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Math Expert V
Joined: 02 Sep 2009
Posts: 60561
A number of students have to be selected from a class of 25 students  [#permalink]

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9 00:00

Difficulty:   65% (hard)

Question Stats: 47% (01:25) correct 53% (01:24) wrong based on 226 sessions

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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.

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Senior Manager  G
Joined: 24 Apr 2016
Posts: 313
Re: A number of students have to be selected from a class of 25 students  [#permalink]

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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.

Intern  B
Joined: 18 Aug 2015
Posts: 17
Location: United States
GPA: 3.38
Re: A number of students have to be selected from a class of 25 students  [#permalink]

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

Thanks!
Senior Manager  G
Joined: 24 Apr 2016
Posts: 313
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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.
Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: A number of students have to be selected from a class of 25 students  [#permalink]

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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"..
Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: A number of students have to be selected from a class of 25 students  [#permalink]

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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.

Dear,

I don't understand the first statement.
How do you get 12 or 13?
Thank you so much
Manager  B
Joined: 23 Jul 2015
Posts: 79
Re: A number of students have to be selected from a class of 25 students  [#permalink]

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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.

How did you arrive at 12 or 13?
Intern  B
Joined: 21 Jun 2017
Posts: 4
Re: A number of students have to be selected from a class of 25 students  [#permalink]

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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.

Intern  B
Joined: 19 Jul 2018
Posts: 12
A number of students have to be selected from a class of 25 students  [#permalink]

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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.

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.
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(Always do your best. What you plant now, you will harvest later.) A number of students have to be selected from a class of 25 students   [#permalink] 20 Jul 2019, 14:48
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