# 12th Class Mental Ability Series Notes - Inserting the Missing Number

Notes - Inserting the Missing Number

Category : 12th Class

# Inserting the Missing Number

In this chapter questions contain a figure, a set of figures, an arrangement or a matrix, each of which bears certain characters, be it numbers, letters or group/combination of Setters numbers which follow a particular pattern. You are required to identify and decipher this pattern and accordingly find the missing character in the figure.

Example: No. (1 to 6)

Direction: Find the missing character from among the given alternatives.

1.

(a) 45                            (b) 35

(c) 25                            (d) 15

(e) None of these

Ans.     (c)

Explanation: The pattern is $\to \text{ }{{\left( 16\text{ }-\text{ }6 \right)}^{2}}+\text{ }{{\left( 5\text{ }-\text{ }2 \right)}^{2}}=\text{ }100\text{ }+\text{ }9\text{ }=\text{ }109$

$\to \,\,\,{{\left( 22\text{ }-\text{ }15 \right)}^{2}}+\text{ }{{\left( 21\text{ }-\text{ }19 \right)}^{2}}=\text{ }49\text{ }+\text{ }4\text{ }=\text{ }53$

$\to \,\,\,{{\left( 17\text{ }-\text{ }13 \right)}^{2}}+\text{ }{{\left( 51\text{ }-\text{ }48 \right)}^{2}}=\text{ }16\text{ }+\text{ }9\text{ }=\text{ }$

2.

(a) 50                            (b) 39

(c) 26                            (d) 1

(e) None of these

Ans.     (b)

Explanation: The pattern is:       $\to \,\,\,3\,\times \,2-1=5$

$\to \,\,5\,\,\times \,\,2\,\,-\,\,2\,\,=\,\,8$

$\to \,\,8\,\,\times \,\,2\,\,-\,\,3\,\,=\,\,13$

$\to 13\,\,\times \,\,2\,\,-\,\,4\,\,=\,\,22$

So, $So,\,\,\,\to \,\,\,22\,\,\times \,\,2\,\,-\,\,5\,\,=\,\,39$

3.

(a) 18                            (b) 36

(c) 135                          (d) 175

(e) None of these

Ans.     (c)

Explanation: The pattern is:       $15\times \,2=30$

$2\,\,\times \,\,7\,\,=\,\,63$

So, the missing number is:            $9\times 15=135.$

4.

(a) 860                          (b) 1140

(c) 2880                         (d) 3240

(e) None of these

Ans.     (c)

Explanation: Clearly, moving clockwise, we observe the following pattern:

$4\times 1=4;\text{ }4\times 2=8;\text{ }8\times 3=24;\text{ }24\times 4=96;\text{ }96\times 5=480$

So required number = $\left( 480\times 6 \right)=2880$

5.

(a) 5                              (b) 4

(c) 3                              (d) 2

(e) None of these

Ans.     (c)

Explanation: In the first column, $12\,\,\times \,\,(18\,\,\div \,\,3)\,\,=\,\,72$

In the third column, $16\,\,\times \,\,(32\,\,\div \,\,4)\,\,=\,\,128$

Let the missing number be x. Then, in the second column, we have

$14\times \left( 24\text{ }\div \text{ }x \right)\text{ }=112\text{ }\Rightarrow \text{ }24\div x\,=8\text{ }\Rightarrow \,\text{ }x=3$

6.

(a) P                             (b) R

(c) S                              (d) V

(e) None of these

Ans.     (b).

Explanation: Putting $A\,\,=\,\,1,\,\,B\,\,=\,\,2,\,\,C\,\,=\,\,3,\,\,........,\,\,M\,\,=\,\,13,.......,\,\,X\,\,=\,\,24,\,\,Y\,\,=\,\,25,\,\,Z\,\,=\,\,26,$

we have:

In the first row, $F\,\,+\,\,I\,\,=\,\,6\,\,+\,\,9\,\,=\,\,15\,\,=\,\,O$

In the second row, $A\,\,+\,\,J\,\,=\,\,1\,\,+\,\,10\,\,=\,\,11\,\,=\,\,K$

So, in the third row, missing letter $=E\,\,+\,\,M\,\,=\,\,5\,\,+\,\,13\,\,=\,\,18\,\,=\,\,R$