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In a certain class consisting of 36 students, some boys and [#permalink]

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08 Feb 2011, 04:33

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In a certain class consisting of 36 students, some boys and some girls, exactly 1/3 of the boys and exactly 1/4 of the girls walk to school. What is the greatest possible number of students in this class who walk to school?

In a certain class consisting of 36 students, some boys and some girls, exactly 1/3 of the boys and exactly 1/4 of the girls walk to school. what is the greatest possible number of students in this class who walk to school? a)9 b)10 c)11 d)12 e)13

Let # of boys be \(b\), then # of girls will be \(36-b\). We want to maximize \(\frac{b}{3}+\frac{36-b}{4}\) --> \(\frac{b}{3}+\frac{36-b}{4}=\frac{b+3*36}{12}=\frac{b}{12}+9\), so we should maximize \(b\), but also we should make sure that \(\frac{b}{12}+9\) remains an integer (as it represent # of people). Max value of \(b\) for which b/12 is an integer is for \(b=24\) (b can not be 36 as we are told that there are some # of girls among 36) --> \(\frac{b}{12}+9=2+9=11\).

Answer: C.

Or: as there are bigger percentage of boys who walk then we should maximize # of boys, but we should ensure that \(\frac{b}{3}\) and \(\frac{36-b}{4}\) are integers. So \(b\) should be max multiple of 3 for which \(36-b\) is a multiple of 4, which turns out to be for \(b=24\) --> \(\frac{b}{3}+\frac{36-b}{4}=11\).

Re: In a certain class consisting of 36 students, some boys and [#permalink]

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14 Oct 2013, 23:07

GMATD11 wrote:

In a certain class consisting of 36 students, some boys and some girls, exactly 1/3 of the boys and exactly 1/4 of the girls walk to school. What is the greatest possible number of students in this class who walk to school?

A. 9 B. 10 C. 11 D. 12 E. 13

let number of boys in a class are x then number of gals become 36-x

1/3x+1/4(36-x)=9+x/12

x cannot be 36 as there are some gals in class so maximum value of x/12 can be 2

Answer C

any other method to solve this question.

Lets apply process of elimination

option A: See, 9 cannot be expressed as sum of multiple of 3 and 4. neither can 10, 12 or 13. only 11 can be expressed a sum of multiples of 3 and 4.

11= 3+ 2(4)

since we need 1/3 of boys, 1/4th of girls. and number of boys and girls have to be integers.

11 is the only option that satisfies the situation.

Re: In a certain class consisting of 36 students, some boys and [#permalink]

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13 Dec 2013, 11:27

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Answer is C.

It can be easily solve by using a number which is multiple of 3 & 4 together and less than 36. So the number would be 12 & 24 only. Consider one of the number as count of boys or girls.

Say B=12 then G=24 which means 1/3 of 12 + 1/4 of 24=10 Now try for 24. Say B=24 then G=12 which means 1/3 of 24 + 1/4 of 12=11

So answer is C in less than a minute. +1 for me. cheers.

Re: In a certain class consisting of 36 students, some boys and [#permalink]

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28 Jan 2015, 06:18

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Re: In a certain class consisting of 36 students, some boys and [#permalink]

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02 Feb 2016, 00:37

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