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At a certain hedge fund, there are only CFAs and MBAs. The average num

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At a certain hedge fund, there are only CFAs and MBAs. The average num  [#permalink]

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New post 06 Oct 2018, 11:30
6
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (03:49) correct 44% (02:02) wrong based on 34 sessions

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At a certain hedge fund, there are only CFAs and MBAs. The average number of vacation days taken by the CFAs is 5 fewer than the average number of vacation days taken per employee at the hedge fund. The average number of vacation days taken by the MBAs is 10 more than the average number of vacations days taken per employee at the hedge fund. What fraction of the hedge fund employees are CFAs?


A)\(\frac{1}{8}\)

B)\(\frac{1}{4}\)

C)\(\frac{1}{2}\)

D)\(\frac{2}{3}\)

E)\(\frac{3}{4}\)

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Re: At a certain hedge fund, there are only CFAs and MBAs. The average num  [#permalink]

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New post 07 Oct 2018, 06:17
Abhi077 wrote:
At a certain hedge fund, there are only CFAs and MBAs. The average number of vacation days taken by the CFAs is 5 fewer than the average number of vacation days taken per employee at the hedge fund. The average number of vacation days taken by the MBAs is 10 more than the average number of vacations days taken per employee at the hedge fund. What fraction of the hedge fund employees are CFAs?


A)\(\frac{1}{8}\)

B)\(\frac{1}{4}\)

C)\(\frac{1}{2}\)

D)\(\frac{2}{3}\)

E)\(\frac{3}{4}\)


Use weighted average method ..
C... Average....M
x-5.....x.......x+10
So C/total = \(\frac{(x+10)-x}{x+10-(x-5)}\)=\(\frac{10}{15}=\frac{2}{3}\)
D

Or

Total number of leave by CFA= C*(x-5)
Total number of leave by MBA= M*(x+10)
Total number of leave = T*x
So T*x=Cx-5C+Mx+10M=(C+M)*X.......5C=10M....C=2M
Total =C+M=2M+M=3M
So C/T=2M/3M=2/3
D
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Re: At a certain hedge fund, there are only CFAs and MBAs. The average num  [#permalink]

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New post 07 Oct 2018, 09:22
Abhi077 wrote:
At a certain hedge fund, there are only CFAs and MBAs. The average number of vacation days taken by the CFAs is 5 fewer than the average number of vacation days taken per employee at the hedge fund. The average number of vacation days taken by the MBAs is 10 more than the average number of vacations days taken per employee at the hedge fund. What fraction of the hedge fund employees are CFAs?


A)\(\frac{1}{8}\)

B)\(\frac{1}{4}\)

C)\(\frac{1}{2}\)

D)\(\frac{2}{3}\)

E)\(\frac{3}{4}\)


If we let X be the number of CFAs and Y the number of MBAs.

A be the sum of leaves taken by CFAs
B be the sum of leaves taken by MBAs

Let the average of leaves for all employees be z

We want to know x/(x+y)

We are given a/x = z - 5

a = x(z-5)

b/y = z + 10

b = y (z + 10)

Average of all = (a+b)/(x+y) = z

we get x = 2y

x/x+y = 2y/(2y+y) = 2/3 answer choice D

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At a certain hedge fund, there are only CFAs and MBAs. The average num  [#permalink]

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New post 15 Oct 2018, 22:47
This problem can be solved by treating it like a weighted average prooblem.

Let the average number of holidays/employee be x (the weighted average).
From the stem we know that the average number of holidays/CFA = x-5 and the average number of holidays/MBA = x+10.

Apppying the teeter totter method (from MGMAT): Thus, the the total distance between x-5 and x+10 = 15.

x-5--------------------x-----------------------x+10
distance from x=5 , distance from x=10

As we want to determine the number of CFAs, we can use the above teeter totter to conclude CFAs make up \(\frac{10}{15}=\frac{2}{3}\)of the total number of employees.

Using the teeter totter is a great way to simplify and visualise. Moreover, this approach is quite fast and took me around 1.5 minutes.

Please hit Kudos if you liked this approach :)
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At a certain hedge fund, there are only CFAs and MBAs. The average num &nbs [#permalink] 15 Oct 2018, 22:47
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