Waltz

[N:Dure]

??

[anshumishra]

z = XC2 = X*(X-1)/2

Now only value which can satisfy this is 6, because
X*(X-1) = 12 = 4*3
X = 4

For all other given options you can't get an integral solution for X.

Thanks

[N:Dure]

Gotcha! So the other solutions will be like 4 which is 2x2 (doesn't fit), 18 which is 9x2 or 18x1 (doesn't fit)..etc

[anshumishra]

Gotcha! So the other solutions will be like 4 which is 2x2 (doesn't fit), 18 which is 9x2 or 18x1 (doesn't fit)..etc

You are right !

Probably I use some short cuts while posting the solution. Sorry if that make it ambiguous. Actually, I try to solve how I would do in real test.

So, the easiest way would be to solve the quadratic equations :

Equation 1: x*(x-1)/2 = 2 => x*(x-1) = 2 => x^2-x-2 = 0
Now, can when you solve for x, if you get the integral solution for x, then the answer would be right.

Equation 2: x*(x-1)/2 = 6 => x*(x-1) = 12 => x^2 -x -12 = 0

Similarly for the other 3 cases.

Now the short-cut part : when I see x*(x-1), as you might have realized, the trick I used saved me from solving the 5 quadratic equations.