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

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Math Expert
Joined: 02 Sep 2009
Posts: 53768
If x^(a - b) = 1, what is the value of x ?  [#permalink]

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24 Mar 2015, 04:25
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Difficulty:

55% (hard)

Question Stats:

51% (01:11) correct 49% (01:14) wrong based on 101 sessions

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

(1) a ≠ b

(2) x > 0

Kudos for a correct solution.

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Joined: 07 Aug 2011
Posts: 523
GMAT 1: 630 Q49 V27
If x^(a - b) = 1, what is the value of x ?  [#permalink]

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24 Mar 2015, 05:11
Bunuel wrote:
If x^(a - b) = 1, what is the value of x ?

(1) a ≠ b

(2) x > 0

Kudos for a correct solution.

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.
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Joined: 28 Feb 2014
Posts: 294
Location: United States
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Re: If x^(a - b) = 1, what is the value of x ?  [#permalink]

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24 Mar 2015, 20:09
1
Bunuel wrote:
If x^(a - b) = 1, what is the value of x ?

(1) a ≠ b

(2) x > 0

Kudos for a correct solution.

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

Manager
Joined: 26 Dec 2012
Posts: 146
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WE: Information Technology (Computer Software)
Re: If x^(a - b) = 1, what is the value of x ?  [#permalink]

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24 Mar 2015, 22:45
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;

Thanks,
Manager
Joined: 06 Jan 2014
Posts: 56
Re: If x^(a - b) = 1, what is the value of x ?  [#permalink]

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25 Mar 2015, 01:13
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
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Math Expert
Joined: 02 Sep 2009
Posts: 53768
Re: If x^(a - b) = 1, what is the value of x ?  [#permalink]

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30 Mar 2015, 04:39
Bunuel wrote:
If x^(a - b) = 1, what is the value of x ?

(1) a ≠ b

(2) x > 0

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

xraisedtoaminusbequals1_text.PNG [ 18.15 KiB | Viewed 3457 times ]

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Re: If x^(a - b) = 1, what is the value of x ?  [#permalink]

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01 Jan 2019, 03:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x^(a - b) = 1, what is the value of x ?   [#permalink] 01 Jan 2019, 03:53
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