M01-12

Question

What is the value of  p^3 - q^3 ?

(1)  p - q = 0 
 
(2)  p + q = 0

Bunuel · Accepted Answer

Official Solution:

What is the value of  p^3 - q^3 ? 
 
(1)  p-q=0 . 
 
This statement implies  p=q . Thus,  p^3-q^3=p^3-p^3=0 . Sufficient.
 
(2)  p+q=0 . 
 
The above implies that  q=-p . Hence,  p^3-q^3=p^3-(-p^3)=2p^3 . The value of this expression depends on the value of  p . Not sufficient.

Answer: A

mvrravikanth · Answer

Hi Bunuel,
I solved the question in the following way.
1)p-q=0;
(p-q)^3=0;
p^3-q^3-3p^2q-3pq^2=0;
p^3-q^3-3pq(p-q)=0;
//But we know that p-q=0
p^3-q^3=0//Sufficient

2)p+q=0;
From this we will get p^3+q^3 which is not sufficient.

Is this approach correct?

Thanks in advance.

AndrewN · Answer

Hello,  mvrravikanth . I doubt you are still hanging around this forum, but your question is, and my thinking is that if you approached the problem in such a way, then other people probably have (or will), too. My post is an effort to clarify a matter or two. In your assessment of statement (1), the third line should have a  plus  sign before  3p  q^2 . However, you correctly factored out that  -3pq  in the next step, and your solution for statement (1) is quite interesting to me. Yes, since you know that  p - q = 0 , you could substitute and end up answering the exact question that is being asked,  p^3 - q^3 = 0 . It may not be the fastest way to solve the question, but I like the creativity.

In your assessment of statement (2), it is not quite clear what you mean by  we will get  p^3 + q^3  . That is, you get  p^3 + q^3  as  part of  an expanded distribution, but what about the other terms? I know from the other analysis that you know how to distribute binomials, and how to further distribute a binomial into a quadratic. Did you just decide that the  p^3 + q^3  part was enough to write off the sufficiency of the statement? Did you try numbers? I ask because I know from tutoring that a rookie mistake is to assume that a binomial raised to an exponent, for example  (p + q)^3 , is the same as distributing the power,  p^3 + q^3 , and that is not correct.

- Andrew

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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M01-12

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