12th Class Mental Ability Coding-Decoding Notes - Mathematical Operation

Mathematical Operations

Introduction: This is a new type of verbal reasoning question which is being frequently asked in the various competitive examination. Here, a mathematical symbols is damaged with another symbol to confuse and then you are asked to solve an equation using the new instructions with changed symbols.

Example:

1. If + means -, - means \[\mathbf{x},\,\,\div \] means + and \[\mathbf{x}\] means \[\,\mathbf{\div }\], then \[\mathbf{15}-\mathbf{3}+\mathbf{10}\,\,\times \,\,\mathbf{5}\div \mathbf{5}\]?

            (a) 5                                          (b) 22           

            (c) 48                                        (d) 52

Ans.     (c)

            Explanation: Using the correct symbols, we have:

            Given expression = \[15\,\,\times \,\,3\,\,-\,\,10\,\,\div \,\,5\,\,+\,\,5\,\,=\,\,45-2\,\,+\,\,5\,\,=\,\,50-2=\text{ }48.\]

2. If x means +, + means \[\mathbf{\div }\], - means \[\mathbf{\times }\] and - means -, then \[\mathbf{8}\,\,\mathbf{\times }\,\,\mathbf{7}\,\,\mathbf{-}\,\,\mathbf{8}\,\,\mathbf{+}\,\,\mathbf{40}\,\,\mathbf{\div }\,\,\mathbf{2=?}\]

            (a) 1                                                       (b) \[\,7\frac{2}{5}\]

            (c) \[\,8\frac{3}{5}\]                      (d) 44

Ans.     (b)

            Explanation: Using the correct symbol, we have :

            Given expression = \[8\,\,+\,\,7\,\,\times \,\,8\text{ }40\,\,\,\div \,\,\,2\,\,=\,\,8\,\,+\,\,7\times \frac{1}{5}\,\,-\,\,2\,\,\,\,=\,\,\,\,6+\frac{7}{6}\,\,=\frac{37}{5}\,\,=\,\,7\frac{2}{5}.\]

3. If ‘Q’ means ‘add to’, J means ‘multiply by’, T means ‘subtract from’ and K means ‘divided by’, then \[\mathbf{30}\,\mathbf{K}\,\mathbf{2}\,\mathbf{Q}\,\mathbf{3}\,\mathbf{J}\,\mathbf{6}\,\mathbf{T}\,\mathbf{5=?}\]

            (a) 18                                        (b) 28

            (c) 31                                        (d) 103

Ans.     (b)

            Explanation: Using the correct symbols, we have:

            Given expression \[=\text{ }30\,\,\div \,\,2+3\,\,\times \,\,6\,\,-\,\,5\,\,=\,\,15\,\,+\,\,18\,\,-\,\,5\,\,=\,\,28.\]

4. If P means’ division’, T means ‘addition’, M means ‘subtract’ and D means ‘multiplication’, then what will be the value of the expression 12 M 12 D 28 P 7 T 15?

            (a) - 30                                      (b) - 21         

            (c) 15                                        (d) 45

Ans.     (b)

            Explanation: Using the correct symbols, we have:

            Given expression \[=\text{ }12\text{ }-\text{ }12\text{ }\times \text{ }28\text{ }\div \text{ }7\text{ }+\text{ }15\text{ }=\text{ }12\text{ }-\text{ }12\text{ }\times \text{ }4\text{ }+\text{ }15\]

            \[=12\,\,-\,\,48\,\,+\,\,15\,\,=\,\,27\,\,-\,\,48\,\,=-21.\]

5. If $ means +, # means -, @ means x and * means \[\mathbf{\div }\], then what is the value of 16 $ 4 @ 5 # 7 2 * 8?

            (a) 25                                        (b) 27           

            (c) 29                                        (d) 36

Ans.     (b)

            Explanation: Using the correct symbols, we have:

            Given expression = \[16\text{ }+\text{ }4\text{ }\times \text{ }5\text{ }-\text{ }72\text{ }\div \text{ }8\text{ }=\text{ }16\text{ }+\text{ }20\text{ }-\text{ }9\text{ }=\text{ }36\text{ }-\text{ }9\text{ }=\text{ }27.\]

Snap Test

1. If ‘x’ stands for ‘addition’, ‘<’ for ‘subtraction’, ‘+’ for division’, ‘>‘ for ‘multiplication = for <, then which of the following alternatives is correct?

            (a) \[3\,\,\times \,\,4\,\,>\,\,2\,\,-\,\,9\,\,+\,\,3\,\,<\,\,3\]     

            (b) \[5\,\,\times \,\,3\,\,<\,\,7\,\,\div \,\,8+4\,\,\times \,\,1\]

            (c) \[5\,\,>\,\,2+2=10<4\,\,\times \,\,8\]  

            (d) \[3\,\,\times \,\,2\,\,<\,\,4\,\,\div \,\,16\,\,>\,\,2+4\]

Ans.     (c)

            Explanation: We get the statement as:

            \[5\,\,\times \,\,2\,\,\div \,\,2\,\,<\,\,10\,\,-\,\,4+8\,\,or\,\,5\,\,\times \,\,1\,\,<\,\,18\,\,-\,\,4\,\,or\,\,5<14\], which is true.

2. If ‘-’ stands for ‘division’, ‘+’ for ‘multiplication’,’ +’ for ‘subtraction’ and Y for ‘addition’, then which one of the following equations is correct?

           (a) \[4\,\,\times \,\,5\,\,+\,\,9\,\,-\,\,3\,\,\div \,\,4\,\,=\,\,15\]                        

           (b) \[4\,\,\times \,\,5\,\,\times \,\,9\,\,+\,\,3\,\,\div \,\,4\,\,=\,\,11\]

           (c) \[4-5\,\,\div \,\,9\,\,\times \,\,3\,\,-\,\,4=17\]                  

           (d) \[4\,\,\div \,\,5\,\,+\,\,9\,\,-\,\,3\,\,+\,\,4\,\,=\,\,18\]

Ans.     (a)

            Explanation: We get the statement as:

            \[4\,\,+\,\,5\,\,\times \,\,9\,\,\div \,\,3-4=4\,\,+\,\,5\,\,\times \,\,3-4\,\,=\,\,4+15\,\,-\,\,4\text{ }=15.\]

3. If x stands for ‘add’ y stands for ‘subtract’, z stands for ‘divide’ and P stands for ‘multiply, then what is the value of \[\left( \mathbf{7P}\text{ }\mathbf{3} \right)\mathbf{y}\,\mathbf{6}\text{ }\mathbf{\times }\text{ }\mathbf{5}\]?

            (a) 30                                                    (b) 20

            (c) 10                                                    (d) 5

Ans.     (b)

            Explanation: Using the correct symbols we have given expression \[=\text{ }\left( 7\text{ }\times \text{ }3 \right)\,\,-\,\,6\,\,+\,\,5\,\,=\,\,21\,\,-\,\,6\,\,+\,\,5\,\,\,=\,\,20\]

4. If - means \[\div \], + means \[\times \], \[\div \] means -, \[\times \] means +, then which of the following equation is correct?

            (a) \[36-12\,\,\times \,\,6\,\,\div \,\,3+4=60\]                     

            (b) \[36\,\,\times \,\,4\,\,-\,\,12\,\,+\,\,5\,\,\div \,\,3\,\,=\,\,420\]

            (c) \[43\,\,\times \,\,7\,\,\div \,\,5\,\,+\,\,4\,\,-\,\,9\,\,=\,\,25\]                       

            (d) \[52\,\,\div \,\,4\,\,+\,\,5\,\,\times \,\,8\,\,-\,\,2\,\,=\,\,36\]

Ans.     (d)

            Explanation: We get the statement.

            \[=52-4\,\,\times \,\,5+8\,\,\div \,\,2\]

            \[=52-4\,\,\times \,\,5\,\,+\,\,4\]

            \[=52-20+4=36\]

5. If \[\mathbf{\times }\] means ‘addition’, - means ‘division’, \[\mathbf{\div }\] means ‘subtraction’ and + means ‘multiplication’, then which of the following is correct?

            (a) \[16-5\,\,\times \,\,10\,\,\div \,\,4\,\,\div \,\,4\,\,=\,\,12\]             (b) \[16+5-10\,\,\times \,\,4\,\,\div \,\,3=9\]           

            (c) \[16\,\,+\,\,5\,\,\div \,\,10\,\,\times \,\,4\,\,-\,\,3\,\,=\,\,9\]            (d) \[16\,\,\times \,\,5\,\,\div \,\,10\,\,+\,\,4\,\,-\,\,3\,\,=\,\,19\]

Ans.     (b)

            Explanation: We get the statement as

            \[=\,\,\,16\,\,\times \,\,5\div 10+4-3\]       

            \[=16\,\,\times \,\,\frac{1}{2}\,\,+\,\,4\,\,-\,\,3\]    

            \[=8+4-3=9.\]