If x^(a - b) = 1, what is the value of x ?

Question

(1) a ≠ b

(2) x > 0

Kudos for a correct  solution .

Lucky2783 · Answer

three possibilities in which  x^(^a ^- ^b^) = 1  
Case 1: X=1 
Case 2: X=-1 and A-B=Even
Case 3: X= Number and A-B=0

(1) a ≠ b
 this option tell us that case 3 is not possible . we still have 2 cases left.  Insufficient .

(2) x > 0
 this option tells us that Case 2 is not possible and left us with case 1 and case 3 so still  Insufficient .

Combining :
 from 1 we know case 3 is not possible and from 2 we know that Case 2 is not possible so we are left with case 1 only . i.e. X=1

Sufficient. 
Answer C.

peachfuzz · Answer

Statement 1:
x can be either -1 or 1 depending on whether a-b is even or odd
Insufficient

Statement 2:
x is positive. however, x can be any positive number if a=b
Insufficient

Combined, we know that x must be 1

Answer:C

lipsi18 · Answer

X^(a-b) = 1,

1. a not =b; X can be anything 1 or -1 to satisfy above criteria 
2. X>0; X can be anything and a=b to satisfy above criteria
1+2 ; X can be 1 only;
Hence C is the answer

Thanks,

dream21 · Answer

X^(a-b) = 1,

1. X can be 1 or -1 InSufficient
2. X>0; a=b , X = 1,2,3,4.....
1and 2 X = 1

Ans C

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: xraisedtoaminusbequals1_text.PNG

Basshead · Answer

In questions in which we have  x^{some exponent}  = 1, we always have to check for several scenarios:

Scenario 1: x = 1

Scenario 2: x = -1 & the exponent is  even .

Scenario 3: x = any number  AND  the exponent is 0.

If x{(a - b} = 1, what is the value of x ?

(1) a ≠ b

If a ≠ b, then a - b can't be 0. However, we don't know if x = -1 and the exponent is even. Insufficient.

(2) x > 0

If x >0, then x can't be -1. However, we don't know if the exponent is 0.

(1&2) Statement 1 eliminates scenario 3; statement 2 eliminates scenario 2. We are only left with x = 1. Sufficient.

Answer is C.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x^(a - b) = 1, what is the value of x ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If x^(a - b) = 1, what is the value of x ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards