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

Question

If  x
eq{0} , what is the value of  (\frac{x^p}{x^q})^4 ?

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

Bunuel · Accepted Answer

SOLUTION

If  x
eq{0} , what is the value of  (\frac{x^p}{x^q})^4 ?

(\frac{x^p}{x^q})^4=(x^{p-q})^4=x^{4(p-q)} .

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

(2) x = 3 -->  x^{4(p-q)}=3^{4(p-q)} . Not sufficient.

Answer: A.

WoundedTiger · Answer

Sol: The given question can be re-phrased " what is the value of (x^(p-q))^4

St 1: Given p=q so we have (x^0)^4 ----> Any number to the power 0 is 1 so Value of expression is 1 
St 2: Just tells us the value of x. But wait the expression becomes 3^4(p-q).....Thus for any integer value of (p-q) the expression will give us different values

Consider p-q= 1 So the expression becomes 3^4 (81)
p-q= 2 so the expression becomes 3^8 ------> (81^2)-----> 6561...So 2 ans

Hence Our Ans is A

Difficulty level of 600 is okay.

stne · Answer

(\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 
eq 0 
Sufficient

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

Answer A

kanusha · Answer

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

akadiyan · Answer

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

GmatPrime · Answer

St 1: p=q

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

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

Not sufficient.

Answer A

ScottTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

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

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