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# At a technology firm, employees are categorizes as either engineers or

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Math Expert
Joined: 02 Sep 2009
Posts: 54544
At a technology firm, employees are categorizes as either engineers or  [#permalink]

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29 Aug 2017, 23:44
2
3
00:00

Difficulty:

25% (medium)

Question Stats:

77% (02:40) correct 23% (03:06) wrong based on 88 sessions

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At a technology firm, employees are categorizes as either engineers or non-engineers. 80% of the engineers have a masters degree and 55% of the non-engineers have a masters degree. If 70% of all employees have a masters degree, what percent of all employees are engineers?

A. 55%
B. 60%
C. 65%
D. 70%
E. 75%

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Re: At a technology firm, employees are categorizes as either engineers or  [#permalink]

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02 Sep 2017, 07:11
4
1
Bunuel wrote:
At a technology firm, employees are categorizes as either engineers or non-engineers. 80% of the engineers have a masters degree and 55% of the non-engineers have a masters degree. If 70% of all employees have a masters degree, what percent of all employees are engineers?

A. 55%
B. 60%
C. 65%
D. 70%
E. 75%

We can let the total employees = 100.

Thus, 70 have a master’s degree and 30 do not.

We can let n = the number of engineers and create the following equation:

0.8n + 0.55(100 - n) = 70

0.8n + 55 - 0.55n = 70

0.25n = 15

n = 60

Thus, engineers are 60% of the employees.

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At a technology firm, employees are categorizes as either engineers or  [#permalink]

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Updated on: 30 Aug 2017, 01:07
4
1
Bunuel wrote:
At a technology firm, employees are categorizes as either engineers or non-engineers. 80% of the engineers have a masters degree and 55% of the non-engineers have a masters degree. If 70% of all employees have a masters degree, what percent of all employees are engineers?

A. 55%
B. 60%
C. 65%
D. 70%
E. 75%

...................M..............NM..............Total
E...............0.8x............0.2x...............x
NE............0.55y...........0.45y..............y
Total.....0.8x+0.55y....0.2x+0.45y.......x+y

$$0.8x+0.55y = 0.7(x+y)$$
$$0.1x = 0.15y$$
$$x=1.5y$$
Since we have to calculate the % of engineers from all employees..eqn would be x/(x+y)
$$1.5y/(1.5y+y)$$
1.5/2.5 = 60%
B
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Luckisnoexcuse

Originally posted by Luckisnoexcuse on 30 Aug 2017, 00:28.
Last edited by Luckisnoexcuse on 30 Aug 2017, 01:07, edited 1 time in total.
##### General Discussion
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Re: At a technology firm, employees are categorizes as either engineers or  [#permalink]

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30 Aug 2017, 01:01
Luckisnoexcuse wrote:
Bunuel wrote:
At a technology firm, employees are categorizes as either engineers or non-engineers. 80% of the engineers have a masters degree and 55% of the non-engineers have a masters degree. If 70% of all employees have a masters degree, what percent of all employees are engineers?

A. 55%
B. 60%
C. 65%
D. 70%
E. 75%

M NM Total
E 0.8x 0.2x x
NE 0.55y 0.45y y
Total 0.8x+0.55y 0.2x+0.45y x+y

0.8x+0.55y = 0.7(x+y)
0.1x = 0.15y
x=1.5y
1.5/2.5 = 60%
B

Would you be kind enough to explain how you got the denominator in the highlighted step??? Luckisnoexcuse
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At a technology firm, employees are categorizes as either engineers or  [#permalink]

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30 Aug 2017, 01:04
kill3rlook5 wrote:
Luckisnoexcuse wrote:
Bunuel wrote:
At a technology firm, employees are categorizes as either engineers or non-engineers. 80% of the engineers have a masters degree and 55% of the non-engineers have a masters degree. If 70% of all employees have a masters degree, what percent of all employees are engineers?

A. 55%
B. 60%
C. 65%
D. 70%
E. 75%

M NM Total
E 0.8x 0.2x x
NE 0.55y 0.45y y
Total 0.8x+0.55y 0.2x+0.45y x+y

0.8x+0.55y = 0.7(x+y)
0.1x = 0.15y
x=1.5y
1.5/2.5 = 60%
B

Would you be kind enough to explain how you got the denominator in the highlighted step??? Luckisnoexcuse

Sure kill3rlook5
We have to calculate x/(x+y) since x = 1.5y
x/(x+y) = 1.5y/(1.5y + y) = 1.5/2.5..which is 60% in % terms
Hope it helps
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Thanks
Luckisnoexcuse
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Re: At a technology firm, employees are categorizes as either engineers or  [#permalink]

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30 Aug 2017, 01:18
Quote:
Sure kill3rlook5
We have to calculate x/(x+y) since x = 1.5y
x/(x+y) = 1.5y/(1.5y + y) = 1.5/2.5..which is 60% in % terms
Hope it helps

Thanks a ton for explaining that. I was on the verge of tearing my hair trying to understand that....
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Posts: 2654
At a technology firm, employees are categorizes as either engineers or  [#permalink]

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30 Aug 2017, 18:01
Luckisnoexcuse wrote:
Bunuel wrote:
At a technology firm, employees are categorizes as either engineers or non-engineers. 80% of the engineers have a masters degree and 55% of the non-engineers have a masters degree. If 70% of all employees have a masters degree, what percent of all employees are engineers?

A. 55%
B. 60%
C. 65%
D. 70%
E. 75%

...................M..............NM..............Total
E...............0.8x............0.2x...............x
NE............0.55y...........0.45y..............y
Total.....0.8x+0.55y....0.2x+0.45y.......x+y

$$0.8x+0.55y = 0.7(x+y)$$
$$0.1x = 0.15y$$
$$x=1.5y$$
Since we have to calculate the % of engineers from all employees..eqn would be x/(x+y)
$$1.5y/(1.5y+y)$$
1.5/2.5 = 60%
B

I used your equation, but not your chart, and confused myself for a LONG time about total, despite the fact that I had just used both variables in a weighted average to find the ratio of x to y.

I kept thinking that I had failed to account for the other 30 percent who were not included in the equation. I chose B, unconvinced.

Then I saw your post. I'm still not sure I understand what happened to the other 30 percent, but I believe you.

Nice work. And kudos.
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Re: At a technology firm, employees are categorizes as either engineers or  [#permalink]

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10 Sep 2017, 21:04
Overlapping sets problem. we can use 2X2 table.
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Screen Shot 2017-09-11 at 9.33.11 AM.png [ 34.29 KiB | Viewed 980 times ]

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Re: At a technology firm, employees are categorizes as either engineers or  [#permalink]

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10 Sep 2017, 22:14
1
Bunuel wrote:
At a technology firm, employees are categorizes as either engineers or non-engineers. 80% of the engineers have a masters degree and 55% of the non-engineers have a masters degree. If 70% of all employees have a masters degree, what percent of all employees are engineers?

A. 55%
B. 60%
C. 65%
D. 70%
E. 75%

70 = .8x + (100 - x)* .55
solving for x we can get the answer ...

hope this helps
cheers ..
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At a technology firm, employees are categorizes as either engineers or  [#permalink]

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11 Sep 2017, 11:57
Explaining the photo below using the see-saw method:

Please forgive the crudeness of the drawing!

The ratio of masters degrees is 3:2 (15:10), weighted towards engineers. So, engineers comprise 60% of the company. We get this because we know 55% of non engineers have their degree, and 80% of engineers do as well, so you can determine the weight of each, given that 70% of the total company have their degree.

Notice the tilt towards the engineer side, so you don't get confused with the 15 and 10.
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picture 1.png [ 13.12 KiB | Viewed 893 times ]

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At a technology firm, employees are categorizes as either engineers or   [#permalink] 11 Sep 2017, 11:57
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