what is the value of x

[showbu]

Q3:
If n is an integer and x^n – x^(-n) = 0, what is the value of x ?
(1) x is an integer.
(2) n ≠ 0
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

oa: Spoiler Code E

[yalanand]

My answer is : C


xn – x-n = 0

Hence x(n-1)=n

ie x=n/(n-1)

given n is an integer = (...-2,-1,0,1,2...)

1)x is an integer

x can be integer if n = 0, x=0/-1 = 0
x can be integer if n =2, x=2/2-1=2

Insuff

2) n ≠ 0


this alone cannot get us to the value of x, because x can be value, ineger or a real number

Insuff

toger we can infer n=2.

[showbu]

Sorry, my typo. Try again.

My answer is : C


xn – x-n = 0

Hence x(n-1)=n

ie x=n/(n-1)

given n is an integer = (...-2,-1,0,1,2...)

1)x is an integer

x can be integer if n = 0, x=0/-1 = 0
x can be integer if n =2, x=2/2-1=2

Insuff

2) n ≠ 0


this alone cannot get us to the value of x, because x can be value, ineger or a real number

Insuff

toger we can infer n=2.

[amitabhprasad]

I am getting "E"
Whats OA

[sachinkr]

IMO it should be B.

X^n - X ^(-n) = 0
=> X^n = X ^(-n)

A. X is an integer
This is true for all X when n = 0, so we cannot determine the value of X.
(Insufficient)

B. n ≠ 0
In this case, X can only be 1. There is no other value for which X^n = X^ (-n) .Sufficient.

[thechamp]

'E' IMO
X^n - X ^(-n) = 0
=> X^n = X ^(-n) i.e. X^(2n)=1

A. X is an integer
n is unknown. If n=1, X^2=1 & X=+/-1

Insufficient

B. n ≠ 0
No info on X.

Insufficient

Taken together, X is integer & n ≠ 0
Whatever the value of n, X=+/-1

Insufficient.

Answer is E

[madhur_ahuja]

Why is the answer not B in this case ?

X^2n=1. And If n<>0, this can only happen when x=1.

[Ian Stewart]

x could be either 1 or -1, so the answer is E.

[Brent@GMATPrepNow]

Q3:
If n is an integer and x^n - x^(-n) = 0, what is the value of x ?
(1) x is an integer.
(2) n ≠ 0
OA: E

If we combine both statements, we see that there are some contradictory cases.
case a) x=1 and n=3, which means the answer to the target question is 1
case b) x=-1 and n=3, which means the answer to the target question is -1

Since we cannot answer the target question with certainty, the answer is E

Cheers,
Brent

[Brent@GMATPrepNow]

There is an important takeaway that is somewhat related to this question.

Some will assume that if X^a = X^b, then we can conclude that a=b. This is not the case.
There are 3 values for X where we cannot immediately conclude that a=b
These values for X are -1, 0 and 1

Examples:
0^3 = 0^5, but 3 does not equal 5
1^3 = 1^5, but 3 does not equal 5
(-1)^3 = (-1)^5, but 3 does not equal 5

Aside: If we know that a and/or b is negative, and we are told that X^a = X^b, it is not possible for X to equal 0, since 0^(negative number) is undefined.

Cheers,
Brent

[bblast]

the equation solves out to :


x^n - 1/x^n = 0

(x^2n - 1)/x^n = 0

x^2n=1

thus x can be 1 or -1 given the statements.