7th Class Mathematics Related to Competitive Exam MISSING CHARACTER

Learning Objectives

• To learn how to complete a partially filled chart with the help of information given.
• To learn how to find missing characters from given alternatives.

Chart logic problems present you with a partially filled in chart or table and ask you to fill it in completely given either the information in the chart, or some information given by the question.

Example 1: 

In the figure above, each of the nine boxes must be filled by an integer from 1 to 9, so that each row and column is equal. No integer may be repeated. What is the value of\[x+y\]?

Solution:

The bottom row is equal to 15. Since the question states that each row is of equal value

\[\therefore \]  \[8+x+4=15\]  \[x=15-8-4\Rightarrow x=3\]

The question also states that each box must be filled with a number from 1 and 9 and that each number can only be used once. The numbers 2, 3, 4, 8 and 9 have already been used, leaving you with 1, 5, 6, and 7 to fill in the remaining boxes. You should see immediately that the 7 can't go in the same row or diagonal with the

8, because that would add up to 15 for just two boxes in a row, and the entire row must add up to fifteen.

Hence, 7 therefore must go here:

\[\therefore \] \[x=3\]and\[y=6\]

Hence, value of\[x+y=3+6=9\]

Example 2:

Find the missing character from among the given alternatives

(a) 121                                  (b) 61                 

(c) 74                                     (d) 101

Solution:

(a) Here \[{{\left( 6+3 \right)}^{2}}={{9}^{2}}=81\]

\[{{\left( 2+6 \right)}^{2}}={{8}^{2}}=64\]

\[{{\left( 5+8 \right)}^{2}}={{13}^{2}}=169\]

\[\therefore \]\[{{\left( 8+3 \right)}^{2}}={{11}^{2}}=121\]

Example 3:

In the above matrix, what is the value of\[B-C\]?

Solution:

Here, the sum of each row, each column and each diagonal is 30.

\[\therefore \] \[A=9,B=13,C=11\]

Hence \[B-C=2.\]

Example 4:

Find the value of X in the following figure:

(a) 3                                       (b) 4

(c) 8                                       (d) 12

Solution:

(b) The top left hand number is obtained by adding the bottom two numbers. The top right hand number is the result of dividing the bottom two numbers.

Thus, \[12+3=15,\,12\div 3=4;\]

\[22+11=33,\,\,22\div 11=2.\]

\[18+9=27,\,\,18\div 9=2.\]

So, \[32+X=36\] and \[32\div X=8\]or\[X=4.\]

Example 5: Find the missing character from amongst the given alternatives.

(a) 18                     (b) 17                  

(c) 19                    (d) 12

Solution:

(b) Start at 2 and, working clockwise, jump two spaces each time adding 3.