Saturday, June 09, 2018

Series Shortcuts, Practice Problems and Solutions with Explanation

Source (Internet): IACE Material. - Nareddula Rajeev Reddy (NRR)

What is SERIES ?

SERIES is an important part of the Reasoning section in competitive Examinations. Series is a group of elements which follows a fixed pattern.

Example: 1) 2,4,6,8,10,12 (Number Series)
                2) A,C,E,G,I,K (letter Series)
                3) -,=, △, ▭ (Non-verbal Series)

NUMBER SERIES: For better understanding , we will classify this in to five types.

1. Difference Series :If the given Series is increase (or) decrese with a normal difference then that Series is Difference Series.

Example:18,22,26,30,34,38 (constant difference) .
Example:9,14,18,21,23,24 .

2.Product Series : If the given series is increase (or) decrease with a abnormal difference then that Series might be product Series .

Example:3,6,18,7,360,2160 (Here multiplying *2 ,*3,*4,*5,and *6).
Example:16,8,8,12,24,60,180 (Here multiplying *0.5,*1,*1.5,*2,*2.5 and *3 ).

3.Combination Series: If the given Series has more than one type of operation performed (or) more than one series combined together is a combination Series.

Example:6,18,22,110,116,812 (*3,+4,*5,+6 and *7).
Example:6,20,43,131,265,789 (*3+2,*2+3,*3+2, and *2+3).

4.Squares and Cubes Series: If the given Series is related to the squares of the numbers (or) cubes of numbers (or) near to squares and cubes then that Series is called squares and cubes Series .

Example:4,16,5,25,6,36,7,49( Here number and its squares).
Example:16,36,64,100 ( Here even numbers squares).
Example:16,36,64,81( Here composite numbers squares).

5.General Series:
Example:2,3,5,7,11,13,17,19 ( A Series of Prime Numbers).
Example:2,3,5,8,13,21,34,55 ( A Series of Fibonacci Numbers).
Example:M,T,W,F,S,S ( A Series of starting letter of a week).


             1.Problem 11,13,17,19,23,29 _
             Answers:a) 30 b) 32 c) 31 d) 45 e) None of these.
             Solution:c) 31 (Next prime number).

             2.Problem 2,14,18,46,82,172, _
             Answers:a) 238 b) 338 c) 218 d) 418 e) None of these.
             Solution:b) 338 (*2+10,*2-10,*2+10,*2-10,*2+10 and *2-10).

             3.Problem 0,6,24,60,120,210, _
             Answers:a) 630 b) 436 c) 536 d) 336 e) None of these.
             Solution:d) 336 (13-1,23-2,33-3,43-4,53-5,63-6 and 73-7).

             4.Problem 15,21,39,77,143, _
             Answers:a) 245 b) 346 c) 243 d) 276 e) None of these.
             Solution:a) 245 (Difference +6,+18,+38,+66,+102 next difference +12,+20,+28,+36 next difference +8,+8 and +8).

             5.Problem 1,2,8,_,148,765
             Answers:a) 42 b) 33 c) 52 d) 65 e) None of these.
             Solution:b) 33 (*1+1,*2+4,*3+9,*4+16 and *5+25 ).

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*To get the concept, read the Series Shortcuts, Practice Problems and Solutions with Explanation.

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