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 = \[\left( 480\times 6 \right)=2880\]

            Hence, the answer is (c).

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

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

            Hence, the answer is (c).

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 \[=E\,\,+\,\,M\,\,=\,\,5\,\,+\,\,13\,\,=\,\,18\,\,=\,\,R\]

            Hence, the answer is (b)