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

Notes - Mathematical Operation

Category : 12th Class

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 = $15\,\,\times \,\,3\,\,-\,\,10\,\,\div \,\,5\,\,+\,\,5\,\,=\,\,45-2\,\,+\,\,5\,\,=\,\,50-2=\text{ }48.$

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

1. 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 $=\text{ }30\,\,\div \,\,2+3\,\,\times \,\,6\,\,-\,\,5\,\,=\,\,15\,\,+\,\,18\,\,-\,\,5\,\,=\,\,28.$

1. 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 $=\text{ }12\text{ }-\text{ }12\text{ }\times \text{ }28\text{ }\div \text{ }7\text{ }+\text{ }15\text{ }=\text{ }12\text{ }-\text{ }12\text{ }\times \text{ }4\text{ }+\text{ }15$

$=12\,\,-\,\,48\,\,+\,\,15\,\,=\,\,27\,\,-\,\,48\,\,=-21.$

1. 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.

1. 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:

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

1. 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 $=\text{ }\left( 7\text{ }\times \text{ }3 \right)\,\,-\,\,6\,\,+\,\,5\,\,=\,\,21\,\,-\,\,6\,\,+\,\,5\,\,\,=\,\,20$

1. 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.

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

$=52-4\,\,\times \,\,5\,\,+\,\,4$

$=52-20+4=36$

1. 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

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

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

$=8+4-3=9.$

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##### Notes - Mathematical Operation

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