Question

# Each week a certain salesman is paid a fixed amount equal to 300,plusacommissionequalto5percentoftheamountofhissalesthatweekover1,000. What is the total amount the sales man was paid last week?(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.

A
Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
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B
Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
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C
Both statements together are sufficient, but neither statement alone is sufficient.
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D
Each statement alone is sufficient.
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E
Statements (1) and (2) together are not sufficient.
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Solution

## The correct option is E Each statement alone is sufficient.Let P be the salesman’s pay for last week and let S be the amount of his sales last week. Then P=300+0.05(S−1000). We have to determine the value of P. Given P=0.10S, then 0.10S=300+0.05(S−1000). This equation can be solved for a unique value of S, from which the value of P can be determined; sufficient. Given S=5000, then P=300+0.05(5000−1000). Thus, sufficient. The correct answer is D; each statement alone is sufficient.

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