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# QOTD # 11 Of the students in a school, 20 percent are in the

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QOTD # 11 Of the students in a school, 20 percent are in the [#permalink]  13 Sep 2016, 06:11
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Question Stats:

57% (01:43) correct 42% (02:03) wrong based on 71 sessions
Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band?

A) 5%
B) 20%
C) 25%
D) 60%
E) 75%

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Question: 11
Page: 204
[Reveal] Spoiler: OA

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Re: QOTD # 11 Of the students in a school, 20 percent are in the [#permalink]  20 Sep 2016, 12:13
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Explanation

Use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- in the science club or not in the science club
- in the band or not in the band

So, we can set up our matrix as follows:

Since we aren't told the total population AND we're asked to find a percentage, let's say that the TOTAL population is 100 (an easy number to work with)

20 percent of the students are in the science club, and 30 percent of the students are in the band
Since the total population is 100, this means that there are 20 students in the science club. Also, since there are 100 students, we can conclude that 80 students are NOT in teh science club.
Likewise, if 30 students are in the band, then 70 students are NOT in the band.
So, let's add all of this to the diagram:

25 percent of the students in the school are in the band but are not in the science club
Great. We'll add this to our diagram:

Since the two boxes in the left-hand column must add to 30, we can see that the top box must hold 5 students

Since the two boxes in the top row must add to 20, we can see that the top right box must hold 15 students

Using similar logic, we can see that the last box holds 55 students

What percent of the students who are in the science club are not in the band?
Our diagram tells us that there are 20 students in the science club.
Of those 20 students, 15 are NOT in the band.
15/20 = 75%

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Re: QOTD # 11 Of the students in a school, 20 percent are in the [#permalink]  30 Dec 2019, 12:34
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Let there be 100 students in the school.

Number of Students in Science Club= 20.
Number of students in Band = 30.
Number of students in a band but not science club= 25.

Number of students in a band and science club= 5.

No of students that are in science club but not in a band= 20 -5 =15.

% of students that are in science club but not in a band = $$\frac{15}{20}*100$$ =75
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Re: QOTD # 11 Of the students in a school, 20 percent are in the [#permalink]  09 May 2020, 11:24
Hi Brent,

Would the answer have been 15% if the question asked "what percent of students are in the science club but are not in the band?" So in this case it would be students who are in science but not in band over the total number of students. I think the reason I got confused with the original question was because I was finding the percentage of students who were in science and not in band from the overall total number of students instead of calculating the percent as a total of students who took Science.

[quote="GreenlightTestPrep"]Explanation
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Re: QOTD # 11 Of the students in a school, 20 percent are in the [#permalink]  09 May 2020, 13:20
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GREStudent2020 wrote:
Hi Brent,

Would the answer have been 15% if the question asked "what percent of students are in the science club but are not in the band?" So in this case it would be students who are in science but not in band over the total number of students. I think the reason I got confused with the original question was because I was finding the percentage of students who were in science and not in band from the overall total number of students instead of calculating the percent as a total of students who took Science.

That's correct.
15 percent of all students are in the science club but not in the band.

Cheers,
Brent
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Re: QOTD # 11 Of the students in a school, 20 percent are in the [#permalink]  29 Jun 2020, 04:58
15%
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Re: QOTD # 11 Of the students in a school, 20 percent are in the [#permalink]  29 Jun 2020, 04:59
But I could be wrong
Re: QOTD # 11 Of the students in a school, 20 percent are in the   [#permalink] 29 Jun 2020, 04:59
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