CAT Exam

The local park at Raghu's house is in the shape of a triangle. There are 4 posts along the longest side of the park and 2 and 3 posts along the other two sides respectively. If none of these posts is at any of the corners of the park, find the number of triangles that are possible with vertices at these posts.

Option
(1) 84
(2) 79
(3) 72
(4) None of these

Read Solution (Total 1)

answer is option (2): 79

Given there are 4 posts on the longest side of the park and 2 and 3 posts on the other two sides.
So total number of posts are 4+3+2=9

To form a triangle we require 3 points,
so with 9 points we can form 9C3 triangles i.e. 84 triangles
but as we know one of the side has 3 points in same line and other side has 4 points on same line, which means they are collinear.
since collinear points do not form a triangle we need to eliminate those possibilities.

i.e. 9C3-(3C3+4C3)
=> 84-(1+4)
=>84-5
=>79

so answer is option (2): 79
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CAT Other Question

PQRS is a square, while diagonals PR and QS coincide with the x and y-axis respectively. Side PQ lies on the line x + y + 3 = 0.
Side RS lies on which of the following lines?
(1) x + y + 3 = 0 (2) x – y + 3 = 0 (3) x – y – 3 = 0 (4) None of these All Analysts are Engineers. One-third of all Engineers are Analysts. Half of all Technicians are Engineers. Only one Technician is an Analyst. Eight Technicians are Engineers. If the number of Engineers is 90, how many Engineers are neither Analysts nor Technicians?

Option
(1) 65
(2) 79
(3) 82
(4) 53