OG2016 - A manufacturer of a certain

boomgoesthegmat wrote:A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $ 2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?

(A) Between $15,000 and $25,000
(B) Between $30,000 and $50,000
(C) Between $60,000 and $100,000
(D) Between $150,000 and $250,000
(E) Between $300,000 and $500,000

OA: D

Let's first determine the lower end of the range. So, we'll find 0.3 percent of 20,000
We know that 1% of 20,000 is 200, which means 0.1% of 20,000 is 20
If 0.1% of 20,000 is 20, then 0.3% of 20,000 is 60
So, at the lower end, there will be 60 defective units.
If each unit costs $2500, then the lower end of refunds = (60)($2500) = $150,000

Check the answer choices...D!

Cheers,
Brent

Hi All,

We're told that a manufacturer of a certain product can expect between 0.3 percent and 0.5 percent of the units manufactured to be defective, the retail price is $ 2,500 per unit and the manufacturer offers a full refund for defective units. We're asked how much money the manufacturer will need to cover the refunds on 20,000 units. While this question can be solved with standard Arithmetic, there is a great 'shortcut' in the answers that you can take advantage of to avoid some of the extra work. Notice that there is NO 'overlap' among the 5 answer choices - meaning that when a result 'fits' one of the answer choice 'ranges', then that answer is the ONLY option. Thus, we just have to do enough work to find one result that fits the given range and we'll have the correct answer.

You might find that taking 1% of the total and then cutting that value in HALF (to get .5%) would save you a little time, so we'll do that here:

1% of (20,000)($2500) =
(200)($2500) = $500,000

HALF of that would be $250,000
Thus, .5% of the units, if defective, would lead to a $250,000 refund. There's only one answer that includes that result...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich