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boys' average marks and the girls' average marks

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by sanju09 » Sat Jan 09, 2010 2:35 am
The average marks of the girls in a class is equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class?
(A) 24
(B) 35
(C) 48
(D) 50
(E) 64
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by rohan_vus » Sat Jan 09, 2010 5:45 am
Should be D..

Let avg marks of boys = X --then numberr of girls = x
Let avg marks of girls = y.. then avg number of boys = y

Based on the condition we get
Class avg = (X*y + x*y) / ( x + y) = 2xy/(x + y)

==>2xy/(x+y) = ( x+y)/2 - 4
==>(x-y)^2 = 8(x+y)
Now x-y is an integer ---so (x-y)^2 got be a perfect square , so 8*(x+y) must be a perfect square..Only 50 in the choices given gives this
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by sanju09 » Sat Jan 09, 2010 6:20 am
rohan_vus wrote:Should be D..

Let avg marks of boys = X --then numberr of girls = x
Let avg marks of girls = y.. then avg number of boys = y

Based on the condition we get
Class avg = (X*y + x*y) / ( x + y) = 2xy/(x + y)

==>2xy/(x+y) = ( x+y)/2 - 4
==>(x-y)^2 = 8(x+y)
Now x-y is an integer ---so (x-y)^2 got be a perfect square , so 8*(x+y) must be a perfect square..Only 50 in the choices given gives this
excellent rohan, simply excellent
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
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The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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