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by Aman verma » Sat Oct 19, 2013 1:38 am
Q: The average salary paid to all its employees by Mckinsey & Co. is $ 15500. The average salary of the senior employees is $ 18000 per month and the average salary of junior employees is $ 12000 per month. If there are only two levels of employees viz. junior and senior level, then what fraction of the total employees is the junior level employees ?

A) 7/10

B) 5/12

C) 5/16

D) 7/16

E) 7/12
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by theCodeToGMAT » Sat Oct 19, 2013 1:51 am
Average = 15500

Senior = x

Junior = y

y / x = (18000-15500)/(15500-12000) = 2500/3500 = 5/7

So, fraction of employees = 5/7+5 = 5/12

Is the Answer [spoiler]{B}[/spoiler]?
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by riz_gmat » Sat Oct 19, 2013 2:25 am
Avg(t) = 15,500
Avg(s) = 18,000
Avg(J) = 12,000

S - no Of Seniors
J - no Of Juniors

18,000 (S) + 12,000 ( J) / S + J = 15,500

=> 2500 S = 35 00 J
S/J = 7/5
Asked => No Of Juniors / Total = [spoiler]5 / 12[/spoiler]
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by GMATGuruNY » Sat Oct 19, 2013 2:32 am
Aman verma wrote:Q: The average salary paid to all its employees by Mckinsey & Co. is $ 15500. The average salary of the senior employees is $ 18000 per month and the average salary of junior employees is $ 12000 per month. If there are only two levels of employees viz. junior and senior level, then what fraction of the total employees is the junior level employees ?

A) 7/10

B) 5/12

C) 5/16

D) 7/16

E) 7/12
This is a WEIGHTED AVERAGE/MIXTURE problem.
Let S = senior employees and J = junior employees.
Average salary for S = 18000.
Average salary for J = 12000.
Average salary for the MIXTURE of S+J = 15500.
To determine the ratio of S to J in the mixture, use ALLIGATION.

Step 1: Plot the 3 averages on a number line, with the averages for S and J on the ends and the average for the mixture in the middle.
S 18000---------------15500--------------12000 J

Step 2: Calculate the distances between the averages.
S 18000-----2500-----15500-----3500-----12000 J

Step 3: Determine the ratio in the mixture.
The required ratio of S to J is equal to the RECIPROCAL of the distances in red:
S:J = 3500:2500 = 7:5.

Since S=7 and J=5, of every 12 employees, 7 are senior and 5 are junior.
Thus, junior/total = 5/12.

The correct answer is B.

For more practice will alligation, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html
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by [email protected] » Sat Oct 19, 2013 11:20 am
Hi Aman,

Rahul and Mitch both provided algebra solutions to this question. Here's a slightly different version that's based on "math logic" and TESTING THE ANSWERS...

Since all of the "numbers" in this question end in "00", you can eliminate all of those extra digits and work with:

Average = 155
Sen. Pay = 180
Jr. Pay = 120

If we had an equal number of Seniors and Juniors, then the average would be (180+120)/2 =150. Since the actual average is 155, that means that there are MORE Seniors than Juniors. So, the fraction that are Juniors is LESS THAN 1/2. Eliminate A and E.

With the remaining 3 answers, we just need to TEST THEM until we find a match.

Answer B:
12 Total
5 Juniors x 120 = 600
7 Seniors x 180 = 1260

1860/12 = 155 This is a MATCH.

Final Answer: B

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