Questions on Patterns

Patterns

Patterns problems focuses on "changes" made from one figure to another. Such changes follow a definite "pattern" or a set of rule when moving from one figure to another. The purpose here is to identify the pattern and then apply it to solve the given question.

Solved Questions:




Q1. Examine the following matchstick patterns :

If the pattern continues, how many matchsticks are needed in the 15th stage ?
(1) 105
(2) 65
(3) 61
(4) 62

Answer :(4) 62

Solution : Ist stage has 1 triangle and requires 6 matchsticks, second stage has two triangle and requires 10 (2 x 6 - 2 x1) matchsticks and third stage has 3 triangle and requires 14 ( 3 x 6 - 2 x 2) matchsticks. Hence the general formula for this pattern will come out to be { n x 6 - 2 x (n -1)}, where n is the nth stage. Therefore, for 15th stage, the matchsticks required will be 
{ 15 x 6  - 2 x (15 - 1)} = { 90 - 28} = 62 

Q2 : 

Answer:(D)

Q3.

Answer: (B)

Q4.

Answer: (A)

 
Q5.

Answer: (C)


Q6.

Answer: (B)

Q7.

Answer:(D)