Latest CAT Aptitude Question SOLUTION: Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points wit

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(#M40029269) CAT Logical Reasoning question CAT quant Keep an EYE

Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (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

Asked In CAT (10 years ago)

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RAKESH  (10 years ago)

draw the triangle and view it carefully
The number of points with integer coordinates inside the triangle are
(1,39)
(1,38),(2,38)
(1,37),(2,37),(3,37)
.......................
...........................
(1,2),(2,2),(3,2),........(38,2)
(1,1),(2,1),(3,1),(4,1)...(38,1),(39,1)
so total no of points are=1+2+3+...+38+39
=39*(39+1)/2=39*20=780
ANS(1)

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shanmugapriya  (7 years ago)

he equation of the line will be x + y = 41. So, we need to find out all the possible integer combinations in such a way that x > 0, y > 0 and x + y < 41.

Let x + y = 40. Then x = 1,2…..39 and y = 39,38…1. So, there are 39 combinations.

Let x + y = 39. Then x = 1,2…..38and y =38, 37.…1. So, there are 38 combinations.

Let x + y = 2. Then x = 1 and y = 1. So, there is 1 combination.

Totally, there are 1+2+…38+39 combinations.

It’s an AP with a =1, d =1.

Hence sum is 39*40/2 = 780

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