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A salesman is paid a fixed amount - Data sufficiency

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A salesman is paid a fixed amount - Data sufficiency

by sgnikc45 » Sat Feb 15, 2014 1:06 am

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I have a doubt regarding the following question. My dollar sign on my phone is not working so bare with me.
Each week a certain salesman is paid a fixed amount equal to dollar 300, plus a commission equal to 5 percent of the amount of his sales that week over dollar 1000. What was 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 amount of his sales last week.

2. The salesman's sales last week totaled dollar 5,000.
Let's take statement 1.

We don't know whether the salesman made a sale above 1000 in the last week. That means the salesman was either paid dollar 300 or dollar 300 + commission. Since we have two possibilities here, statement 1 is insufficient.

Let's take statement 2.
We know that the salesman made a sale above 1000. Therefore, there is only one possible answer using this statement. SUFFICIENT.

But the right answer is D. Can someone help me in understanding why my logic for eliminating statement 1 incorrect? I don't see any part of the question mentioning that the salesman made a sale above 1000.
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by GMATGuruNY » Sat Feb 15, 2014 4:27 am

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sgnikc45 wrote:I have a doubt regarding the following question. My dollar sign on my phone is not working so bare with me.
Each week a certain salesman is paid a fixed amount equal to dollar 300, plus a commission equal to 5 percent of the amount of his sales that week over dollar 1000. What was 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 amount of his sales last week.

2. The salesman's sales last week totaled dollar 5,000.
Let's take statement 1.

We don't know whether the salesman made a sale above 1000 in the last week. That means the salesman was either paid dollar 300 or dollar 300 + commission. Since we have two possibilities here, statement 1 is insufficient.

But the right answer is D. Can someone help me in understanding why my logic for eliminating statement 1 incorrect? I don't see any part of the question mentioning that the salesman made a sale above 1000.
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.
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by [email protected] » Sat Feb 15, 2014 3:57 pm

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Hi sgnikc45,

The information in the prompt provides enough information for us to create an equation for the salesman's pay: $300 + a 5% commission on any sales above $1000

300 + .05(X - 1000)

**It's important to note that if he sells less than $1000, there is no "penalty" (meaning that he won't lose money if he sells just $500).

The question asks for the amount the salesman was paid last week.

Fact 1: The salesman's pay last week = 10% of the total sales last week.

With this information, we can create a new equation...

.1X = 300 + .05(X - 1000)

This equation has just one variable, so we CAN solve it and there will be just one answer.
Fact 1 is SUFFICIENT

Fact 2: Total sales last week = $5,000

We can plug this info into the original equation and answer the question.
Fact 2 is SUFFICIENT

Final Answer: D

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by Scott@TargetTestPrep » Fri Nov 09, 2018 12:24 pm

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Each week a certain salesman is paid a fixed amount equal to dollar 300, plus a commission equal to 5 percent of the amount of his sales that week over dollar 1000. What was 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 amount of his sales last week.

2. The salesman's sales last week totaled dollar 5,000.
We are given that a salesman is paid $300, plus a commission equal to 5 percent of the amount of his sales over $1,000. If we set variable T as the total amount of his sales and A as the amount he earned last week, we can create the following equation:

A = 300 + 0.05(T - 1,000)

We need to determine the value of A. We see that if we can determine the value of T, then we can determine the value of A.

Statement One Alone:

The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.

Using the information we can create the following equation:

A = 0.1T

Since A = 0.1T, we can substitute 0.1T for A in the equation A = 300 + 0.05(T - 1,000).

0.1T = 300 + 0.05T - 50

0.05T = 250

5T = 25,000

T = 5,000

Since we have a value for T, we can determine A.

A = 300 + 0.05(5,000 - 1,000)

A = 300 + 0.05(4,000)

A = 300 + 200

A = 500

Statement one is sufficient to answer the question.

Statement Two Alone:

The salesman's sales last week totaled $5,000.

Once again, since we have a value for T, we can determine the value of A. Statement two is sufficient to answer the question.

Answer: D

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