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Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
Taking x – 5 = X and y – 5 = Y, we get |X|+|Y| ≤ 6
Here, if x and y are integers, then X and Y will also be integers.
Case I: X + Y ≤ 6
Case II: X – Y ≤ 6
Case III: – X + Y ≤ 6
Case IV: – X – Y ≤ 6
Plotting the graphs of above inequalities:
Counting the number of integral coordinates (X, Y) in the 1st quadrant, we get 5 + 4 + 3 + 2 + 1 = 15 points. (as shown in the diagram)
So, in all 4 quadrants, total number of points with integral coordinates will be 15 × 4 = 60 points.
Now, counting the number of points with integral coordinate (X, Y) on + x-axis, we get, 6 points.
So, total points on all 4-axes, 6 × 4 = 24 points. Also, the origin (0, 0).
Total number of points (X, Y) with integral coordinates satisfying all the 4 inequalities = 60 + 24 + 1 = 85
Thus, the corresponding pairs of (x, y) will also be 85