percentage difference

Expert replies

lukaswelker: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Wed Mar 26, 2014 6:56 amFollowed by: 1 member

by lukaswelker » Tue Apr 08, 2014 10:23 am

Hey guys, here is the question.

On July 1st 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) employee salary was 10 percent more after the decrease in number of employees than before the decrease. The total of the combined salaries of all of the employees at Company E after July 1 last year was what percent of that before July 1 last year?

90%; 99%;100%; 101%; 110%

I know it has to be under a 100% so the last three option are not possible. But I can't figure out why it's 99% and not 90%.

Any suggestions?
Many thanks
Lukas

Source: Beat The GMAT — Problem Solving | Tue Apr 08, 2014 10:23 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 08, 2014 12:13 pm

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 employee salary was 10 percent more after the decrease in number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent of that before July 1 last year?

90%
99%
100%
101%
110%

Before July 1:
Let the number of employees = 10.
Let the average salary = 10.
Old total payroll = 10*10 = 100.

After July 1:
10% fewer employees = 10 - .1(10) = 9.
Average salary increased by 10% = 10 + .1(10) = 11.
New total payroll = 9*11 = 99.

Thus:
(new total payroll)/(old total payroll) = 99/100 = 99%.

The correct answer is B.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10391; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Apr 08, 2014 3:59 pm

Hi lukaswelker,

I'm a big fan of Mitch's solution (to TEST Values). Here's how you can solve with problem with algebra:

N = Number of Employees
S = Average Salary of Employees

Original Formula:

(Sum of Salaries)/N = S

Sum of Salaries = N(S)

On July 1st, the Formula changes:
10% fewer employees
10% increase to average salary

(Sum of Salaries)/(.9N) = 1.1(S)

Sum of Salaries = (.9(N)(1.1)(S)
Sum of Salaries = .99(N)(S)

The original sum of salaries = NS
The new sum of salaries = .99NS

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review