Ken left a job paying $75,000 per year to accept a sales job

Question

Ken left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?

A. 40
B. 200
C. 266
D. 267
E. 600

A. 40 
B. 200 
C. 266 
D. 267 
E. 600

I can easily compute that 0.15(750) = $112.50 of commission per sale; which means that

sales would be required in order to not lose money when compared to his previous job...

It sounds weird, but I'm having trouble dividing fractions or estimating the correct answer...

I manipulated the fraction to   =   =  *100

are there any tips or topics on learning to divide fractions properly... for example i don't think i'd be able to determine that the answer was D over C...

thanks in advance

Bunuel · Accepted Answer

Ken left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?  
A. 40 
B. 200 
C. 266 
D. 267 
E. 600

In order not to lose money because of the change Ken's total commission must be  at least  $75,000-$45,000=$30,000, so total sales must be  at least  $30,000/0.15=$200,000. Which means that he must make  at least  $200,000/750=800/3=266.6 sales, so 267 sales.

Answer: D.

Hope it helps.

shadabkhaniet · Answer

after simplifying it i got 800/3 = 266.66
In round figure which is 267.

kuttingchai · Answer

Ans : D

75000 = 45000 +   * x]

30000 =   * x
  /   = x
266.6 = x
267 = x

Asifpirlo · Answer

30000 = 15% × 750 × n
or, n = 800/3 = 266.666 
So 267 sales.(Answer)
266 sales would decrease his earnings.

2020MBA · Answer

Let's be smart about these problem types. In fact, once I share this, you will pray you get a problem like this on test day.

The question asks us for the LEAST number of sales Ken must make to break even. Knowing that the makers of the GMAT will try to trap us with the wrong answer, we can quickly narrow the correct answer to one of two choices: C or D. We can assume without even doing any math that the answer will be some fractional answer. The trap here is that we round down instead of rounding up like the question asks us to do by asking for the LEAST number of sales he must make.

Without even putting pen to paper, I can be 99% confident that the answer is D, which is the larger of the two answers since the question asks for the LEAST number of sales he must make.

Now -- if I am short for time on test day, then this can be a fabulous way of making up time. If I have time to work out the answer that I can have 100% confidence in, then I will do the algebra, as others have stated.

Happy GMAT Hunting...

trivest · Answer

Hi, 
We can solve it easily by making a simple eqn..
Consider the no. Of sales as x.

So, 45,000+(15/100)*750*X=75,000
This gives, 
X=266.6
X=267

Option D

Sent from my Lenovo A6020a40 using  GMAT Club Forum mobile app

TheNightKing · Answer

The options almost give away the answer. C or D.

It boils to recovering 30/11.25 which is 266.6666

Which is 267 Sales.

palaknayyar · Answer

solved this by creating an equation : Let number of min sales required= x 45,000+ (750)(0.15)(x)> 75,000 In essence, salary at new job > old job Wasn't the fastest way but got me there

Hope that helped

MathRevolution · Answer

Old job pay: $75,000

New job pay: $45,000 + 15% commission

Difference: $75,000 - $45,000 = $30,000

In order to not lose money, he must earn this $30,000.

Now every sales count for $750 and Ken gets 15% of it which is  \frac{15}{100} * 750 = 112.5.

Number of sales :  \frac{30,000 }{ 112.5} = 266.66 = 267

Answer D

mwauthor · Answer

15% of 750 = 225/2 75000-45000 = 30000 225/2 X = 30000 X>800/3 X=267 x= total number of sales numbers

bumpbot · Answer

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Ken left a job paying $75,000 per year to accept a sales job

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Ken left a job paying $75,000 per year to accept a sales job

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