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

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

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01 Feb 2018, 22:56
00:00

Difficulty:

35% (medium)

Question Stats:

77% (01:18) correct 23% (01:41) wrong based on 101 sessions

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

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

(2) p - q = 0

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

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01 Feb 2018, 23:05
1
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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01 Feb 2018, 23:07
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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15 Feb 2018, 02:49
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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15 Feb 2018, 04:55
Mehemmed wrote:
Hey Bunuel,

Correct answer needs to be changed. Correct answer is B not A.

Edited the OA. Thank you.
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Re: What is the value of p^8 - q^8 ?  [#permalink]

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15 Feb 2018, 06:08
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.

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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17 Feb 2018, 16:31
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 $$p^8 - q^8 = 0$$.

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Re: What is the value of p^8 - q^8 ? &nbs [#permalink] 17 Feb 2018, 16:31
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