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555-605 Level|   Percent and Interest Problems|                              
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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%.
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With Allegation:

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

So F is .5 out of 2.5 total so 1/5 = 20%
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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).
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Bunuel
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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%

Problem Solving
Question: 154
Category: Algebra; Arithmetic First-degree equations; Percents
Page: 82
Difficulty: 600

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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
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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.
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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
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Bunuel
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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%

Problem Solving
Question: 154
Category: Algebra; Arithmetic First-degree equations; Percents
Page: 82
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
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4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

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


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

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

\(0.20F=0.05S\)

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

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

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

The answer is \(B\)
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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 ?

Attachment:
Screenshot 2020-12-06 at 7.11.20 PM.png
Screenshot 2020-12-06 at 7.11.20 PM.png [ 29.21 KiB | Viewed 30866 times ]

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

IMO B
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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%.
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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.
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Hi GMATters,

Here is my video solution to this problem:

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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
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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!
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