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...
OG Seems to Ignore an Implied Restriction...
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The salesman makes a base salary of $300.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...
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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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
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Hi Chriskahdian,
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich