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In a certain company, a third of the workers do not have a retirement

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New post 09 Aug 2015, 11:44
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In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?

A. 80
B. 95
C. 105
D. 120
E. 210

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Re: In a certain company, a third of the workers do not have a retirement  [#permalink]

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New post 09 Aug 2015, 23:36
reto wrote:
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?

A. 80
B. 95
C. 105
D. 120
E. 210



I think the question is not correct. Could you please check for errors.

"20% of the workers who do not have a retirement plan are women" - implies 80% of the workers who do have a retirement plan are men
But the very next line says "40% of the workers who do have a retirement plan are men"
So what are the rest of the 40% workers? Children? I don't think the question could imply that at all.
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In a certain company, a third of the workers do not have a retirement  [#permalink]

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New post 10 Aug 2015, 02:54
VeritasPrepKarishma wrote:
reto wrote:
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?

A. 80
B. 95
C. 105
D. 120
E. 210



I think the question is not correct. Could you please check for errors.

"20% of the workers who do not have a retirement plan are women" - implies 80% of the workers who do have a retirement plan are men
But the very next line says "40% of the workers who do have a retirement plan are men"
So what are the rest of the 40% workers? Children? I don't think the question could imply that at all.


Dear VeritasPrepKarishma

Yes the question is 1:1 from Economist and imo is not flawed. Why would you imply that 80% of the workers who do have a retirement plan are men? I colored your statement red above.

20% of the workers without retirement plan are women, this means 80% of the workers without retirement plan are men right? Makes 100% = no retirement plan.

Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroups "Retirement plan = Yes" and "No Retirement Plan".

Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.
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In a certain company, a third of the workers do not have a retirement  [#permalink]

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New post 10 Aug 2015, 23:01
reto wrote:
VeritasPrepKarishma wrote:
reto wrote:
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?

A. 80
B. 95
C. 105
D. 120
E. 210



I think the question is not correct. Could you please check for errors.

"20% of the workers who do not have a retirement plan are women" - implies 80% of the workers who do have a retirement plan are men
But the very next line says "40% of the workers who do have a retirement plan are men"
So what are the rest of the 40% workers? Children? I don't think the question could imply that at all.


Dear VeritasPrepKarishma

Yes the question is 1:1 from Economist and imo is not flawed. Why would you imply that 80% of the workers who do have a retirement plan are men? I colored your statement red above.

20% of the workers without retirement plan are women, this means 80% of the workers without retirement plan are men right? Makes 100% = no retirement plan.

Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroups "Retirement plan = Yes" and "No Retirement Plan".

Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.



Yes, you are right. I read the question incorrectly! I glazed over "not" for some reason.

If "20% of the workers who do not have a retirement plan are women," 80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.

Cavg = (80*1 + 40*2)/3 = 160/3% are men

Total = 120*300/160 = 225

No. of women = 225 - 120 = 105

It is not a 700+ problem, that is, if you read it correctly! :)
I would say 650-700.
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In a certain company, a third of the workers do not have a retirement  [#permalink]

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New post 11 Aug 2015, 03:20
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reto wrote:
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?

A. 80
B. 95
C. 105
D. 120
E. 210


Let x be the total no of workers => \(\frac{x}{3}\) workers without retirement plan, \(\frac{2x}{3}\) workers with retirement plan.

Without Retirement Plan:

Women without Retirement Plan => \(\frac{1}{5}\) * \(\frac{x}{3}\)
Men Without Retirement Plan => \(\frac{4}{5}\) * \(\frac{x}{3}\)

With Retirement Plan:

Men with Retirement Plan => \(\frac{2}{5}\) * \(\frac{2x}{3}\)
Women with Retirement Plan => \(\frac{3}{5}\) * \(\frac{2x}{3}\)

Hence Total Men => \(\frac{4}{5}\) * \(\frac{x}{3}\) + \(\frac{2}{5}\) * \(\frac{2x}{3}\) = 120

Solving for x => x= 225, where x is the total workers.

Hence Total women workers => 225 - 120 = 105

Option C


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Re: In a certain company, a third of the workers do not have a retirement  [#permalink]

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New post 12 Aug 2015, 05:36
reto wrote:
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?

A. 80
B. 95
C. 105
D. 120
E. 210



Set up equation:
x = total number of workers

120 = 0,4 * 2/3 * x + 0,8 * 1/3 * x

120 = 16/30 x

x = 225

225 - 120 = 105

Answer C
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Re: In a certain company, a third of the workers do not have a retirement  [#permalink]

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New post 14 Aug 2015, 01:10
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reto wrote:
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?

A. 80
B. 95
C. 105
D. 120
E. 210

Let us use a convenient number, 15 (LCM of 3 and 5)
No R=5 R=10
w=1 m=4 w=6 m=4
The ratio of m:w= 8:7
Therefore, the number of women=120*(7/8)=105
correct option is C
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Re: In a certain company, a third of the workers do not have a retirement  [#permalink]

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Re: In a certain company, a third of the workers do not have a retirement   [#permalink] 06 Feb 2019, 19:42
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