A survey of employers found that during 1993 employment costs rose 3.5

SOLUTION

A survey of 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 amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);

On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.055*fringe benefit costs;

So, \(35(S+F) = 30S+55F\);

\(S = 4F\);

\(\frac{F}{S} = \frac{1}{4}\);

\(\frac{F}{(S+F)} = \frac{1}{(1+4)} = \frac{1}{5} = 0.2\).

Answer: B.
_________________

Answer = (B) 20%

Please refer chart below:



\(\frac{103x}{100} + \frac{105.5y}{100} = \frac{103.5 (x+y)}{100}\)

103x + 105.5y = 103.5x + 103.5y

2y = 0.5x

\(\frac{y}{x} = \frac{1}{4}\)

\(\frac{y}{x+y} = \frac{1}{1+4} = \frac{1}{5}\)

\(\frac{y}{x+y} % = \frac{1}{5} * 100 = 20%\)

s(1.03) + f(1.055) = (s+f) (1.035)
=> (s/f) = 0.02/0.005 = 4
=> f/(s+f) = 1/5 = 20%

Option (B).

This can also be solved by weighted average method.

Let x be the percentage for Fringe Benefit in the overall employee cost of 100 %

5.5 (x) + 3 (100 -x) / 100 = 3
5.5 (x) + 3 (100 -x) = 3.5 * 100
2.5 x = 3.5 * 100 - 3 * 100
2.5 x = 0.5 * 100
x = (0.5* 100)/ 2.5
x = 20

A survey of 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%
(0) 55%
(E) 65%
S = salary, F = fringe-benefit, E = employment cost
F/(S+F) x 100 = ?

S + .035S = 1.03S // F + .055F = 1.055F // S + F = E // E + .035E = 1.035E
1.03S + 1.055F = 1.035E = 1.035 (S + F)
1.03S + 1.055F = 1.035S + 1.035F
1.055F - 1.035F = 1.035S - 1.03S
.02F=.005S
(.02/.005)F=S
4F=S

F/(S+F) x 100 = ?
F/(4F + F) x 100 = (F/5F) x 100 = (1/5) x 100 since the variable cancels. The answer is 20.

With Allegation:

S -------------F
3----3.5------5.5
--.5------2-----

So F is .5 out of 2.5 total so 1/5 = 20%

The easiest way to solve this problem is by drawing graph as in the pic. The total distance = 5.5 -3 = 2.5. The rose of the employment costs is closer to rose of the salary costs. This means salary cost weight more than fringe-benefit costs. So fringe-benefit costs represents 0.5/2.5 = 20%.

The solution is easy using Weighted mapping strategy.
What is not easy is the level of poor grammar in the question stem. That's the tough part of GMAT quant- finding out what exactly the the question is trying to say. I'm straggling on that.
The question was asking about beginning of the year. But the costing is about what happened in the said year. It doesn't make sense at all

Posted from my mobile device

This Q can be done easily using weighted averages.

Scale: 3_____3.5_____5.5
Weights: 1 4

Weight of F (i.e. 5.5) = 1/5 = 20%

ANSWER: B

Let x be the percentage for Fringe Benefit in the overall employee cost of 100 %

5.5 (x) + 3 (100 -x) / 100 = 3
5.5 (x) + 3 (100 -x) = 3.5 * 100
2.5 x = 3.5 * 100 - 3 * 100
2.5 x = 0.5 * 100
x = (0.5* 100)/ 2.5
x = 20

VeritasKarishma Bunuel generis
Can we also solve this by picking dummy numbers for S and F ? I am getting garbage answer.

What you need to find in this question is the value of F as a percentage of (S + F). Then how can we assume values for these variables?

Use weighted average here:

S/F = (5.5 - 3.5)/(3.5 - 3) = 4/1

So fringe benefit is 1/(4+1) = 1/5th of total employment cost i.e. 20%

\(Given \ that\), \(0.035(S+F) = 0.30S+0.055F\);

\(0.035S+0.035F=0.03S+0.055F\)

\(0.20F=0.05S\)

\(\frac{F}{S}=\frac{5}{20}=\frac{1}{4}\)

\(\frac{F}{F+S}=\frac{1}{1+4}=\frac{1}{5}\)

\(\frac{F}{F+S}=\frac{1}{5}*100=20\)%

The answer is \(B\)

Given: A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. Asked: 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 ?



Fringe benefit cost as a percentage of total costs = 20%

IMO B

OFFICIAL GMAT EXPLANATION

Algebra; Arithmetic First-degree equations; Percents

Let E represent employment costs, S represent salary costs, and F represent fringe-benefit costs. Then E = S + F. An increase of 3 percent in salary costs and a 5.5 percent increase in fringe-benefit costs resulted in a 3.5 percent increase in employment costs. Therefore 1.03S + 1.055F = 1.035E. But, E = S + F, so 1.03S + 1.055F = 1.035(S + F) = 1.035S + 1.035F.

Combining like terms gives (1.055 − 1.035)F = (1.035 − 1.03)S or 0.02F = 0.005S. Then, S = 0.020/.005F = 4F. Thus, since E = S + F, it follows that E = 4F + F = 5F. Then, F as a percent of E is F/E = F/5F = 1/5 = 20%.

Any time you have different volumes of two inputs that yield one average, the percentage of the larger one is:
(the spread between the smaller one and the average)/(the spread between the smaller one and the larger one).

Look at the spreads between the numbers we are working with.

3 salary costs
3.5 employment costs
5.5 fringe-benefit costs

The spread between 3 and 3.5 is 0.5.
The spread between 3 and 5.5 is 2.5.

0.5/2.5 = 20%.

Answer choice B.

Hi GMATters,

Here is my video solution to this problem:

Short video solution here, using the Teeter Totter Timesaver Method (2:11):




Teeter Totter Method Steps:

1) Draw the Endpoints and Weighted Average numbers on the Teeter Totter Diagram (the weighted average represents the final mixture, and goes above the triangle-shaped fulcrum)

2) Draw the weights on each side. The LARGER weight goes on the side with the SHORTER distance from the fulcrum

3) Draw the distances from the Endpoints to the Weighted Average

4) Solve the equation: (W2)/(W1) =(D1)/(D2)
(the weights and distances are in an INVERSE RATIO)­


Teeter Totter Basic Examples Playlist: https://www.youtube.com/playlist?list=PL2exXfCUscn8Hvafet5-IPH1eNNLSjQBP

KarishmaB

A bit confused here on the wording 'beginning of the year'.

What if the Q had asked for 'End of the year'? How do we go about it?

Thank you!