CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from the topic quadrilaterals. There are some set of parallel lines and we need to find out the maximum number of parallelograms that can be formed. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 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

Explanatory Answer

Method of solving this CAT Question from Quadrilaterals: To get 12 points, either 6 and 2 lines can intersect or 4 and 3 lines can intersect!

Given: 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 * 1 = 15
When x = 4 and y = 3, the number of parallelograms formed = ⁴C₂ * ³C₂ = 6 x 3 = 18
Maximum = 18

The question is "find the maximum number of parallelograms that can be formed."

Hence, the answer is 18.

Choice C is the correct answer.