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Of the 180 students in a school, at least 45% attended the prom night

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Of the 180 students in a school, at least 45% attended the prom night [#permalink]

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New post 13 Mar 2016, 10:45
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Of the 180 students in a school, at least 45% attended the prom night and at least 40% took part in the debating session. What is the maximum number of students who would have neither attended the prom night nor the debating session?

A. 27
B. 81
C. 90
D. 99
E. 153
[Reveal] Spoiler: OA

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Of the 180 students in a school, at least 45% attended the prom night [#permalink]

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Bunuel wrote:
Of the 180 students in a school, at least 45% attended the prom night and at least 40% took part in the debating session. What is the maximum number of students who would have neither attended the prom night nor the debating session?

A. 27
B. 81
C. 90
D. 99
E. 153


I hope I'm not misreading anything, but if we are looking to maximize the number of folks that did not do any of the activities mentioned in the question, then all we have to do is minimize the number of people that did participate in any one of the activities.

In this case, let's make it so that ONLY 45% of students went to prom and ONLY 40% of students debated. Furthermore, let's create as much overlap between those two groups of students as possible, so that we can maximize the number of students that did not participate in either one of those activities. Let's say that all 40% of students that debated also engaged in prom shenanigans. What that essentially means is we played with the numbers in such a way so that only 45% of the school ended up engaging in at least one of those activities. Which means the other 55% didn't do either prom or the debate.

55% of 180 is 99 (D)

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Re: Of the 180 students in a school, at least 45% attended the prom night [#permalink]

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New post 29 Oct 2017, 08:01
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Re: Of the 180 students in a school, at least 45% attended the prom night [#permalink]

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New post 29 Oct 2017, 08:16
To maximize the persons who don't attend any of the sessions is to maximize the common members between the two sessions. Hence, when all debating session students attend the prom night. So total persons who attend the prom night and debate = 45%
Remaining persons who don't attend prom or debating session = 55% of 180 = 99

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Re: Of the 180 students in a school, at least 45% attended the prom night [#permalink]

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New post 19 Nov 2017, 10:04
To maximize one quantity we need to minimize the other quantity.
In this case we have minimized those who went to debating session but not the prom night.
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Re: Of the 180 students in a school, at least 45% attended the prom night [#permalink]

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New post 22 Nov 2017, 12:27
Bunuel wrote:
Of the 180 students in a school, at least 45% attended the prom night and at least 40% took part in the debating session. What is the maximum number of students who would have neither attended the prom night nor the debating session?

A. 27
B. 81
C. 90
D. 99
E. 153


To determine the maximum number of students who would have neither attended the prom night nor the debating session, we need the smallest possible number of students attending the prom night and the debating session. Thus, we can assume that exactly 45% of the students attended the prom night and exactly 40% took part in the debating session. Next we will assume that all students who took part in the debating session were also the students who attended the prom night. If that is the case, this will leave 55% of students who would have done neither, and 55% of 180 is 0.55 x 180 = 99. Thus, a maximum of 99 students would have done neither of the two activities.

Answer: D
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Re: Of the 180 students in a school, at least 45% attended the prom night   [#permalink] 22 Nov 2017, 12:27
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