Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Don’t actually multiply these numbers out! The key here is to substitute a variable for a tiny value that shows up in several places.
Specifically, let x = 0.0001. Now you can rewrite all the numbers as 1 plus or minus x or 2x.
(1.0002)(0.9999) – (1.0001)(0.9998)
= (1 + 2x)(1 – x) – (1 + x)(1 – 2x)
Now, distribute each product in the expression separately.
First product: (1 + 2x)(1 – x) = 1 + 2x – x – 2x2 = 1 + x – 2x2
Second product: (1 + x)(1 – 2x) =1 + x – 2x – 2x2 = 1 – x – 2x2
Subtract the two products:
1 + x – 2x2 – (1 – x – 2x2)
= 1 + x – 2x2 – 1 + x + 2x2
= 2x
Notice how much cancels out!
Finally, substitute back in for x. The difference is 2(0.0001) = 0.0002.
It might seem odd to solve an arithmetic problem by turning it into algebra! But in this case, doing so saves you a ton of work.
The correct answer is E.