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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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12 Mar 2014, 00:01
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71% (02:11) correct 29% (02:42) wrong based on 593 sessions

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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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[Reveal] Spoiler: OA

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

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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 --> F/S = 1/4 --> F/(S+F) = 1/(1+4) = 1/5 = 0.2.

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

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12 Mar 2014, 20:01
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sal.png [ 34.41 KiB | Viewed 5437 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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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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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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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.

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

Thanks!
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Posts: 44298
Re: A survey of employers found that during 1993 employment cost [#permalink]

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28 May 2014, 05:02
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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.

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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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:
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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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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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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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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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:

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

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

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22 Nov 2015, 18:45
1
KUDOS
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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07 Apr 2017, 22:29
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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22.JPG [ 79.8 KiB | Viewed 1414 times ]

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