100 students were selected to participate in a survey by the school

Question

100 students were selected to participate in a survey by the school in May 2013. The next month, another 100 students were randomly selected to participate in the same survey, out of which 2 had already participate in the survey the previous month. If the number of students did not change from May to June then what is the approximate number of students in the school?

A) 3,600
B) 2,400
C) 2,000
D) 4,700
E) 5,000

A) 3,600
B) 2,400
C) 2,000
D) 4,700
E) 5,000

KarishmaB · Accepted Answer

The problem is based on the concept of sampling. 100 people who were surveyed first were say, marked with a stamp. Once the survey was over, they were mixed back into the school population. Next when another 100 were randomly selected, 2 of the marked students were selected. This means that we are likely to see 2% people marked in every random sample that we take (as long as it is large enough). So 2% of the students in the school are marked. Hence 100 = 2% of Total Students Total Students = 5000 Answer (E) To understand sampling, check the topic of Statistics from a test prep curriculum. Also check this official question: https://gmatclub.com/forum/in-a-certain ... l#p1580642

AGN21164 · Answer

Total population = (first capture * second capture)/ no of students captured in the first capture and second capture
 = (100*100)/2
 = 5000

sherlocked221B · Answer

KarishmaB   Bunuel   GMATNinja   gmatophobia   MartyMurray   @ b_sudharsan  GMATinsight

Could you please help with the approach and solution here?/

Thank you!

princevora · Answer

please explain the logic of doing this.

twobagels · Answer

I accept the answer. Can you help me understand a bit better how or why it works? Thank you! Excellent question.

Hoehenheim · Answer

twobagels  Here is how I look at it. We are presented with a class of x number of students out of which 100 are randomly selected. A month later, another random selection is carried out and we find out of 100 from selection set #2, there are two students who overlap. Which means, there is a 2% or 0.02 chance of finding a student from set 1 in set 2.

Thus, 100/0.02 shall give 5000 students in the cohort.

I guess the friction in understanding the question and arriving at the answer is because of the subjective nature of probability. Since 5000 is just an approximate, the real size of the class could be anything from 198 and upwards.

twobagels · Answer

That's a very good problem. ChatGPT with Mathematica plug-in came up with the same answer or approximation.

Thank you for helping and the reply!

Umber · Answer

But every logic fails if we have total 198 students, as in second sections we will always find two different people repeating. I think the answer to this problem is not concrete, please help me understand if I am wrong.

UdhavK · Answer

I applied the below logic:

Since in June the number of students out of the 100 selected, students who were also selected in May is 2, this implies that the probability of selecting a student who has already been selected is - P(selecting a student who has been selected previously) = 2/100 = 1/50.

Now, Probability of an event = Favourable Outcomes/Total No. of Outcomes = 100/Total No. of Outcomes = 1/50

=> Total No. of Outcomes = 50*100 = 5000.

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100 students were selected to participate in a survey by the school

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100 students were selected to participate in a survey by the school