Expert: Steve Holleran - 4/2/2008

Question
Hi.Please help me with these 2 questions:

1.The number of ways of selecting  2 numbers from the set {1,2,3,......,18} whose sum is divisible by 3 is?

2.Through the point P(h,k)(where p lies in the first quadrant) the straight line bx+ay=ab is drawn to form a triangle of area S with the co-ordinate axes.If ab is positive the least value of S is?

Thanks..

Answer
Hi Apurvaa,

Okay, on the first question, I just made a list of each number, together with the ones which gave sums divisible by three, like this:

 1 +  (2,5,8,11,14,17)

 2 +  (4,7,10,13,16)
   

   etc , and I counted 27 total.  It gets easier as you go, because you rule out any pairs you already had (like in the list for 2, I didn't use 1, because it was in the first list).

2.  I have no solution for this one.  I really don't get what the (h,k) has to do with anything.  I can figure that the triangle has a y-int of b and an x -int of a, so its area is 1/2 * a * b, but that 's as far as I can get.  Sorry

Steve