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In a certain class consisting of 36 students some boys and

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In a certain class consisting of 36 students some boys and [#permalink] New post 23 Nov 2005, 15:40
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A
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C
D
E

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In a certain class consisting of 36 students some boys and some girls exactly 1/3 OF THE BOY AND 1/4 OF THE GIRLS walk to the school
what is the greatest possible number of students in this class who walk to school ?

9
10
11
12
13

PLZ explain your work

i actually found that the number of boy will be 12 and the girl student be 24 and the ones that walk be 10
Why is that wrong ?
thanks

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 [#permalink] New post 23 Nov 2005, 15:47
24 boys and 12 girls would result in 8+3=11 walking children
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 [#permalink] New post 23 Nov 2005, 16:42
X = Number of boys
Y = Number of girls
36 = X + Y

What is the greatest possible value of (1/3)X + (1/4)Y ?

====================================

Z =(1/3)X + (1/4)Y
12Z = 4X+3Y
108 = 3X + 3Y
12Z - 108 = X
12(Z - 9) = X

If Z = 9, X = 0 & Y = 36
If Z = 10, X = 12 & Y = 24
If Z = 11, X = 24 & Y = 12
If Z = 12, X = 36 & Y = 0

If Z = 9, (1/3)X = 0 & (1/4)Y = 9
If Z = 10, (1/3)X = 4 & (1/4)Y = 6
If Z = 11, (1/3)X = 8 & (1/4)Y = 3
If Z = 12, (1/3)X = 9 & (1/4)Y = 0

Thus, 8 + 3 = 11

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 [#permalink] New post 23 Nov 2005, 21:37
Good way to practice your plug-ins

look for way to split 36 between 1/3 and 1/4.
As noted above, you get 24 +12 = 36

ie.11
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 [#permalink] New post 23 Nov 2005, 22:41
the maximum possibility will be 36/3 = 12 girls. but in this case we have to assume that there are boys, which is invalid.

the second highest possibility is 24/3= 8 girls and 12/4 =3 boys

so 8+3 =11 students walks home.

so C is the answer.

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 [#permalink] New post 04 Apr 2007, 03:35
Hi guys!

Smth's wrong with those explanations above. Let's revise this hard PS :P
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 [#permalink] New post 04 Apr 2007, 14:34
boys+girls = 36

no of boys should be divided by 4 and no of girls should be divided by 3.

Now start plugging no..i.e 4+32(no), 8+28(no), 12+24(yes) => 3 boys + 8 girls => 11
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 [#permalink] New post 04 Apr 2007, 14:56
Juaz wrote:
boys+girls = 36

no of boys should be divided by 4 and no of girls should be divided by 3.

Now start plugging no..i.e 4+32(no), 8+28(no), 12+24(yes) => 3 boys + 8 girls => 11


Sorry, don't understand the logic. The stem gives us 1/3 (not 1/4) OF THE BOY. Why should we divide boys by 4? :?:
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 [#permalink] New post 04 Apr 2007, 15:50
Answer is 11.
Total students = 36
To maximise the number of students who walk, boys should be greater than the girls. Maximum number of boys can be 24. Number of girls will be 12.
Hence students who walk = 8 + 3 = 11
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 [#permalink] New post 05 Apr 2007, 01:53
vshaunak@gmail.com wrote:
Answer is 11.
Total students = 36
To maximise the number of students who walk, boys should be greater than the girls. Maximum number of boys can be 24. Number of girls will be 12.
Hence students who walk = 8 + 3 = 11


But why should the boys be greater than the girls? Why 24? Because it is divided by 3? But 12 is also divided by 3. What's the logic? I can't see it :roll:
  [#permalink] 05 Apr 2007, 01:53
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