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

Question

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

(2) p - q = 0

rahul16singh28 · Answer

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.

Sasindran · Answer

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

Mehemmed · Answer

Hey  Bunuel ,

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

Bunuel · Answer

Edited the OA. Thank you.

GMATBusters · Answer

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

MathRevolution · Answer

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.

KanishkM · Answer

When we factorize  p^8 - q^8 , using  a^2 - b^2 = (a-b) (a+b)

Only from 2, we will get a value of p-q as 0, which will make the value of expression = 0

B

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

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

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