Chriskahdian wrote:OG 2016 Data Sufficiency #95

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?
P = 300+(x-1000)*.05

1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.
2) The salesman's sales last week totaled $5,000.

My issue is with statement 1. I have no problem getting all that info into a mathematical expression:
1) 300+(x-1000)*.05 = .1x
Which is perfectly solvable, but my question is:

He must have sold over $1,000 to earn any commission. This seems to be ignored in the explanation, which solves the problem and lists 1) as sufficient. I myself actually did the same, and then realized that we don't know if he sold over $1,000, and went back on my answer for 1).

How do we explain this? Is it just, "don't overthink it," because that doesn't feel reliable enough...

The salesman makes a base salary of $300.
Statement 1 indicates that his total earnings -- including his base salary -- are equal to 10% of his total sales.
Since 300 is 10% of 3000, his total sales cannot be less than $3000.

One way to evaluate Statement 1 is to test whether the value given in Statement 2 -- $5000 in sales -- is the ONLY value that will also satisfy Statement 1.

Statement 1: The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.
Case 1: Let his total sales = 5000, as indicated in statement 2.
Since he earns a 5% commission on all but the first $1000, his commission = 5% of $4000 = $200.
Total earnings = base salary + commission = 300+200 = 500.
Here, his total earnings (500) are equal to 10% of his total sales (5000).

Case 2: Let his total sales = 4000.
Since he earns a 5% commission on all but the first $1000, his commission = 5% of $3000 = $150.
Total earnings = base salary + commission = 300+150 = 450.
Here, his total earnings (450) are NOT equal to 10% of his total sales (4000).

Implication:
For his total earnings to be 10% of his total sales, his total sales must be 5000, as indicated in statement 2.
Thus, his total earnings = 500.
SUFFICIENT.

GMATGuruNY wrote: The salesman makes a base salary of $300.
Statement 1 indicates that his total earnings -- including his base salary -- are equal to 10% of his total sales.
Since 300 is 10% of 3000, his total sales cannot be less than $3000.

AHHHHHH, got it! Genius! Thank you! Plus that next level stuff, crazy