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.

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

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GMAT Data Sufficiency (DS) Questions

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