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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
All the students of a class are to be divided into 20 individual study  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 59% (01:33) correct 41% (02:05) wrong based on 81 sessions

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All the students of a class are to be divided into 20 individual study groups. What should be the minimum number of candidates present in the least populated group?

I. The total number of students in the class is 238.
II. Any group cannot have more than 20% of the number of students of any other group.

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Originally posted by EgmatQuantExpert on 13 Mar 2019, 01:43.
Last edited by EgmatQuantExpert on 28 Mar 2019, 01:20, edited 3 times in total.
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: All the students of a class are to be divided into 20 individual study  [#permalink]

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Solution

Given:
• All the students of a class are to be divided into 20 individual study groups.

To find:
• The minimum number of candidates present in the least populated group.

Analysing Statement 1
As per the information given in statement 1, the total number of students in the class in 238.
• From this statement, we do not have any information about the number of students in the least populated of the 20 groups.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, any group cannot have more than 20% if the number of students of any other group.
• Let us assume the minimum number of students present in the least populated group is n
• Therefore, the maximum number of students present in any of the groups will be 1.2n

Now to minimize n, we should have only one group with n students, and all other groups should have maximum possible number of students (which is 1.2n).
Therefore, we can say
• Total number of students = n + 19 x 1.2n = n + 22.8n = 23.8n

But from this statement, we cannot determine the value of n, as we don’t know the total number of students.
Hence, statement 2 is not sufficient to answer the question.

Combining Both Statements
Combining both statements, we can say
• 23.8n = 238
Or, $$n = \frac{238}{23.8} = 10$$

Therefore, the minimum number of students present in the least populated group is 10.

Hence, the correct answer is option C.

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Intern  Joined: 21 May 2016
Posts: 5
Re: All the students of a class are to be divided into 20 individual study  [#permalink]

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EgmatQuantExpert wrote:

Solution

Given:
• All the students of a class are to be divided into 20 individual study groups.

To find:
• The minimum number of candidates present in the least populated group.

Analysing Statement 1
As per the information given in statement 1, the total number of students in the class in 238.
• From this statement, we do not have any information about the number of students in the least populated of the 20 groups.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, any group cannot have more than 20% if the number of students of any other group.
• Let us assume the minimum number of students present in the least populated group is n
• Therefore, the maximum number of students present in any of the groups will be 1.2n

Now to minimize n, we should have only one group with n students, and all other groups should have maximum possible number of students (which is 1.2n).
Therefore, we can say
• Total number of students = n + 19 x 1.2n = n + 22.8n = 23.8n

But from this statement, we cannot determine the value of n, as we don’t know the total number of students.
Hence, statement 2 is not sufficient to answer the question.

Combining Both Statements
Combining both statements, we can say
• 23.8n = 238
Or, $$n = \frac{238}{23.8} = 10$$

Therefore, the minimum number of students present in the least populated group is 10.

Hence, the correct answer is option C.

But the same can be found by the 1st statement itself - 238 students and 20 groups - if 1 group is of 10 , rest 228 can be evenly divided in 19 groups , 12 per group, so the least populated group is 10. So in that case answer would be A.Let me know if this is not correct.
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: All the students of a class are to be divided into 20 individual study  [#permalink]

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But the same can be found by the 1st statement itself - 238 students and 20 groups - if 1 group is of 10 , rest 228 can be evenly divided in 19 groups , 12 per group, so the least populated group is 10. So in that case answer would be A.Let me know if this is not correct.

As per statement 1, we know that the total number of students in the class in 238. From the question statement, we also know that we need to form 20 groups.

Now, from this available information, can you tell me:
1. Why you have assumed the 1 group as 10? Can't we take the strength of the first group as 9 or 8 or 11?

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Director  P
Joined: 18 Dec 2017
Posts: 819
Location: United States (KS)
All the students of a class are to be divided into 20 individual study  [#permalink]

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EgmatQuantExpert wrote:
But the same can be found by the 1st statement itself - 238 students and 20 groups - if 1 group is of 10 , rest 228 can be evenly divided in 19 groups , 12 per group, so the least populated group is 10. So in that case answer would be A.Let me know if this is not correct.

As per statement 1, we know that the total number of students in the class in 238. From the question statement, we also know that we need to form 20 groups.

Now, from this available information, can you tell me:
1. Why you have assumed the 1 group as 10? Can't we take the strength of the first group as 9 or 8 or 11?

EgmatQuantExpert

I see You have not got a reply on this one but I am thinking on the same lines so I will try to answer your question.

I am not assuming the 1 group to be of 10. If I need to have one group as minimum then I need to have maximum number of students in other 19 groups. Now the highest possible multiple of 19 which is less than 238 is 228. And hence 19 groups can be of size 12 and the last group can be of the size 10.

Bunuel Only if you want to provide your 2 cents.
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