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Equation - need expert help

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by voodoo_child » Sun Sep 02, 2012 10:22 am
Why does this equation have infinite solutions ? I am not able to figure out why. Thoughts?

nc = (n+10) (c-15).... (i)
nc = (n-10)(c+15) ..... (ii)

The solution is 3n = 2c. However, when you substitute the values, you get weird ...-150 = 0!

Source - GMATClub

Thoughts...I am too much engrossed the problem that I can't think of a reason. Another perspective will help. I think it's something related to circular properties we did in JEE ...can't think of it right now....


Thanks
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by rijul007 » Sun Sep 02, 2012 11:41 am
THe two equations are not the equations of a circle.

SImplify equation (i)
nc = (n+10)(c-15)
nc = nc +10c - 15n -150
10c -15n = 150 (which is a straight line)

similarly for equation (ii)
nc = (n-10)(c+15)
nc = nc -10c +15n -150
-10c + 15n = 150 (also a straight line)

Since the two lines have the same slope, the two lines are parellel to each other.
Hence, they have no solution.
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by voodoo_child » Sun Sep 02, 2012 1:17 pm
rijul007 wrote:THe two equations are not the equations of a circle.
Oh thanks .... You are correct the equations are parallel. When I said "circular properties", I didn't mean equation of circle.[:D] ....circular properties are when, as you said, the slope is same, OR for instance, if the unique solution to the equation is x= 3; y= 2 then multiplying the equations with an integer will result in the integral multiples, for instance 3x = 9 and 3y=6. There is an OG question on this concept.

I think that it was in Bernard and Child book...any way thanks....My mind was too much exhausted :(
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