MISSING CHARACTER
Category : 7th Class
Learning Objectives
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
\[\therefore \] \[8+x+4=15\] \[x=1584\Rightarrow x=3\]
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\[BC\]?
Solution:
Here, the sum of each row, each column and each diagonal is 30.
\[\therefore \] \[A=9,B=13,C=11\]
Hence \[BC=2.\]
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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