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CAT 2005 | Question: 12

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Consider a triangle drawn on the $\text{X-Y}$ plane with its three vertices at $(41, 0), (0, 41),$ and $(0, 0)$ each vertex being represented by its $\text{(X, Y)}$ coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

  1. $780$
  2. $800$
  3. $820$
  4. $741$

1 Answer

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If we just see with vertices (0,8) , (8, 0) and (0, 0) then we can ans for any similer question.

Total no of points = 6 + 5 + 4 + ....... + 1.

Similarly, for general case, with vertices (0, n), (n, 0), and (0, 0 ).

Total no of points = (n-2) + (n-3) + (n-4) + .................. + 1.

                                 = $\frac{(n-1)(n-2)}$/2.

So ans for this question = $\frac{39*40}{2}$

                                            = 780.

Ans- A.

 

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