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If 75 percent of the employees of a certain company take a winter

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If 75 percent of the employees of a certain company take a winter [#permalink]

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New post 25 Jul 2016, 18:31
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If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer vacation, and 20 percent take neither a winter nor a summer vacation, what percent of the employees take a summer vacation but not a winter vacation?

A) 5%
B) 15%
C) 25%
D) 35%
E) 45%
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If 75 percent of the employees of a certain company take a winter [#permalink]

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New post 25 Jul 2016, 19:04
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Winter = 75
Both = 40
Neither = 20

Winter + Summer - Both + Neither = 100
75 + Summer - 40 + 20 = 100
Summer = 45

Summer but not winter = Summer only = Summer - Both(i.e. summer overlap with winter) = 45 - 40 = 5

Answer: A

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Re: If 75 percent of the employees of a certain company take a winter [#permalink]

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New post 27 Jul 2016, 19:30
Vyshak wrote:
Winter = 75
Both = 40
Neither = 20

Winter + Summer - Both + Neither = 100
75 + Summer - 40 + 20 = 100
Summer = 45

Summer but not winter = Summer only = Summer - Both(i.e. summer overlap with winter) = 45 - 40 = 5

Answer: A

Why cant we just stop at 45? X=45
Why this question is different from other overlapping question where we just stop at finding the X (X could be a or b or both or neither)
We subtract "both" only once
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Re: If 75 percent of the employees of a certain company take a winter [#permalink]

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New post 27 Jul 2016, 20:18
Answer should be 5% ie A

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Re: If 75 percent of the employees of a certain company take a winter [#permalink]

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New post 27 Jul 2016, 20:38
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zxcvbnmas wrote:
Vyshak wrote:
Winter = 75
Both = 40
Neither = 20

Winter + Summer - Both + Neither = 100
75 + Summer - 40 + 20 = 100
Summer = 45

Summer but not winter = Summer only = Summer - Both(i.e. summer overlap with winter) = 45 - 40 = 5

Answer: A

Why cant we just stop at 45? X=45
Why this question is different from other overlapping question where we just stop at finding the X (X could be a or b or both or neither)
We subtract "both" only once

Refer the venn diagram. You will be able to understand it clearly.

Image

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Re: If 75 percent of the employees of a certain company take a winter [#permalink]

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New post 27 Jul 2016, 21:25
zxcvbnmas wrote:
Vyshak wrote:
Winter = 75
Both = 40
Neither = 20

Winter + Summer - Both + Neither = 100
75 + Summer - 40 + 20 = 100
Summer = 45

Summer but not winter = Summer only = Summer - Both(i.e. summer overlap with winter) = 45 - 40 = 5

Answer: A

Why cant we just stop at 45? X=45
Why this question is different from other overlapping question where we just stop at finding the X (X could be a or b or both or neither)
We subtract "both" only once


It is the difference between summer vacations (including winter) and only summer vacations (not in winters).

45 people take vacations in summer. 40 of them take vacation in winters too. Since we are looking for the number that take vacations in summer BUT NOT in winter, we get 45 - 40 = 5.
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Re: If 75 percent of the employees of a certain company take a winter [#permalink]

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New post 29 Jul 2016, 10:13
Using some of the high school set theory
n(a)=75
n(b)=40
n(aUb)=80
n(intersection)=75+40-80=35
n(onlyb)=40-35=5
Smash A
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If 75 percent of the employees of a certain company take a winter [#permalink]

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zxcvbnmas wrote:
If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer vacation, and 20 percent take neither a winter nor a summer vacation, what percent of the employees take a summer vacation but not a winter vacation?

A) 5%
B) 15%
C) 25%
D) 35%
E) 45%


Here's a step-by-step approach using the Double Matrix method.

We have a population of employees, and the two characteristics are:
- take a winter vacation or don't take a winter vacation
- take a summer vacation or don't take a summer vacation

So, we'll set up our matrix as follows:
Image
NOTE: Since we're need to find a PERCENT (rather than the actual number of people), we'll say that there are 100 employees altogether. This will make our calculations easier.

75 percent of the employees of a certain company take a winter vacation
If 75% TAKE a winter vacation, the remaining 25% DON'T take a winter vacation.
Since we've let 100 = the total number of employees, we can see that 75 take a winter vacation and 25 don't. We'll add this to our diagram:
Image

40 percent take a winter and a summer vacation
So, 40 employees take a winter AND a summer vacation, which we can add to our diagram.
Image


20 percent take neither a winter nor a summer vacation
Add that here:
Image

what percent of the employees take a summer vacation but not a winter vacation
We'll place a heart in the box that represents the value we're trying to solve for.
Image

IMPORTANT: Since the bottom 2 boxes must add to 25, we can see that the bottom left box must equal 5.
Image

Answer:
[Reveal] Spoiler:
A


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Re: If 75 percent of the employees of a certain company take a winter [#permalink]

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New post 11 Dec 2017, 16:02
zxcvbnmas wrote:
If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer vacation, and 20 percent take neither a winter nor a summer vacation, what percent of the employees take a summer vacation but not a winter vacation?

A) 5%
B) 15%
C) 25%
D) 35%
E) 45%


Winter Vacation: 75%
Winter + Summer= 40%
Neither= 20%
Summer=?

S+W-(W-S)+N=100
S+75-(40)+20=100
S+55=100
S=45

Summer -Winter +Summer=only summer
45-40=5

Answer A

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Re: If 75 percent of the employees of a certain company take a winter   [#permalink] 11 Dec 2017, 16:02
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