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# The ratio of boys to girls in the junior class is 2 to 3

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VP
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The ratio of boys to girls in the junior class is 2 to 3 [#permalink]

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21 Feb 2005, 08:43
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The ratio of boys to girls in the junior class is 2 to 3 respectively and the ratio of girls to boys in the senior class is 7 to 3 respectively. If there are 300 more students in the senior class than in the junior class and the combined ratio of boys to girls in both classes is 8 to 17 respectively, how many students are in the senior class?

a) 100
b) 300
c) 375
d) 400
e) 500
VP
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21 Feb 2005, 09:16
"D"...400

If X is number in junior then X+300 in senior

Boys/Girls = 8/17

{2X/5 + 3(X+300)/10}/{3X/5 + 7(X+300)/10} = 8/17

instead of solving for X we can see that choice a,b,c are not possible as X > 0 and an integer.....try "D".....it works
VP
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22 Feb 2005, 05:25
Alternative Solution:

(2/5)x + 3/10(x+300) = 8/25 (2x+300) => solve for x
Senior Manager
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05 Mar 2005, 19:15
christoph wrote:
Alternative Solution:

(2/5)x + 3/10(x+300) = 8/25 (2x+300) => solve for x

brilliant!

I was wasting time on 3 equations with 3 variables...
Manager
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05 Mar 2005, 20:37
400

Same method as banerjee's but didn't think of the lil trick that banerjea gave us. Thanks banerjee
Manager
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08 Mar 2005, 13:18

I coudnt understand the problem until reading the answer, and then, it looked so simlpe....
I think I need to practice more.....

thank you for the post!
_________________

discipline is what I need.

Intern
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11 Mar 2005, 05:55
Junior Class:
Let Boys be X
Girls be 3 /2 X

Total Number = X + 3 /2 X = 5 / 2 X

Senior Class:
Lets Boys be Y
Girls by 7 / 3 Y
Total Number = Y + 7 / 3 Y = 10 / 3 Y

10 / 3 Y - 5 / 2 X = 300

or 20 Y - 15 X = 300 : eq 1
4 Y - 3 X = 60
X = (4 Y - 60 ) / 3

(X + Y ) / (3 / 2 X + 7 / 3 Y ) = 8 / 17

(4 Y - 60 + 3 Y ) * 17 * 6 = 8 * 3 * [3 ( 4 y - 60) + 14 Y]
(7 y - 60 ) * 17 = 4 [ 12 Y - 180 + 14 Y]

after
Director
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11 Mar 2005, 08:27
I did pretty much what baner did and i think his is a brilliant idea.. will save a lot of time !!!
Intern
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11 Mar 2005, 18:46
after performing long calculations i saw what bannerjee did and i feel it great inovative thinking. The kind GMAT expect from us. Thankx a ton guys for sharing a great tip.
regards,
hindsight   [#permalink] 11 Mar 2005, 18:46
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