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What is the value of p^8 - q^8 ?

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What is the value of p^8 - q^8 ?  [#permalink]

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New post 01 Feb 2018, 23:56
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

81% (00:55) correct 19% (01:18) wrong based on 99 sessions

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Re: What is the value of p^8 - q^8 ?  [#permalink]

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New post 02 Feb 2018, 00:05
Bunuel wrote:
What is the value of p^8 - q^8 ?

(1) p^7 + q^7 = 127

(2) p - q = 0


We have to find the value of \((p^4 + q^4)(p^4-q^4)\)
Statement I:

Let \(p = 2 , q = -1 & p = -1 & q = 2\)..... So, Insufficient.

Statement II:

As \(p = q\)
\(p^8 - q^8\) = 0... So, sufficient.
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Re: What is the value of p^8 - q^8 ?  [#permalink]

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New post 02 Feb 2018, 00:07
1
B

p^8 - q^8 can be written as (p^4)² - (q^4)²

= (p^4 + q^4)*(p^4 - q^4)

= (p^4 + q^4)*((p²)² - (q²)²)

= (p^4 + q^4)*((p² + q²) * (p² - q²))

= (p^4 + q^4)*((p² + q²) * (p + q)(p - q))

= (p^4 + q^4)(p² + q²)(p + q)(p - q)

Now,

St1-clearly insufficient

St2-sufficient, as (p-q)=0 question stem becomes 0. ie p^8-q^8=0
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Re: What is the value of p^8 - q^8 ?  [#permalink]

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New post 15 Feb 2018, 03:49
1
Hey Bunuel,

Correct answer needs to be changed. Correct answer is B not A.
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Re: What is the value of p^8 - q^8 ?  [#permalink]

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New post 15 Feb 2018, 05:55
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Re: What is the value of p^8 - q^8 ?  [#permalink]

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New post 15 Feb 2018, 07:08
Hi
The factorization is correct but it is a bit lengthy.

Another Approach

St1 : p^7 + q^7 = 127
p= 0, q = (127)^(1/7), or p = (127)^(1/7), q = 0.
Now these two sets of values give different answer.
hence insufficient.

St2: p=q
hence p^8-q^8 = 0
hence sufficient.

Answer = B

Sasindran wrote:
B

p^8 - q^8 can be written as (p^4)² - (q^4)²

= (p^4 + q^4)*(p^4 - q^4)

= (p^4 + q^4)*((p²)² - (q²)²)

= (p^4 + q^4)*((p² + q²) * (p² - q²))

= (p^4 + q^4)*((p² + q²) * (p + q)(p - q))

= (p^4 + q^4)(p² + q²)(p + q)(p - q)

Now,

St1-clearly insufficient

St2-sufficient, as (p-q)=0 question stem becomes 0. ie p^8-q^8=0

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Re: What is the value of p^8 - q^8 ?  [#permalink]

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New post 17 Feb 2018, 17:31
Bunuel wrote:
What is the value of p^8 - q^8 ?

(1) p^7 + q^7 = 127

(2) p - q = 0


The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

We can modify the question as follows.

\(p^8 - q^8 = (p^4 + q^4)(p^4 - q^4) = (p^4 + q^4)(p^2 + q^2)(p^2 - q^2) = (p^4 + q^4)(p^2 + q^2)(p + q)(p - q)\)

Condition 1)
\(p = 2, q = -1\) : \(p^8 - q^8 = 255\)
\(p = -1, q = 2\) : \(p^8 - q^8 = -255\)
Since the answer is not unique, condition 1) is not sufficient.

Condition 2)
Since \(p^8 - q^8 = (p^4 + q^4)(p^2 + q^2)(p + q)(p - q)\), if \(p - q = 0\) then \(p^8 - q^8 = 0\).

Therefore, the answer is B.
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Re: What is the value of p^8 - q^8 ? &nbs [#permalink] 17 Feb 2018, 17:31
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