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

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Of the 800 employees of Company X, 70 percent have been with  [#permalink]

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New post Updated on: 03 Dec 2012, 01:14
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Question Stats:

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Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of these "long-term" members were to retire and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60 percent ?

A. 200
B. 160
C. 112
D. 80
E. 56

Originally posted by LM on 06 May 2010, 12:34.
Last edited by Bunuel on 03 Dec 2012, 01:14, edited 1 time in total.
Renamed the topic and edited the question.
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Re: GMAT PREP (PS)  [#permalink]

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New post 06 May 2010, 14:44
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Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of these "long-term" members were to retire and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60 percent ?

A. 200
B. 160
C. 112
D. 80
E. 56

The # of "long-term" employees is 70%*800=560.

After y of them retire new # of "long-term" employees would become 560-y.
Total # of employees would become 800-y.

We want 560-y to be 60% of 800-y --> 560-y=(800 -y)*60% --> y = 200.

Answer: A.
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Re: GMAT PREP (PS)  [#permalink]

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New post 07 May 2010, 23:50
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Agree with Bunuel - I got A as well

Remember that when you're "removing" the y members, you're removing y members from both the long term employees AND the total employees
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Re: Of the 800 employees in a certain company, 70% have serviced  [#permalink]

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New post 02 Dec 2012, 00:10
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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
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Of the 800 employees of Company X, 70 percent have been with  [#permalink]

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New post 16 Sep 2019, 17:16
Bunuel wrote:
Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of these "long-term" members were to retire and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60 percent ?

A. 200
B. 160
C. 112
D. 80
E. 56

The # of "long-term" employees is 70%*800=560.

After y of them retire new # of "long-term" employees would become 560-y.
Total # of employees would become 800-y.

We want 560-y to be 60% of 800-y --> 560-y=(800 -y)*60% --> y = 200.

Answer: A.



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?
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Re: Of the 800 employees of Company X, 70 percent have been with  [#permalink]

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New post 18 Sep 2019, 04:43
1
dabaobao wrote:
Bunuel wrote:
Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of these "long-term" members were to retire and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60 percent ?

A. 200
B. 160
C. 112
D. 80
E. 56

The # of "long-term" employees is 70%*800=560.

After y of them retire new # of "long-term" employees would become 560-y.
Total # of employees would become 800-y.

We want 560-y to be 60% of 800-y --> 560-y=(800 -y)*60% --> y = 200.

Answer: A.



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)
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Re: Of the 800 employees of Company X, 70 percent have been with  [#permalink]

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New post 23 Sep 2019, 09:39
LM wrote:
Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of these "long-term" members were to retire and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60 percent ?

A. 200
B. 160
C. 112
D. 80
E. 56


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
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Re: Of the 800 employees of Company X, 70 percent have been with  [#permalink]

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New post 28 Sep 2019, 15:00
LM wrote:
Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of these "long-term" members were to retire and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60 percent ?

A. 200
B. 160
C. 112
D. 80
E. 56


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

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

ANSWER: A
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Re: Of the 800 employees of Company X, 70 percent have been with  [#permalink]

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New post 13 Oct 2019, 05:01
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!
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Re: Of the 800 employees of Company X, 70 percent have been with   [#permalink] 13 Oct 2019, 05:01
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