In order to answer this question what do we need to know? We need to know the sale price divided by the list price. (And what they’re really testing is how well you know the “algebraic identity” of consecutive percent changes. See below.)
Let's start by writing equations.
Suppose the list price is equal to L, the retail price is equal to R, and the sale price is equal to S.
R = L * (1 - p/100)
S = L * (1 - p/100) * (1 - r/100)
We want to find S/L, which means we want to find (1 - p/100) * (1 - r/100)
Let’s use “FOIL” from algebra class to re-write that value (an excellent exercise – go ahead and give it a try on a piece of paper) in a way that’s more similar to what we see in statements 1 and 2.
(1 - p/100) * (1 - r/100) = 1 – r/100 – p/100 + rp/10,000
This equation, the algebraic identity of consecutive percent changes, is important to know for the GMAT.
So the question behind the question – what we need to know in order to answer this question – is, “What is the value of (1 – r/100 – p/100 + rp/10,000)”?
That can be re-written as
(1 – (r/100 + p/100 - rp/10,000) ), so we could also phrase our question as
“What is the value of (r/100 + p/100 - rp/10,000)?”
Statement 1:
p – r + pr/100 = 10
Divide both sides by 100 and we have
p/100 – r/100 + pr/10,000 = 10/100. But p/100 – r/100 + pr/10,000 is not the same as either expression written above.
NOT SUFFICIENT
Statement 2:
p + r - pr/100 = 40
Divide both sides by 100 and we have
p/100 + r/100 – pr/10,000 = 40/100
The expression p/100 + r/100 – pr/10,000 is equal to our expression above r/100 + p/100 - rp/10,000.
SUFFICIENT