A salesperson for an automobile dealer earns an annual salary of $25,0

Question

A salesperson for an automobile dealer earns an annual salary of $25,000 plus a commission of 10% of the salesperson's sales over $100,000. If x is the dollar amount of sales in a certain year and x is greater than $100,000, which of the following expresses the salesperson's total earnings, in dollars, for the year?

A) 25,000 + 0.1x
B) 35,000 + 0.1x
C) 125,000 + 0.1x
D) 25,000 + 0.1(100,000 - x)
E) 25,000 + 0.1(x - 100,000)

(A) 25,000 + 0.1x
(B) 35,000 + 0.1x
(C) 125,000 + 0.1x
(D) 25,000 + 0.1(100,000 - x)
(E) 25,000 + 0.1(x - 100,000)

PS04071

Bizzle · Answer

what I understand from the question is that the salesperson earns 10% of sales over $100,000.
meaning:
- if sales were $90,000 he gains 0% of that amount
- if sales were of $110,000 he gains 10% of $110,000 which equals $11,000

but according to the solution he gains 10% of $10,000. Where is my misconception. I don't understand.

AccipiterQ · Answer

hi!

so his salary is 25,000+.1(x-100,000), when X>100,000 let's use some numbers to illustrate. say his sales are 120,000, in the formula this would be 25000+.1(120,000-100,000). So he is earning 25,000 + .1(20,000). His commission is ONLY on the amount above 100,000. He doesn't gain a commission on the entire 120,000 in this example. So his total salary would then be 27,000

Bizzle · Answer

I know what the answer is and how the math around it works. but regar dint the question stem, how do we know for sure he wins comissions of 10%(x-100,000) and not 10%(x). Thanx

DrFeelgood · Answer

I suppose because the question states "plus a commission of 10% of the salesperson's sales over $100,000 ." So the highlighted part indicates that the 10% commission applies to any excess sales above $100,000. At least that's how I interpreted it. I thought of the same thing at first, but i read the question again and it made more sense the second time. Also it'd be far too easy and just be 0.1x, there has to be a catch somewhere :-D

.

Bunuel · Answer

Stem says that "a salesperson earns a commission of 10% of the salesperson's sales    over    $100,000".

Bizzle · Answer

Haha it all seems so simple right? But then again if that is so.... How would the GMAT test-makers, or how would you word the question stem if you wanted to actually mean that the salesperson would gain a 10% of sales commission but only if his sales are greater than a certain amount. For example, that we would actually mean that if he sold $120,000 we would gain 10% of $120,000 since it was OVER the qualifying amount of $100,000. And another salesperson who just sold $70,000 would not gain any commission because his sales amount did no reach the minimum amount for the 10% over sales to take effect.

So what i really want to understand is then how would the wording be any different if the answer was (A) ?

Because personally i would write, the question for answer (E) as "10% of the difference in the salesperson’s sales over $100,000" .... But i couldnt think of any other way to write the question other than how it is already wrtitten, if i would actually want to mean answer (A).

Please help me get my head around this...

Or maybe its just the language barrier that english is not my native language that is making me understand that statement erroneously

ScottTargetTestPrep · Answer

We can create the equation:

Earnings = 25,000 + 0.1(x - 100,000)

Answer: E

cm291093 · Answer

From the question we gather :

Salary = $25000 + 10% of Sales(above $100,000)

This means if the sale is over $100,000, lets say $110,000 the person gets a 10% cut from $10,000.

According to the question,

x is the sale which is above $100,000.

So salary = $25000 + 10% (x-100,000)
 = $25000 + 0.1 (x-100,000) { x-100,000 is to find the amount which is above 100,000 }

Hence E

Basshead · Answer

Annual salary =  $25,000 
Commission = 10% of sales over $100,000

Total earnings = annual salary + commission
 Total earnings = $25,000 + 0.1(x - 100,000)  -- since we only get commission from sales over $100,000.

Answer is E.

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A salesperson for an automobile dealer earns an annual salary of $25,0

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A salesperson for an automobile dealer earns an annual salary of $25,0

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