CAT Practice : Coordinate Geometry

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To get 12 points, either 6 and 2 lines can intersect or 4 and 3 lines can intersect!

Number of parallelograms

    Q.34: There is a set of parallel lines with x lines in it and another set of parallel lines with y lines in it. The lines intersect at 12 points. If x > y, find the maximum number of parallelograms that can be formed.
    1. 16
    2. 15
    3. 18
    4. 33

 

  • Correct Answer
    Choice (C). 18

Detailed Solution

The lines intersect at 12 points
Therefore x * y = 12
Since x > y possibilities are x = 6 and y = 2 or x = 4 and y = 3

We need 4 points to form a paralleogram, 2 points forming 1 line and the other 2 points forming the other line.
When x = 6 and y = 2, the number of parallelograms formed = 6C2 × 2C2
= 15 x 1 = 15

When x = 4 and y = 3, the number of parallelograms formed = 4C2 × 3C2
= 6 x 3 = 18

Maximum = 18



Correct Answer: (C). 18 paralleograms



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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.