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Geometry Questions For CAT

This document contains 5 geometry questions that appeared on past CAT exams. 1) The maximum number of coins that can be placed around a central coin is 6. 2) There are 10 possible obtuse-angled triangles with sides of lengths 8 cm, 15 cm, and an integer value of x cm. 3) If a polygon has 25 convex corners, it must have 21 concave corners. 4) A farmer needed to space fence posts 6 meters apart but bought 5 fewer posts than needed. With 8 meter spacing the posts he bought would be sufficient. The length of the property is 120 meters and he bought 16 posts. 5) For a triangle with sides of lengths 17.

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712 views6 pages

Geometry Questions For CAT

This document contains 5 geometry questions that appeared on past CAT exams. 1) The maximum number of coins that can be placed around a central coin is 6. 2) There are 10 possible obtuse-angled triangles with sides of lengths 8 cm, 15 cm, and an integer value of x cm. 3) If a polygon has 25 convex corners, it must have 21 concave corners. 4) A farmer needed to space fence posts 6 meters apart but bought 5 fewer posts than needed. With 8 meter spacing the posts he bought would be sufficient. The length of the property is 120 meters and he bought 16 posts. 5) For a triangle with sides of lengths 17.

Uploaded by

Tina Saini
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Geometry Questions for CAT

18 Oct 2017
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Question 1:

A one rupee coin is placed on a table. The maximum


number of similar one rupee coins which can be placed on
the table, around it, with each one of them touching it and
only two others is

A. 8

B. 6

C. 10

D. 4

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Question 2:

Consider obtuse-angled triangles with sides 8 cm, 15 cm


and x cm. If x is an integer then how many such triangles
exist?

A. 5

B. 10

C. 21

D. 15

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Question 3:

Each side of a given polygon is parallel to either the X or the


Y axis. A corner of such a polygon is said to be convex if the
internal angle is 90° or concave if the internal angle is 270°.
If the number of convex corners in such a polygon is 25, the
number of concave corners must be

A. 20

B. 0

C. 21

D. 22
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Question 4:

A farmer has decided to build a wire fence along one


straight side of this property. For this, he planned to place
several fence-posts at six metre intervals, with posts fixed at
both ends of the side. After he bought the posts and wire, he
found that the number of posts he had bought was five less
than required. However, he discovered that the number of
posts he had bought would be just sufficient if he spaced
them eight metres apart. What is the length of the side of his
property and how many posts did he buy?

A. 20

B. 0

C. 21

D. 22

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Question 5:

In a triangle ABC, the lengths of the sides AB and AC equal


17.5 cm and 9 cm respectively. Let D be a point on the line
segment BC such that AD is perpendicular to BC. If AD = 3
cm, then what is the radius (in cm) of the circle circumscribing
the triangle ABC?

A. 17.05

B. 27.85

C. 22.45

D. 26.25

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Solutions:

1) Answer (B)

If we join centres of 2 outer circles with the centre circle, it will


make an equilateral triangle.
Hence at the centre it will make an angle of 60 so total
360/60=6 triangles will be there
Hence, 6 outer circles will be there.

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2) Answer (C)

For obtuse-angles triangle,

and c < a+b


If 15 is the greatest side, 8+x > 15 => x > 7 and
=>
So, x = 8, 9, 10, 11, 12

If x is the greatest side, then 8 + 15 > x => x < 23

So, x = 18, 19, 20, 21, 22

So, the number of possibilities is 10

3) Answer (A)

Let the total number of sides be x.

(25*90)+(x-25)*270 = (x-2)180

x = 46

Number concave corners = x-25 = 46-25 = 21

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4) Answer (D)

Solution: Let the number of posts the farmer bought = x


Length of the side = (x+5-1)*6 = 6*(x+4)
Length of the side is also equal to (x-1)*8
=> 8x - 8 = 6x + 24 => x = 16
Length of side = 6*20 = 120 m

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5) Answer (C)

Let the sides be x, y and 14-(x+y)


x+y > 14-(x+y) => x+y > 7
x+14-x-y > y => y < 7
Similarly, x < 7
If x = 1, y = 7 (not possible)
So, if x = 2, y = 6
if x = 3, y = 5 if x = 4, y = 4, 5
The cases for x = 5 and 6 are already taken care of by y.
Number of possible cases = 4

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