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A number of students have to be selected from a class of 25 students
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Author:  Bunuel [ 16 Jul 2017, 22:34 ]
Post subject:  A number of students have to be selected from a class of 25 students

A number of students have to be selected from a class of 25 students to form a group. What is the number of students in the group?

(1) The number of possible selections of the students to form the group is the largest possible value.

(2) The number of students selected is less than 50 percent of the strength of the class.

Author:  quantumliner [ 17 Jul 2017, 07:48 ]
Post subject:  Re: A number of students have to be selected from a class of 25 students

Statement (1) The number of possible selections of the students to form the group is the largest possible value.

The largest possible value will come when the number of students is either 12 or 13. In either case the number of possible selections will be same. But since we have two possible answers, this statement is insufficient.

Statement (2) The number of students selected is less than 50 percent of the strength of the class.

As per this statement the number of students can be anything less than 13. This statement is not sufficient.

Combining both statements we know the number of students is 12.

Answer is C

Author:  mcm2112 [ 17 Jul 2017, 10:59 ]
Post subject:  Re: A number of students have to be selected from a class of 25 students

I am confused by Statement 1 - Am I not reading enough into that statement properly.

Thanks!

Author:  quantumliner [ 17 Jul 2017, 11:52 ]
Post subject:  A number of students have to be selected from a class of 25 students

mcm2112 wrote:
I am confused by Statement 1 - Am I not reading enough into that statement properly.

Thanks!


mcm2112 What are you confused about?

Question says there are total of 25 students. A Group has to be made of 'n' from these 25 students.

Now before we go to first statement. If 'n' students have to be selected from 25 students, how many different combinations of 'n' students can be made? The answer is \(25C_n\)

Now coming back to statement 1. Statement 1 says that the value of n is such that the value of\(25C_n\) is the maximum.

So lets says if we says n=1,then \(25C_1\) = 25; If n=2, then \(25C_2\) = 25*12. Likewise this will continue till n=25.

So what u need to find out is for which value of n is \(25C_n\) is the maximum.

Hope this helps.

Author:  pclawong [ 03 Aug 2017, 08:51 ]
Post subject:  Re: A number of students have to be selected from a class of 25 students

quantumliner wrote:
mcm2112 wrote:
I am confused by Statement 1 - Am I not reading enough into that statement properly.

Thanks!


mcm2112 What are you confused about?

Question says there are total of 25 students. A Group has to be made of 'n' from these 25 students.

Now before we go to first statement. If 'n' students have to be selected from 25 students, how many different combinations of 'n' students can be made? The answer is \(25C_n\)

Now coming back to statement 1. Statement 1 says that the value of n is such that the value of\(25C_n\) is the maximum.

So lets says if we says n=1,then \(25C_1\) = 25; If n=2, then \(25C_2\) = 25*12. Likewise this will continue till n=25.

So what u need to find out is for which value of n is \(25C_n\) is the maximum.

Hope this helps.


It actually helps me too.
It just the english confused me.
I thought statement 1 kind of saying "the maximun of the group = 25 students"..

Author:  pclawong [ 04 Aug 2017, 23:25 ]
Post subject:  Re: A number of students have to be selected from a class of 25 students

quantumliner wrote:
Statement (1) The number of possible selections of the students to form the group is the largest possible value.

The largest possible value will come when the number of students is either 12 or 13. In either case the number of possible selections will be same. But since we have two possible answers, this statement is insufficient.

Statement (2) The number of students selected is less than 50 percent of the strength of the class.

As per this statement the number of students can be anything less than 13. This statement is not sufficient.

Combining both statements we know the number of students is 12.

Answer is C


Dear,

I don't understand the first statement.
How do you get 12 or 13?
Thank you so much

Author:  SPatel1992 [ 30 Jun 2019, 15:45 ]
Post subject:  Re: A number of students have to be selected from a class of 25 students

quantumliner wrote:
Statement (1) The number of possible selections of the students to form the group is the largest possible value.

The largest possible value will come when the number of students is either 12 or 13. In either case the number of possible selections will be same. But since we have two possible answers, this statement is insufficient.

Statement (2) The number of students selected is less than 50 percent of the strength of the class.

As per this statement the number of students can be anything less than 13. This statement is not sufficient.

Combining both statements we know the number of students is 12.

Answer is C


How did you arrive at 12 or 13?

Author:  srini2117 [ 01 Jul 2019, 06:31 ]
Post subject:  Re: A number of students have to be selected from a class of 25 students

quantumliner wrote:
Statement (1) The number of possible selections of the students to form the group is the largest possible value.

The largest possible value will come when the number of students is either 12 or 13. In either case the number of possible selections will be same. But since we have two possible answers, this statement is insufficient.

Statement (2) The number of students selected is less than 50 percent of the strength of the class.

As per this statement the number of students can be anything less than 13. This statement is not sufficient.

Combining both statements we know the number of students is 12.

Answer is C



Hi .. isnt 25C12 same as 25C13 ??? why is A incorrect . please help

Author:  wizardofoddz [ 20 Jul 2019, 13:48 ]
Post subject:  A number of students have to be selected from a class of 25 students

srini2117 wrote:
quantumliner wrote:
Statement (1) The number of possible selections of the students to form the group is the largest possible value.

The largest possible value will come when the number of students is either 12 or 13. In either case the number of possible selections will be same. But since we have two possible answers, this statement is insufficient.

Statement (2) The number of students selected is less than 50 percent of the strength of the class.

As per this statement the number of students can be anything less than 13. This statement is not sufficient.

Combining both statements we know the number of students is 12.

Answer is C



Hi .. isnt 25C12 same as 25C13 ??? why is A incorrect . please help



Yes, 25C12 is the same as 25C13. You can think of this as some kind of a bell curve symmetrical about the n/2 mark - if n/2 is an integer it tips the curve. So here 12 and 13 are equidistant from n/2 (12.5) and hence 25C12 and 25C13 are equal. However, we cannot conclude whether the group contains 12 or 13 students from Statement 1 alone. Possible values are 12 and 13. Hence, NOT SUFFICIENT!

Statement 2 states the number of people in the group is less than half of 25. NOT SUFFICIENT.

But when you combine both, you have the answer: 12. Therefore, the answer is C.

Author:  BALAGURU [ 10 Jun 2020, 09:12 ]
Post subject:  A number of students have to be selected from a class of 25 students

\(25C_n\) = \(25C_{25-n}\)

there are two values possible ( 12 and 13)

from statement 2, only 12 is acceptable

Author:  Crytiocanalyst [ 03 Aug 2021, 09:30 ]
Post subject:  Re: A number of students have to be selected from a class of 25 students

Let the group be selected with n people

chosing of n students from 25 is given by 25Cn

(1) The number of possible selections of the students to form the group is the largest possible value

both at 25C12 and 25C13 the function of chosing the group peaks so we cannot determine at which group it will peak

Clealry insufficient

(2) The number of students selected is less than 50 percent of the strength of the class.
Individually it can form group of 1 to 12

However when 1 and 2 is combined we get
12 as the requisite answer therefore sufficient

Hence IMO C

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