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# One-tenth of the employees at a company dinner are vice-presidents

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
One-tenth of the employees at a company dinner are vice-presidents  [#permalink]

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15 Nov 2015, 08:44
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:42) correct 20% (02:02) wrong based on 141 sessions

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One-tenth of the employees at a company dinner are vice-presidents, and one-third of the remaining employees are assistant vice-presidents. If there are e employees in attendance, how many employees in attendance are neither vice-presidents nor assistant vice-presidents?

A. e/30
B. 2e/5
C. 13e/30
D. 17e/30
E. 3e/5

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Posts: 3442
Re: One-tenth of the employees at a company dinner are vice-presidents  [#permalink]

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15 Nov 2015, 09:41
Bunuel wrote:
One-tenth of the employees at a company dinner are vice-presidents, and one-third of the remaining employees are assistant vice-presidents. If there are e employees in attendance, how many employees in attendance are neither vice-presidents nor assistant vice-presidents?

A. e/30
B. 2e/5
C. 13e/30
D. 17e/30
E. 3e/5

One approach is to use the INPUT-OUTPUT approach (described in our free video - http://www.gmatprepnow.com/module/gmat- ... /video/933)

We have two fractions (1/10 and 1/3), so let's let e = the least common denominator of these two fraction.
We'll let e = 30

If there are 30 employees, then the number of vice-presidents = (1/10)(30) = 3

one-third of the remaining employees are assistant vice-presidents
There are 27 employees remaining.
1/3 of 27 = 9, so there are 9 assistant vice-presidents

So, the total number of vice-presidents AND assistant vice-presidents = 3 + 9 = 12
So, the number of employees who are NEITHER vice-presidents nor assistant vice-presidents = 30 - 12 = 18

So, when the INPUT e = 30, the OUTPUT is 18 people who are NEITHER vice-presidents nor assistant vice-president

Now check the answer choices to see which one yields an OUTPUT of 18, when we INPUT e = 30

A. e/30 = 30/30 = 1 - NO - ELIMINATE
B. 2e/5 = 2(30)/5 = 12 - NO - ELIMINATE
C. 13e/30 = 13(30)/30 = 13 - NO - ELIMINATE
D. 17e/30 = 17(30)/30 = 17 - NO - ELIMINATE
E. 3e/5 = 3(30)/5 = 18 - YES - KEEP

Cheers,
Brent
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Re: One-tenth of the employees at a company dinner are vice-presidents  [#permalink]

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15 Nov 2015, 09:47
Bunuel wrote:
One-tenth of the employees at a company dinner are vice-presidents, and one-third of the remaining employees are assistant vice-presidents. If there are e employees in attendance, how many employees in attendance are neither vice-presidents nor assistant vice-presidents?

A. e/30
B. 2e/5
C. 13e/30
D. 17e/30
E. 3e/5

Here's the algebraic approach:
There are e employees

One-tenth of the employees at a company dinner are vice-presidents
So, (1/10) of e = number of employees who are vice-presidents
So, e/10 = number of employees who are vice-presidents

one-third of the remaining employees are assistant vice-presidents
So, number of remaining employees = e - e/10 = 9e/10
1/3 of 9e/10 = (1/3)(9e/10) = 3e/10
So, 3e/10 = number of employees who are assistant vice-presidents

TOTAL # of vice-presidents AND assistant vice-presidents = e/10 + 3e/10 = 4e/10 = 2e/5

How many employees in attendance are neither vice-presidents nor assistant vice-presidents?
We get e - 2e/5 = 3e/5

Cheers,
Brent
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Joined: 11 Sep 2015
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Re: One-tenth of the employees at a company dinner are vice-presidents  [#permalink]

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15 Nov 2015, 09:48
Here some additional videos that will help with this question:
- Tips for the Algebraic Approach - http://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - http://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
Brent
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Re: One-tenth of the employees at a company dinner are vice-presidents  [#permalink]

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15 Nov 2015, 11:17
Bunuel wrote:
One-tenth of the employees at a company dinner are vice-presidents.................... If there are e employees in attendance.........

vp = E/10
Non Vp = 9E/10

Bunuel wrote:
.....and one-third of the remaining employees are assistant vice-presidents. .....

Avp = (9E/10)*(1/3) =>3E/10
Non AVP = 9E/10 - 3E/10 => 3E/5

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Re: One-tenth of the employees at a company dinner are vice-presidents  [#permalink]

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03 Dec 2015, 23:39
Hi All,

TESTing VALUES (the approach that Brent used) works perfectly on these types of questions. Rather than rehash the work that he did, I want to point out one of the ways to choose the 'perfect' starting value in these types of situations. Looking at the 5 answer choices, the common denominator is 30, so we should use 30 as the value for the total number of employees. From there, the remaining steps are essentially just basic arithmetic. A bit of note-taking and math will get you to the correct answer.

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One-tenth of the employees at a company dinner are vice-presidents  [#permalink]

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22 Oct 2018, 09:50
Bunuel wrote:
One-tenth of the employees at a company dinner are vice-presidents, and one-third of the remaining employees are assistant vice-presidents. If there are e employees in attendance, how many employees in attendance are neither vice-presidents nor assistant vice-presidents?

A. e/30
B. 2e/5
C. 13e/30
D. 17e/30
E. 3e/5

let total number of employees be x

One-tenth of the employees at a company dinner are vice-presidents $$\frac{1}{10}$$ x

One-third of the remaining employees are assistant vice-presidents ($$x$$ - $$\frac{1}{10}$$x) * $$\frac{1}{3}$$ = $$\frac{3}{10}$$x

$$\frac{1}{10}+\frac{3}{10} = \frac{4}{10}$$ i.e. $$\frac{2}{5}$$

how many employees in attendance are neither vice-presidents nor assistant vice-presidents = $$\frac{3}{5}$$

pushpitkc is my solution correct ?
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One-tenth of the employees at a company dinner are vice-presidents  [#permalink]

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22 Oct 2018, 20:20
1
Yeah, dave13

Your solution is correct. However we are told that there are e employees in attendance, so it's better to have the number of employees as "e"
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One-tenth of the employees at a company dinner are vice-presidents   [#permalink] 22 Oct 2018, 20:20
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