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# There were n boys and m girls in a class.

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Intern
Joined: 12 Jun 2017
Posts: 6
GMAT 1: 710 Q49 V38
There were n boys and m girls in a class.  [#permalink]

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18 Jun 2018, 10:13
4
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:42) correct 46% (01:45) wrong based on 117 sessions

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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?
I. n+3m = 20
II. 2n + 2m = 22
Retired Moderator
Joined: 27 Oct 2017
Posts: 1233
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: There were n boys and m girls in a class.  [#permalink]

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18 Jun 2018, 10:29
1
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.

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Re: There were n boys and m girls in a class.  [#permalink]

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18 Jun 2018, 23:44
2

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.

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Concentration: General Management, Finance
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Re: There were n boys and m girls in a class.  [#permalink]

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16 Jul 2018, 06:44
DarshilPandya wrote:
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?
I. n+3m = 20
II. 2n + 2m = 22

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)
Re: There were n boys and m girls in a class.   [#permalink] 16 Jul 2018, 06:44
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