VJesus12 wrote: ↑

Sat Jan 30, 2021 10:47 pm

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the number of his sales that week over $1,000. What is the total amount the salesman was paid last week?

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

Answer: D

Source: Official Guide

Given: 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.
Let T = Total sales last week
So (T - 1000) = the amount that EXCEEDS $1000
Total paycheck = $300 + 5% of (T - 1000)
Or we can write: Total paycheck last week = $300 + 0.05(T - 1000)

Target question: What is the total amount the salesman was paid last week?

Statement 1: The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.
We can write: 300 + 0.05(T - 1000) = 10% of T
In other words, 300 + 0.05(T - 1000) = 0.1T

ASIDE: at this point, we should recognize that we COULD solve the above equation for T, which means we COULD determine how much the salesman was paid last week.
So, statement 1 is SUFFICIENT.

That said, let's solve the equation (for "fun")
Take: 300 + 0.05(T - 1000) = 0.1T
Simplify: 300 + 0.05T - 50 = 0.1T
Simplify: 250 + 0.05T = 0.1T
Subtract 0.05T from both sides: 250 = 0.05T
Solve: T = 5000
If T = 5000, then: Total paycheck last week = $300 + 0.05(5000 - 1000)
= 300 + 0.05(4000)
= 300 + 200
= 500
So, the answer to the target question is $500
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The salesman's sales last week totaled $5,000
In other words, T = 5000
Total paycheck last week = $300 + 0.05(5000 - 1000)
= 300 + 0.05(4000)
= 300 + 200
= 500
So, the answer to the target question is $500
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent