If a, b and x are integers such that a^6=b^3=|x|/x, what is the value

Question

If a, b and x are integers such that  a^6=b^3=\frac{|x|}{x} , what is the value of  a-b  ?

(1)  a^3*b^7>0

(2)  a+b>0

zhanbo · Answer

|x|/x can only be 1 or -1.
Yet a^6 = |x|/x, so |x|/x = 1
We know then b=1
a=1 or a =-1. 
In order to know the specific value for a-b, we just need to determine whether a is 1 or -1.

(1) Only
a^3 * 1^7 > 0 => a > 0 Sufficient

(2) Only
a + b > 0, meaning a cannot be -1
So a =1. Sufficient.

Answer is (D).

summerbummer · Answer

Not sure if my approach is correct, but here you go:

Pre-analysis: 
a = 1 or -1
b = 1 or -1

To find, a-b =?

S1: 
a^3 * b^7 >0 (Given)
2 cases possible
 Case 1:  -ve * -ve >0

So, a - b = (-1) - ​(-1) = 0

Case 2:  +ve * +ve >0
So, a - B = 1 - 1 = 0

Sufficient!

S2: 
a + b > 0
1 + 1 >0 (Values cannot be negative otherwise the condition collapses)

So, a - b = 1 - 1 = 0

Sufficient

Ans: D

TarunKumar1234 · Answer

If a, b and x are integers such that a^6=b^3=\frac{|x|}{x} b= 1 and a = 1 or -1 Stat1: a^3*b^7>0 ; it means a =1, we can get (a- b) now. Sufficient Stat2: a+b>0 ; it means a = 1, we can get (a- b) now. Sufficient So, I think D.

gmatophobia · Answer

a^6=b^3=\frac{|x|}{x}

Inference :  \frac{|x| }{ x}  can either be 1 or -1. Its given that  \frac{|x| }{ x}  =  a^6 , hence the value of  \frac{|x|}{x}  cannot be negative. Thus  \frac{|x| }{ x}  = 1.

With that pre-thinking, let see if we can infer anything further

a^6 = 1 ; so 'a' can be +1 or -1.

b^3  = 1; therefore 'b' = 1

Question

a-b = ?

We already know the value of a, hence if we can know the value (rather positive negative nature) of a, we can answer the question.

Statement 1

a^3*b^7>0

We already know b = 1, so if  a^3*b^7>0  then a is positive. Hence a = 1.

The statement is sufficient to answer, hence we can eliminate B, C and E.

Statement 1

a+b>0

As b = 1, a cannot be -1 otherwise the sum will be 0 and not greater than 0. So a = 1.

This statement is also sufficient.

Option D

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If a, b and x are integers such that a^6=b^3=|x|/x, what is the value

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