If x ≠ 0, what is the value of (x^p/x^q)^4 ?

\((\frac{x^p}{x^q})^4\) can be written as \(x^{(p-q)4}\)

1) since p=q then equation becomes x^0, so the answer is 1 , as \(x \neq 0\)
Sufficient

2) we have no info about p-q hence insufficient.

Answer A

x could be any value
1, p = q
On substituting any value x , when p=q
results 1
AD
2, x = 3
Do not know what is P,Q
A

If x≠0 , what is the value of (xp/xq)4

(1) p = q
(2) x = 3

\(x^p\) / \(x^q\) = \(x^(p-q)\)

1. p=q, this means p-q is 0 , and irrespective of value of x , any number to the power of 0 will always be 1. so basically its 1^4. Option 1 - Sufficient.

2. x = 3
This does not give any information on p or q. So this statement by itself is not sufficient.

Ans: A

St 1: p=q

=> (x^p-q)^4 => x^0 = 1
Sufficient

St. 2: x=3
(3^p-q)^4 = ??

Not sufficient.

Answer A

Solution:

Question Stem Analysis:

We need to determine the value of (x^p / x^q)^4 given that x is not 0.

Statement One Alone:

Since p = q and x ≠ 0, x^p / x^q = 1 and hence (x^p / x^q)^4 = 1^4 = 1. Statement one alone is sufficient.

Statement Two Alone:

Substituting 3 for x, we have (3^p / 3^q)^4 = (3^(p - q))^4. If p - q = 0, then (3^(p - q))^4 = (3^0)^4 = 1. However, if p - q = 1, then (3^(p - q))^4 = (3^1)^4 = 81. Statement two alone is not sufficient.

Answer: A

I can predict a couple of reasons why x≠0 is given in the question stem. It’s customary for the GMAT to provide such information and convey that certain things are not defined on the GMAT.

Division by ZERO is not defined on the GMAT
\(0^0\) is not defined on the GMAT

These are two things that this question is hinting at by giving x≠0.

Breaking down the expression given in the question stem, we need to find the value of \([x^{(p-q)}]^4\) or \(x^{4(p-q)}\)

From statement I alone, p = q.
Therefore, p – q = 0. Substituting this value in the expression, we see that we need to find the value of \(x^{4(0)}\) or \(x^0\). Since x≠0, \(x^0\) = 1.
Statement I alone is sufficient. Answer options B, C and E can be eliminated.

From statement II alone, x = 3.
Therefore, the given expression can be written as \(3^{4(p-q)}\). Unless we are given the value of (p-q), it is not possible to evaluate the value of this expression.
Statement II alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.

Hope that helps!
Aravind BT

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