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A survey of employers found that during 1993 employment cost

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A survey of employers found that during 1993 employment cost  [#permalink]

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New post 12 Mar 2014, 00:01
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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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A survey of employers found that during 1993 employment cost  [#permalink]

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New post 12 Mar 2014, 00:02
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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.
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A survey of employers found that during 1993 employment cost  [#permalink]

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New post Updated on: 09 Oct 2014, 19:17
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Answer = (B) 20%

Please refer chart below:

Attachment:
sal.png
sal.png [ 34.41 KiB | Viewed 10226 times ]


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

103x + 105.5y = 103.5x + 103.5y

2y = 0.5x

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

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

\(\frac{y}{x+y} % = \frac{1}{5} * 100 = 20%\)
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Originally posted by PareshGmat on 12 Mar 2014, 20:01.
Last edited by PareshGmat on 09 Oct 2014, 19:17, edited 1 time in total.
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Re: A survey of employers found that during 1993 employment cost  [#permalink]

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New post 12 Mar 2014, 20:30
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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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Re: A survey of employers found that during 1993 employment cost  [#permalink]

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New post 27 May 2014, 17:21
Bunuel wrote:
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 --> F/S = 1/4 --> F/(S+F) = 1/(1+4) = 1/5 = 0.2.

Answer: B.


Thanks! I'm assuming that this is considered a weighted averages problem? Can you recommend similar ones please?

Thanks!
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Re: A survey of employers found that during 1993 employment cost  [#permalink]

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New post 28 May 2014, 05:02
russ9 wrote:
Bunuel wrote:
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 --> F/S = 1/4 --> F/(S+F) = 1/(1+4) = 1/5 = 0.2.

Answer: B.


Thanks! I'm assuming that this is considered a weighted averages problem? Can you recommend similar ones please?

Thanks!


Search here: search.php?search_id=tag&tag_id=43 and here: search.php?search_id=tag&tag_id=114
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Re: A survey of employers found that during 1993 employment cost  [#permalink]

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New post 28 May 2014, 06:36
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Bunuel wrote:
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.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


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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Re: A survey of employers found that during 1993 employment cost  [#permalink]

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New post 09 Oct 2014, 17:30
Can someone explain the concept of alligation? How do you identify the questions wherein you can use this concept?

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Re: A survey of employers found that during 1993 employment cost  [#permalink]

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New post 24 May 2015, 01:28
3S + 5,5F = 3,5(F+S)
2F=0,5S
S=4F

F/S+F = F/4F+F = 1/5 = 20%
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A survey of employers found that during 1993 employment costs ro  [#permalink]

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New post 27 May 2015, 13:36
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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Re: A survey of employers found that during 1993 employment costs rose 3.5  [#permalink]

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New post 28 May 2015, 06:15
This is not a difficult question per se. And yet, because it has many information points, the question may seem confusing/convoluted.

A student who felt such a confusion in this question should represent the given information visually. For example, like this:

Image

From this image, it becomes clear that:

E = S + F . . . (1)
Ef (E final) = 1.03S + 1.055F . . . (2)

But we are given: Ef = 1.035E . . . (3)

Substituting (1) and (2) in (3), we get:

1.03S + 1.055F = 1.035(S+F)

From here on, the question is easy to solve.

The crux of this post is that if you find yourself getting overwhelmed by the given information, representing it visually helps. :)

Best Regards

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A survey of employers found that during 1993 employment cost  [#permalink]

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New post 22 Nov 2015, 18:45
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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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A survey of employers found that during 1993 employment cost  [#permalink]

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New post 07 Apr 2017, 22:29
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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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A survey of employers found that during 1993 employment cost  [#permalink]

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New post 12 Aug 2018, 11:40
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

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A survey of employers found that during 1993 employment cost   [#permalink] 12 Aug 2018, 11:40
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