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

Question

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%

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

Luckisnoexcuse · Accepted Answer

...................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

JeffTargetTestPrep · Answer

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

kill3rlook5 · Answer

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

Luckisnoexcuse · Answer

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

kill3rlook5 · Answer

Thanks a ton for explaining that. I was on the verge of tearing my hair trying to understand that....

generis · Answer

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.

gps5441 · Answer

Overlapping sets problem. we can use 2X2 table.

testcracker · Answer

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

hope this helps 
cheers ..

nightblade354 · Answer

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.

adityasuresh · Answer

...................E..............NE..............Total
M...............0.8x........... 55/100 (100-X) 70
NM.....................................................30
Total............x................100-x............100
Assume total = 100
0.8x +  55/100(100-x)  = 70
 8/10x  + 55 -  55/100x  = 70
 80x/100  -  55x/100  = 70 - 55
 1x/4  = 15
x =60
 B

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