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

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

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23 Jan 2014, 03:31
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5% (low)

Question Stats:

86% (00:47) correct 14% (00:53) wrong based on 907 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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

Data Sufficiency
Question: 54
Category: Arithmetic; Algebra Arithmetic operations; Simplifying expressions
Page: 156
Difficulty: 600

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Re: If x ≠ 0, what is the value of (x^p/x^q)^4 ?  [#permalink]

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23 Jan 2014, 03:31
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SOLUTION

If $$x\neq{0}$$, 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.

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Re: If x ≠ 0, what is the value of (x^p/x^q)^4 ?  [#permalink]

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23 Jan 2014, 03:57
1
Bunuel wrote:

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

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

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.
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Re: If x ≠ 0, what is the value of (x^p/x^q)^4 ?  [#permalink]

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24 Jan 2014, 00:30
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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

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

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Re: If x ≠ 0, what is the value of (x^p/x^q)^4 ?  [#permalink]

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23 Jan 2017, 09:35
x could be any value
1, p = q
On substituting any value x , when p=q
results 1
2, x = 3
Do not know what is P,Q
A
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If x ≠ 0, what is the value of (x^p/x^q)^4 ?  [#permalink]

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03 Mar 2018, 14:30
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
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Re: If x ≠ 0, what is the value of (x^p/x^q)^4 ?  [#permalink]

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04 Jun 2019, 02:16
St 1: p=q

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

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

Not sufficient.

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Re: If x ≠ 0, what is the value of (x^p/x^q)^4 ?   [#permalink] 04 Jun 2019, 02:16
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