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Each week a certain salesman is paid a fixed amount equal to

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Each week a certain salesman is paid a fixed amount equal to

by AAPL » Tue Jul 24, 2018 6:50 am

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Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5% of his sales that week over $1000. 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% of the amount of his sales last week.
(2) The salesman's sales last week totaled $5000.

The OA is D.

So, I automatically know that 2 is sufficient. The OA is D, but I don't understand why 1 is sufficient. We don't know anything about his sales this week or last week unless you incorporate #2, which is already sufficient.

Can someone help, please? Thanks.
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Source: — Data Sufficiency |
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by GMATGuruNY » Tue Jul 24, 2018 6:56 am

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AAPL wrote:Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5% of his sales that week over $1000. 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% of the amount of his sales last week.
(2) The salesman's sales last week totaled $5000.

The OA is D.

So, I automatically know that 2 is sufficient. The OA is D, but I don't understand why 1 is sufficient. We don't know anything about his sales this week or last week unless you incorporate #2, which is already sufficient.

Can someone help, please? Thanks.
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.
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