Mental Ability
Category : 6th Class
MENTAL ABILITY
FUNDAMENTALS
Mental Ability: The power to learn or retain knowledge, in law, the ability to understand the fact and significance of your behavior.
Series completion
Look at the example given below
1. Series of odd number
1, 3, 5, 7, 9, ___________
Ans.: Next number is 11.
2. Series of even number.
12, 14, 16, 18, ____________
Ans.: Next number is 20.
3. Series of prime number.
2, 3, 5, 7, 11, 13, 17, __________ .
Ans.: Next number is 19.
4. Series of squares of consecutive odd numbers
1, 9, 25, 49, 81, __________
\[{{1}^{2}},\,\,{{3}^{2}},\,\,{{5}^{2}},\,\,{{7}^{2}},\,\,{{9}^{2}}\]
Ans.: Next number is \[{{11}^{2}}=121.\]
5. Series of square of consecutive even numbers
4, 16, 36, 64, 100, ______
\[{{2}^{2}},\,\,{{4}^{2}},\,\,{{6}^{2}},\,\,{{8}^{2}},\,\,{{10}^{2}}\]
Ans.: Next number is 122 = 144.
6. Series of cube of consecutive even numbers
8, 64, 216, 512, ___________
\[{{2}^{3}},\,\,{{4}^{3}},\,\,{{6}^{3}},\,\,{{8}^{3}},\]
Ans.: Next number is\[{{10}^{3}}=1000\]
7. Series of cube of consecutive odd number
1, 27, 125, 343, _________
Ans.: Next number is\[{{9}^{3}}=729.\]
8. Series of each term is multiplied by a fixed number or certain pattern to get the next number.
Ans.: Next number is\[80\times 2=160\]
9. Series of each term is divided by a fixed number or certain pattern to get the next number.
Ans.: Next number is\[30\div 2=15.\]
Note: Students first remember the square up to 20 and cube up to 20.
Squares:
|
\[{{1}^{2}}=1,\] |
\[{{2}^{2}}=4,\] |
\[{{3}^{2}}=9,\]c |
\[{{4}^{2}}=16,\] |
\[{{5}^{2}}=25\] |
|
\[{{6}^{2}}=36,\] |
\[{{7}^{2}}=49,\] |
\[{{8}^{2}}=64,\] |
\[{{9}^{2}}=81,\] |
\[{{10}^{2}}=100\] |
|
\[{{11}^{2}}=121,\] |
\[{{12}^{2}}=144,\] |
\[{{13}^{2}}=169,\] |
\[{{14}^{2}}=196,\] |
\[{{15}^{2}}=225\] |
|
\[{{16}^{2}}=256,\] |
\[{{17}^{2}}=289,\] |
\[{{18}^{2}}=324,\] |
\[{{19}^{2}}=361,\] |
\[{{20}^{2}}=400\] |
Cubes:
|
\[{{1}^{3}}=1,\] |
\[{{2}^{3}}=8,\] |
\[{{3}^{3}}=27,\] |
\[{{4}^{3}}=64,\] |
\[{{5}^{3}}=125,\] |
|
\[{{6}^{3}}=216,\] |
\[{{7}^{3}}=343,\] |
\[{{8}^{3}}=512,\] |
\[{{9}^{3}}=729,\] |
\[{{10}^{3}}=1000\] |
|
\[{{11}^{3}}=1331\] |
\[{{12}^{3}}=1728,\] |
\[{{13}^{3}}=2197\] |
\[{{14}^{3}}=2744\] |
\[{{15}^{3}}=3375\] |
|
\[{{16}^{3}}=4096\] |
\[{{17}^{3}}=4913\] |
\[{{18}^{3}}=5832\] |
\[{{19}^{3}}=6859,\] |
\[{{20}^{3}}=8000\] |
Series:
An arrangement of letters which follows a particular rule / pattern is called alphabet series.
Note: Students first remember this alphabetical order.
|
\[1\leftarrow A-Z\to 26\] |
\[2\leftarrow B-Y\to 25\] |
\[3\leftarrow C-X\to 24\] |
|
\[4\leftarrow D-W\to 23\] |
\[5\leftarrow E-V\to 22\] |
\[6\leftarrow F-U\to 21\] |
|
\[7\leftarrow G-T\to 20\] |
\[8\leftarrow H-S\to 19\] |
\[9\leftarrow I-R\to 18\] |
|
\[10\leftarrow J-Q\to 17\] |
\[11\leftarrow K-P\to 16\] |
\[12\leftarrow L-O\to 15\] |
|
\[13\leftarrow M-N\to 14\] |
|
|
Look at the examples given below
1. A, B, C, D,_________
Ans.: Next series is E.
2. AB, CD, EF,__________
Ans.: Next series is GH.
3. ABC, EFG, IJK,__________
Ans.: Next series is MNO.
4. AZ, BY, CX,__________
Ans.: Next series is DW
5. 7 A 8, 10 B 11, 13 C 14,_________
Ans.: Next series is 15 D 16.
Analogy;
(i) Safe: Secure:: Protect: __________
(a) Conserve (b) Sure (c) Guard (d) Look
Ans.: (c) Guard: Because, 'safe is synonym of 'secure', similarly, 'protect is synonym of 'Guard'.
(ii) MA: PD : : WA : _____________
(a) YQ (b) YD (c) NA (d) ZD
Solution: The pattern is as follows:
Ans.: ZD
(iii) 
__________
(a) 1331 (b) 1024 (c) 1565 (d) 243
Solution: The pattern is as follows:
Similarly,
Sometimes the questions based on ranking test are puzzle type.
1. In a row of students, Santosh is 9th from the either end of the row. Find the number of students in a row.
(a) 10 (b) 18 (c) 17 (d) 19
Solution: Clearly, the number of students in row are x = Top rank + Bottom rank 
{
total no. of students}
Note: Students let us remember rule
(i) 
(ii) 
(iii) 
2. Rohit ranks eighteenth in a class of 47 students. What is his rank from the last?
(a) 30 (b) 40 (c) 50 (d) 36
Solution: Rohit's rank from the start or front =18th
So, Rohit's rank from the last
(i) North (N) (ii) South (S)
(iii) East (E) (iv) West (W)
(i) North East (NE)
(ii) North West (NW)
(iii) South East (SE)
(iv) South West (SW)
Interesting Note: Students for solving the problem of direction, first learn about right angled triangles.
ABC is a right angled triangle in which
(a) 
or 
(b) 
or 
(c) 
or 
Let us see the example
Example: 1 Rohit starts walking from his home southward a distance of 20 metres. He then took a half turn torwards right. In which direction is he walking now?
(a) East (b) West (c) South west (d) North East
Solution: Draw the direction diagram.
Rohit starts from x towards south and reach y after covering a distance of 20 m. He then takes half right turn and now his position is toward.
Ans. South - west
Example: 2 One day, Rahul left home and cycled 10 kms southwards, turned right and cycled 5 kms and turned right and cycled 10 kms and turned left and cycled 10 kms. How many kilometers will he have to cycle to reach his home staright?
(a) 10 kms (b) 15 kms (c) 20 kms (d) 25 kms
Solution. Draw direction diagram.
A is the starting point goes to B. Then moves to C, then to D and finally he is at E. So, he has to go back a distance EA which is equal to 
i.e. 15 km.
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