A certain car dealership sells only Full-size and Mid-size c

Question

A certain car dealership sells only Full-size and Mid-size cars. One of its sales representatives receives an annual salary of $15,000. He also receives a commission of $800 for each full size car he sells and $500 for each midsize car he sells. What is the least number of cars he must sell in a year to receive total annual earnings of exactly $25,000?

A) 7
B) 12
C) 13
D) 14
E) 17

A) 7
B) 12
C) 13
D) 14
E) 17

I'm getting E can someone explain?

Bunuel · Answer

15,000+800F+500M=25,000  -->  8F+5M=100 .

We need to minimize F+M. To do that we need to minimize M (or which is the same we need to maximize F) -->  M=4  and  F=10  -->  F+M=14 .

Answer: D.

gmatzpractice · Answer

10,000=800*12+400
10,000=800*11+1200
10,000=800*10+2000

Answer C) 14

generis · Answer

He gets $15,000 in salary, so to earn $25,000, he needs $10,000 in sales.

Focus on the $800 cars. In order to  minimize  the total number of cars, we should  maximize  the number of more expensive full size cars, F -- we need fewer of them to get a high total dollar amount.

Another reason to focus in the $800 cars: divisibility. $800 and $500 are awkward together. We need the $800 car number to make a round total that is divisible by $500 for medium cars, M.

He needs exactly $10,000 from commissions.

To be a "round" number divisible by $500, $800 must be multiplied by 5, 10, or 15

$800 * 5F = $4,000 
$6,000 left 
$6,000/$500 per M = 12M
Total cars: 17

$800 * 10F = $8,000 
$2,000 left
$2,000/$500 per M = 4M
Total cars: 14

The next number of $800F that is round is 15, which is a   greater  number of cars than the 14 we just calculated. Reject.

Least number of cars: 14
10 are F
4 are M

Answer D

ScottTargetTestPrep · Answer

Since the sales rep makes $15,000 per year, he needs to make exactly $10,000 in commision.

Let f = the number of full-size cars and m = the number of mid-size cars he sells. We have:

800f + 500m = 10,000

8f + 5m = 100

m = (100 - 8f)/5

Since we want the least number of cars he must sell to make the exact $10,000 commision, he must sell as many full-size cars as possible. We see that the maximum value of f can be 10 where (100 - 8f) is still a multiple of 5. Therefore, he sells 10 full-size cars and (100 - 8(10))/5 = 20/5 = 4 mid-size cars, for a total of 14 cars.

Answer: D

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A certain car dealership sells only Full-size and Mid-size c

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A certain car dealership sells only Full-size and Mid-size c

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