Of the 800 employees of Company X, 70 percent have been with

Of the 800 employees in a certain company, 70% have serviced more than 10 years. A number of y of those who have serviced more than 10 years will retire and no fresh employees join in. What is y if the 10 years employees become 60% of the total employees?

Solution:

TOTAL 10 YRS
Original: 800 560
New: 800-y 560-y

560-y = .6 (800 -y)
560-y = 480 - .6y
80 = .4y
800/4 = y
y= 200

Answer: 200

VeritasKarishma Bunuel I'm trying to use weighted averages for this Q, but I'm getting a different answer. Could you please tell me what am I doing wrong below? Thanks!

People leaving = Pulling the average to 0% => Use 0% for them. Similar to the way how we removereplace/add an ingredient from a mixture, we take it as 0% or 100% respectively. Example: https://gmatclub.com/forum/a-bag-contai ... ml?kudos=1

6:1
0% ------------60%--70%
Left New Avg Old Avg


# of long term employees: 7/10 * 800 = 560

Left = 1/7 * 560 = 80 => One of the answer choices.
or
Left = 1/7 * 800 = Not an int!

I guess this would the correct answer if we were not just "reducing" but instead "replacing" y long term people. So that's my problem? In the beans/pulses example Q, we replace beans with pulses, and that's why we take the weighted average between 0% (after replacement) and 40% (original concentration), something that we can't do here since we're "reducing" and not "replacing". Even if we were replacing in this Q, I guess we would need to use 800 and not 560 for the total mixture?

You can use weighted average here but you have to be very clear about which 2 groups are getting together (or splitting apart) to give you an average group.

Group 1 + Group 2 = Avg Group

If, as per your logic, Group 1 has 70% concentration of long term employees (the total group of 800)
and Group 2 has 0% concentration of long term amp which means this is made of only short term employees - how many people are in this group?
Do the 2 groups combine to give the avg 60% group? No.


This is what the scene is - There is a group 1 which consists of 60% long term employees.
There is a group 2 which consists of all long term employees (that are removed) so concentration of long term employees = 100%
Together these two groups combined to form the 70% concentration group of 800 people (and now we are splitting them).

w1/w2 = (A2 - Avg)/(Avg - A1) = (100 - 70)/(70 - 60) = 3/1

So w2 = 1/4 of total = (1/4) * 800 = 200 = Number of people in group 2 = y

Answer (A)

We see that currently there are 0.7 x 800 = 560 “long-term” employees. We can create the equation:

(560 - y) / (800 - y) = 0.6

560 - y = 0.6(800 - y)

560 - y = 480 - 0.6y

80 = 0.4y

200 = y

Answer: A

Long term employees = 800 * 0.7 = 560
Short term = 800 * 0.3 = 240

(560 - y)/240 = 3/2
2y = 400
y = 200

ANSWER: A

The best approach to solve this question is to frame a simple equation in terms of the unknown y and solve it by considering the constraints mentioned in the question.

Of the 800 employees, 70 percent have been with the company for ten or more (at least ten) years. 70 percent of 800 is equal to 560. Therefore, 560 employees have been with company X for at least 10 years.

Of these 560 members, if y retire, then company X will have a total of (560-y) “long-term” members and a total of (800-y) employees. Be careful not to forget subtracting y from the total employees also, since the question says that no other employee changes occur.

By subtracting y employees, company X wants the percentage of “long-term” employees to reduce to 60 percent. 60 percent is equal to 3/5. Therefore, we can frame an equation as follows:

\(\frac{(560 – y)}{(800 – y)}\) = \(\frac{3}{5}\)

Solving the equation above, the value of y comes out to be 200.

An alternative approach to this could be the back solving approach. If we start with option C, y = 112, 560 – 112 = 448 and 800 – 112 = 688. \(\frac{448}{688}\) is approximately 65 percent. This means that y has to be bigger than 112 so that the percentage reduces to 60 percent. Options D and E can be eliminated.

Of option A and B, A is the easier one to try. If y = 200, 560 – 200 = 360 and 800 – 200 = 600. 360 is definitely 60 percent of 600.
The correct answer option is A.

Hope that helps!

A is the answer.

There are 800 members, 70% (Long term members) means 560 members.

The best way to solve it is to create an equation
(560-y)/(800-y)=0.6
Upon solving we get y=200

is this the correct approach ?

240 is 40% of what . Answer is 600 ,
total given 800 and its given only "old" employees have retired so 200 of the 560 old employees must have retired !

My 2 cents on this:

The thing with questions like these is that it is so easy to use logic and pick D. 80

But honestly, whenever it is so easy, I always think of alarm bells ringing. Something doesn't feel right.

Question asks what value of y would reduce the overall long term employee to 60%. Let's break it down:

Total = 800 employees

Long term emplyees at the moment = 70% of 800 = 560

y of these 560 are to retire. and then the long term employee figure has to be 60%

There 560 - y has to happen, because employees are retiring. At the same time, of 800, y employees are leaving. so 800-y

560-y/800-y = 60%

Solve for y and you get 200.

A.

Tricky but we keep moving on!

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