even if a is +ve/-ve, b>a.
Therefore, (2) alone is sufficient.

Given: |ab| ≠ ab
|ab| ≠ ab if and only if a & b are of different signs

Asked: Is a > b?

(1) |a| > b^3
a may be +ve or -ve
b may be +ve or -ve
NOT SUFFICIENT

(2) a^2 < b
b>a^2>0
Since a & b are of different signs => a is -ve => a<0
a<b => a is NOT >b
SUFFICIENT

IMO B