# 7th Class Mathematics Missing Character MISSING CHARACTER

## MISSING CHARACTER

Category : 7th Class

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:

 8 Y X 4 9 2

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$x+y=3+6=9$

 8 Y X 7 4 9 2

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:

 9 A 12 B 10 7 8 C 11

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.

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