All the students of a class are to be divided into 20 individual study

Question

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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EgmatQuantExpert · Answer

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.

Answer: C

aditya47 · Answer

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.

EgmatQuantExpert · Answer

Hey  aditya47 ,

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?

TheNightKing · Answer

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.

RusskiyLev · Answer

Hi,  EgmatQuantExpert  ,

I was playing devil's advocate and want to understand, maybe I miss something. We can tell, obviously, that there are 10 students in the least populated group, and the other groups have 12 students each, but cannot we say that 9 groups have 13 students each, and in this case the rest of 11 groups will each have 11 students? 
 11 * 11 = 121  
 13 * 9 = 117 
 117 + 121 = 238 
In this case, 13 is still more than 11 by less than 20%. Would it mean that the correct answer to this question should be answer  E  or I am missing some important point in this task?

RusskiyLev · Answer

Minimum.

MBAB123 · Answer

Hey  EgmatQuantExpert ,  chetan2u  and other members,

I had a question on statement 2. I'm not sure I follow the wordings of the statement correct. It sounds like a group cannot have more than 20% of the number of students have any other group, i.e, A cannot be more than 20% of B. This sounds like A < 1/5B.

Of course, I realise how the answer is C with the intended interpretation.

chetan2u · Answer

Yes, you are correct. 
The question is poorly worded. It has tried to replicate a GMAT prep question wherein a certain population is divided amongst 11 cities, but has gone miserably wrong. 
Two mistakes. 
1) Any group cannot have.... does not make sense. It should be ‘No group can have....’
2) As you have correctly mentioned, it gives a different meaning. If it was to mean what it was intended to, then I would write it as: 
No group can have numbers more than 20% greater than the number of students of any other group.

All the students of a class are to be divided into 20 individual study

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