Target question:
What is the value of p^4 - q^4?
Notice that p^4 - q^4 can be factored as (p^2 + q^2)(p^2 - q^2)
So, we can rephrase the target question as:
What is the value of (p^2 + q^2)(p^2 - q^2)?
Statement 1: p^2 - q^2 = 128
Is this enough information to find the value of (p^2 + q^2)(p^2 - q^2)?
No, we're still missing the value of (p^2 + q^2)
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: p+q = 64
Notice that we can take the target expression, (p^2 + q^2)(p^2 - q^2), and factor it further to get (p^2 + q^2)(p + q)(p - q)
So, we now know the value of (p + q), but we're still missing the values of (p^2 + q^2) and (p - q)
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1 says that p^2 - q^2 = 128
If we factor this, we get
(p + q)(p - q) = 128
Statement 2 says that
p + q = 64
So, when we take the first equation plug 64 in for (p +q), we get
(2)(p - q) = 128
So, p - q must equal 2
At this point, we know that:
p + q = 64
p - q = 2
Since, we
could solve this equation for p and for q, we
could then use those values to find the definitive value of
p^4 - q^4.
Since we can now answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
