A mistake in Advanced Manhattan GMAT quant or my fault

[kushagra09]

Dear Experts and Friends,

This is in reference to Try-It #4-9,(page no. 106, 107, Advanced GMAT Quant by Manhattan)

Q- if a is not equal to zero, is 1/a>a/b^2+3, this basically needs us to test whether a is positive or negative as explained in the solution

Statement 1: a^2=b^2

Here a can be either positive or negative for e.g. if a=-2 and b=2 then a^2=b^2 and sa,e applies for a=b=2, hence this statement does not give us a definite answer BUT solution in the book says it an be for sure concluded that a is positive, cant understand the logic presented

Statement 2: a^2=b^4

Here it can be implied a=b^2, now a has to be always positive as b^2 is always positive and hence this statement helps us to conlude for sure that a is positive, the explanation in the book is otherwise

therefore answer should be B as opposed to A suggeted in the explanation...

I might be missing some logic to get the above answer, kindly let me know if i am wrong and the correct logic

[gmatboost]

An error in your write-up is:

Statement 2: a^2=b^4

Here it can be implied a=b^2, now a has to be always positive as b^2 is always positive and hence this statement helps us to conlude for sure that a is positive, the explanation in the book is otherwise

The example of a = -4, b = 2 shows that this is not the case. All that can be concluded is that |a| = b^2.

[sl750]

You could try simplifying the equation

1/a-a/b^2 > 3

Is (b^2-a^2)/ab^2 > 3 ?

Statement 1
a^2=b^2; Is 0>3? N Sufficient

Statement 2
a=b^2 or -b^2. We have two solutions. Insufficient