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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?

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

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29 Aug 2017, 23:28

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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?

\(0.8x+0.55y = 0.7(x+y)\) \(0.1x = 0.15y\) \(x=1.5y\) 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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Thanks Luckisnoexcuse

Last edited by Luckisnoexcuse on 30 Aug 2017, 00:07, edited 1 time in total.

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

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30 Aug 2017, 00:01

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

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

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30 Aug 2017, 00:04

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

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

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30 Aug 2017, 17:01

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?

\(0.8x+0.55y = 0.7(x+y)\) \(0.1x = 0.15y\) \(x=1.5y\) 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.

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.

Answer: B
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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

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10 Sep 2017, 21:14

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This post was BOOKMARKED

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 ...

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

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11 Sep 2017, 10:57

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.