A survey of employers found that during 1993 employment...

[AAPL]

A survey employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?

A. 16.5%
B. 20%
C. 35%
D. 55%
E. 65%

The OA is B.

I solve this PS questions of the following way,
$$s\left(1.03\right)+f\left(1.055\right)=sf\left(1.035\right)$$
$$sf=\frac{0.02}{0.005}=4$$
$$\frac{f}{s+f}=\frac{1}{5}=20\%$$
Is there another approach to solve this PS question? Can any experts help, please? Thanks!

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Hi AAPL,

We're told that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs - and that salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993. We're asked for the percent of employment costs that were represented by fringe-benefit costs at the beginning of 1993. This question is essentially a 'Weighted Average' question. It can be solved Algebraically or by TESTing THE ANSWERS.

Since salary costs rose 3% and fringe-benefit costs rose 5.5%, but the OVERALL employment costs rose just 3.5%, we know that salary costs are a much BIGGER percent of the total costs (if salary costs and fringe-benefit costs were equal, then the overall increase would have been (3+5.5)/2 = 4.25%). Thus, fringe-benefit costs must be a relatively small part of the total. Let's TEST Answer B first....

Answer B: 20%
IF... fringe-benefit costs = 20% of total employment costs, then
salary costs = 100% - 20% = 80% of total employment costs
20:80 = 1:4
[(1)(5.5%) + 4(3%)]/5 = 17.5%/5 = 3.5%
This is an exact match for what we were told, so this must be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[Jeff@TargetTestPrep]

A survey employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?

A. 16.5%
B. 20%
C. 35%
D. 55%
E. 65%

We can let x = original salary costs and y = original fringe benefits and create the equation:

0.03x + 0.055y = 0.035(x + y)

30x + 55y = 35(x + y)

30x + 55y = 35x + 35y

20y = 5x

4y = x

So fringe-benefit costs represented y/(x + y) = y/5y = 1/5 = 20%.

Answer: B

[ygcrowanhand]

Hi GMATters,

Here is my video solution to this question:

https://www.youtube.com/watch?v=UgP1GZkk8p0

Rowan