Category : 5th Class
MENTAL ABILITY
FUNDAMENTALS
This chapter is based on four distinct concepts:
(a) Mathematical Series:
Rule/Pattern may exist in the following ways:
(i) Series of odd number:
Example: 1, 3, 5, 7, ......
Ans. Next number will be 9
(ii) Series of even numbers:
Example: 2, 4, 6, ........
Ans. Next number will be 8.
(iii) Series of prime numbers:
Example: 2, 3, 5, 7, 11, 13.......
Ans. Next number will be 17
(iv) Series of square of natural numbers:
Example: 1,4,9, 16, .......
Ans. Next number will be 25
(v) Series of squares of even natural numbers:
Example: 4, 16, 36, 64
Ans. Next numbers will be 100
(vi) Series of cubes of natural numbers
Example: 1, 8, 27.......
Ans. Next number will be 64
Solved Examples
1. Find the number to fill in the blank:
48, 31, 18, ____?
Ans. Sequence comprises subtraction of prime numbers:
\[\therefore \]It is 7
2. Find 86, 61, 45,......?
\[\therefore \]It is 36
Ans. Square comprises subtraction of squares of natural numbers as follows:
Therefore, you should have the following at finger tips:
1. Sequence of prime numbers from 1 to 100 i.e., 2, 3, 5, 7, 11, 13,........97
2. Sequence of squares of natural numbers from 1 to 20 i.e., 1,4, 9................361,400
3. Sequence of cubes of natural numbers from 1 to 20 i.e., 1, 8, 27......... ..6859, 8000
Alphabetic Series
Example: The three blanks in the sequence can be given by (if the last blank contains ?G')
S, ____; M, ____; G, _____; A, ____ G ____
(a) TPV (b) YSM (c) YSR (d) None
Sol. Now let us understand the pattern
Similarity the gaps can be filled up as:
\[\therefore \]YSM is the answer.
Analogy Type?
In many questions, term 1 is related to terms 2 by some relationship.
Same relationship is to be used to relate term 3 to term 4 in order to find term 4 (which is unknown)
This can be represented as
Term 1 : Term 2 : : Term 3 : ??
Example: Bihar : Patna :: Jharkhand : ?
Sol. Bihar \[\xleftarrow{(is\,Capital\,of)}\]Patna
Similarly Jharkhand\[\xleftarrow{(is\,Capital\,of)}\] (Ranchi)
Here, the analogy was based on states of India and their capitals. Similarly, analogy could be based on.
Example: \[Man\to Mammal;\text{ }Whale\to Mammal;\text{ }Kiwi\to Bird\]
Example: \[Force\to Newton;\text{ }Pressure\to Pascal;\text{ }Current\to Ampere\]
Direction Sense
Elementary Question
Example: If one person is moving east by 100 m, then turns left and goes 100 m. He again turns left and goes 100m. How far and in which direction is he from his original position?
Sol. This is best solved by drawing North-South direction axis. Consider the person at origin.
His final position is 'S' , distance OS = 100 m and he has gone 100 m north of starting point 'O?
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