In a class, a certain number of students opted to participate in a

Question

In a class, a certain number of students opted to participate in a cultural competition comprising of 3 items music, recitation and drama.of these students 53% showed interest for music&35% showed interest for recitation. if 8% students of the whole class showed interest for drama, what percent of the students didn’t participate in the cultural program?
A)12
B)16.33
C)25
D)33.33
E)None of this

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Hello,experts.Please provide a detailed explanation. Thank you

TestPrepUnlimited · Accepted Answer

The question hid the keyword "Of these students  who participated ..." so among those who participated we can break it down to 53% music, 35% recitation, and 12% drama.

Since 12% of those who participated only represents 8% of the entire class, we can set up an equation  12\%*	ext{Participants} = 8\%*	ext{Whole Class} .

\frac{	ext{Participants}}{	ext{Whole Class}} = \frac{2}{3} = 66.67\% . Thus 33.33% did not participate.

Ans: D

Regor60 · Answer

The difference between the total number of students and those not participating has to be a multiple of 100 since that number multiplied by 53% has to equal a whole number.

The total number of students participating has to be a multiple of 25 since that number multiplied by 8% has to be a whole number.

So the total number has to be 125 or greater in multiples of 25 in order to subtract the non participants and leave a result that is a multiple of 100.

Possible combinations are:

125,25;150,50;175,75 and others that will be eliminated due to the following reasoning:

125,25. Gives a maximum number of participants of 88+10 = 98 assuming no overlaps, which suggests a minimum number of non participants of 27. Since the assumed number of non participants is 25, this option is out.

150,50. This gives a total of 88+12=100, leaving a minimum number of non participants of 50.

This works and suggests a nonparticipating percentage of 50/150 = 33%

175,75. This gives 102 as the number of participants maximum without overlap and a minimum of 73 nonparticipating, which works, but suggest a nonparticipating percentage of 75/175= >40% which isn't among the answer choices.

The remaining possibilities that work show increasing nonparticipating percentages which are also not among the answer choices, so the best answer is 33 1/3%

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Kinshook · Answer

Given: In a class, a certain number of students opted to participate in a cultural competition comprising of 3 items music, recitation and drama.of these students 53% showed interest for music&35% showed interest for recitation.

Asked: If 8% students of the whole class showed interest for drama, what percent of the students didn’t participate in the cultural program?​

Percentage of participants showing interest in drama = 100% - 53% - 35% = 12%
Percentage of whole class showing interest in drama = 8%

Since these are same,
Number of participants/ Whole class = 8/12 = 66.67%

The percent of the students didn’t participate in the cultural program = 100% - 66.67% = 33.33%

IMO D

KarishmaB · Answer

This is an overlapping sets problem assuming there is no overlap. That is not ok. Assume 200 students in the class. So 16 showed interest in drama. Say 100 participate (so 50% participate). 53 in music, 35 in recitation and 16 in drama (from above). This is certainly possible. We are not given that each participating student showed interest in exactly one activity. Similarly, the % of students who did not participate could take many other values. Check the overlapping sets concepts here: https://anaprep.com/sets-statistics-thr ... ping-sets/

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