There were n boys and m girls in a class.

Question

There were n boys and m girls in a class. They wanted to sit in a row for an activity. In how many ways can they sit on 30 chairs?

(1) n+3m = 20
(2) 2n + 2m = 22

EgmatQuantExpert · Accepted Answer

Solution

Given:  
 • There were n boys and m girls in a class – they wanted to sit in a row for an activity

To find:  
 • The number of ways n boys and m girls can sit on 30 chairs

Approach and Working:  
We have total 30 chairs available, and there is (n + m) number of people to sit in those 30 chairs

Assuming that (n + m) is less than or equal to 30,
 • The number of ways they can sit in 30 chairs =  ^{30}P_{n+m}

Hence, if we know the value of (n + m), we can answer the question

Analysing Statement 1  
 • As per the information given in statement 1, n + 3m = 20
 o From this equation, we can’t find the value of n + m

Hence, statement 1 is not sufficient to answer

Analysing Statement 2  
 • As per the information given in statement 2, 2n + 2m = 22
 o Or, we can write, n + m = 11

• Replacing the value of (n + m), we can find out the value of  ^{30}P_{n+m}

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option B.

Answer: B

GMATBusters · Answer

There were n boys and m girls in a class. They wanted to sit in a row for an activity. In how many ways can they sit on 30 chairs?
To find the number of ways , we need the total number of students. 
 If N is total number of students, Number of ways will be  30CN *N!

I. n+3m = 20
Value of (n, m) can be (2,6) or (5,5) or (8,4)
So N = n+m= 8 or 10 or 12.
 NOT SUFFICIENT.

II. 2n + 2m = 22
N= n+m = 11
 SUFFICIENT.

Answer B

durgamadhab · Answer

SInce Obviously boys and girls are different....final result is 30/((n+m)! (30-n-m)!) x 11!/(n! x m!).....since values of n and m are not known....(B) is also not sufficient.

(C) doesn't give values of n and m...so answer should be (E).

Had the question asked what the number of ways of selecting chairs for total students...n+m would have been sufficient to answer the question.

Ways of sitting ...it means no. of ways of selecting chairs x no of arrangements of boys and girls.

ANS (E)

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There were n boys and m girls in a class.

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