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

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