GMAT Prep Quant Section, Question #13 of 37

[aaron.polsgrove]

On July 1 of last year, the total number of employees at Company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) empoloyee salary was 10 percent more after the decrease in number of employews than before the decrease. The total of the combine salaries of all the employees at Company E after July 1 last year was what percent of that before July 1 last year?

Possible answers

a. 90%
b. 99%
c. 100%
d. 101%
e. 110%

OA is b. But I am at a loss on how to arrive at this answer mathematically. Can you please help?

[tomslawsky]

Assume 100 Employees initially
Assume cumulative salary = "S" initially

100(S) = (90) (1.1)

Solve for S

[aaron.polsgrove]

How do I solve for S in this equation? And can you explain the math you used to come up with this equation? Thanks.

[tomslawsky]

Try numbers:

BEFORE:

100 Employees
$1 salary each

Total Salary = 100 (1) = 100

AFTER:

100 (0.9) = 90 Employees

Total Salary:
there are 90 Employees each earning ten percent more than their initial salary of $1 or each earning $1.10

Total salary = 90 (1.1)=$99

RATIO to PERCENT:(after/before)*100 =
(99/100) *100 = 99%

These are the "perfect" standardized test questions in my opinion. They can be learned, but most will fall for the "trap" answers. I don't know what the "trick" to these is, but I do think that when one of these shows up on a GMAT type test, plugging in numbers ususlly yields working numbers that are designed to be manipilated quickly, with relationships that "seem" to work. I hope I helped you but if not, I'm sure an instructor will chime in.

[aaron.polsgrove]

Thanks. I agree with your advice about working with real numbers to solve the problem. The original question states that without any change in the salaries of the remaining employees, the average (arithmetic mean) empoloyee salary was 10 percent more after the decrease in number of employews than before the decrease. So the 90 remaining employees are not earning 10% more.

Also, when I first read your response last night, I thought the equation read 100(S) = (90) (1.1) (S). Maybe because it was late. Thanks for trying to help, but I don't think we're there yet. Still trying to figure out the math behind the OA.

[tomslawsky]

1) I was tired too and made a mistake on my original response, which I've since edited.

2) More importantly- to your point of the employees making the same amount- the question does not say that each employee makes the same salary, it just gives an AVERAGE salary. Therefore, you have no idea what each of the employees make. I think it is wrong to assume that every employee makes the same salary. In fact, if you do make the assumption that everyone is paid the same salary, then the answer to the question will ALWAYS be 100%, or in essence, no change.

Therefore, I look at this as the company chopped 10% of the employees on the lower end of the salary scale.

[aaron.polsgrove]

OK, I think I got it. The originial problem statement said there was no change to the salaries of the remaining 90%, but the average salary was 10% greater, so using your figure of an average salary of $1, the new average salary would be $1.10, multiplied by 90 employees equals $99, or 99% of the original total payroll before reduction in employees. Wow, don't know why it took me so long to figure that out. Thanks for sticking with me on this!

[tomslawsky]

no prob- I'm still a learnin' myself!

[stucked]

I understand the number picking strategy explained in one of the previous post, but I was trying to make up an equation where I got lost.
Lets say total employees are 100 and total salary is S. then average salary would be S/90, which is 1.10 of previous salary.
S/90=(1.10S)/100. In one of the posts above the correct equation is S/90=1.10/100. Where did the S in the right hand side of the equation go? Can some one explain this to me. I have exam in couple of weeks

[RonPurewal]

I understand the number picking strategy explained in one of the previous post, but I was trying to make up an equation where I got lost.
Lets say total employees are 100 and total salary is S. then average salary would be S/90, which is 1.10 of previous salary.

Try organizing this information a little better. If you do, you'll notice the mistake.

For instance, try making the following chart:

"” Column labels: # employees, Average salary, Total $ salaries
(so first column - second column = third column)

"” Row labels: Before July 1, After July 1.

Here, you have 100 in the "# employees, Before" box, and 90 in the "# employees, After" box. That much seems straightforward enough.

The question you have to answer, though, is: Where is "S"?
The problem is that you're treating S as though it were the total for "before" (= the definition you explicitly laid out) AND ALSO the total for "after" (since you're trying to divide it by 90).

Can't do that. The whole premise of the problem is that the total changes (hence the percentages in the answer choices).
By (perhaps inadvertently) using "S" for both totals, you are working from the mistaken assumption that the total does not change.

If "S" is the total of the salaries "before", then the average salary "before" is S/100. After the 10% increase, the average salary is 1.10S/100 = 0.011S.
So, the total of all salaries is 90-0.011S = 0.99S. Choice B.

[RonPurewal]

It's easier, by the way, to use a variable for the average salary "before". That way you don't have to create any fractions.

If x is the average (individual) salary "before", then the average (individual) salary "after" is just 1.10x.
The total "before" was 100-x = 100x.
The total "after", with 90 employees making the increased salary, is 90-1.10x = 99x.
Choice B. No fractions.