Paul sells encyclopedias door-to-door. He earns $160 on ever

Paycheck = fixed pay + commissions
\($1,320 = $160\) + commissions
\($(1,320 -160)=$1,160\) in commissions

All of the answer choices are greater than $10,000

\(x=\) first $10,000 in sales
\(y\) = sales amount after the first $10,000
\(x+y=\) total sales amount
\(.10x + .05y=\) total commissions amount

\(.10x+.05y=$1,160\)

\(.10($10,000)+.05(y)=$1,160\)
\($1,000+0.05y=$1,160\)
\(.05y=$160\)

\(y=\frac{$160}{.05}=\frac{$16,000}{5}=$3,200\)

Total sales = \((x+y)=$(10,000+3,200)=$13,200\)

Answer A

Since he earns $160 as base salary and 10% of $10,000 is $1,000, if he sells no more than $10,000 worth of encyclopedias, the maximum he earns is $1,160. However, since he earns $1,320, he must have sold more than $10,000 worth of encyclopedias. Therefore, if we let x = his sales for the paycheck of $1,320, we can create the equation:

160 + 0.1(10,000) + 0.05(x - 10,000) = 1,320

160 + 1,000 + 0.05x - 500 = 1,320

660 + 0.05x = 1,320

0.05x = 660

x = 13,200

Answer: A

Hi All,

We're told that Paul sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells and a commission as follows:

10% on the first $10,000.00 and 5% for any additional sales beyond that.

His largest paycheck of the year was $1,320. We're asked for his sales for that pay period. This question can be approached in a couple of different ways. Based on the given answer choices, we can take advantage of a couple of built-in patterns and avoid some of the extra 'math steps.'

To start, we can see that all of the answers are ABOVE $10,000, so we know that part of his commissions was 10% of $10,000 = $1,000. Paul received $160 on top of that piece of his commission, so we have accounted for $1,160. Now, we just have to account for the extra $1320 - $1160 = $160 he earned...

That extra commission was based on 5% of the sales ABOVE $10,000.
5% of $1,000 = $50
$160 is a little more than (3)($50), so the extra sales had to be a little more than (3)($1000). Thus, his total sales for that period were a LITTLE MORE than $10,000 + $3000 = $13,000...

Final Answer:

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

This post needs to be reworded because it states there is no double commission but in fact that is how it needs to be solved.