boys' average marks and the girls' average marks

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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

The mind is everything. What you think you become. –Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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Source: Beat The GMAT — Problem Solving | Sat Jan 09, 2010 2:35 am

rohan_vus: Master | Next Rank: 500 Posts; Posts: 189; Joined: Thu Apr 03, 2008 2:03 pm; Location: USA; Thanked: 21 times

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

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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