If '-' means '÷', '÷' means 'x', 'x' means '+' and '$+$' means '-', then what will come in place of the question mark (?) in the following equation? $9 \div 12 \times 450 + 8208 - 18 = ?$
102
Understanding Symbol Substitution Rules
The problem asks us to solve a mathematical equation where the standard arithmetic operators have been redefined. We need to apply the given substitutions correctly and then solve the resulting equation using the order of operations (BODMAS/PEMDAS).
The substitution rules are:
- '-' is replaced by '÷'
- '÷' is replaced by 'x'
- 'x' is replaced by '+'
- '+' is replaced by '-'
Applying Substitutions to the Equation
The original equation is:
$9 \div 12 \times 450 + 8208 - 18 = ?$
Let's apply the substitution rules step-by-step to the original equation:
- Replace '÷' with 'x': $9 \times 12 \times 450 + 8208 - 18$
- Replace 'x' with '+': $9 \times 12 + 450 + 8208 - 18$
- Replace '+' with '-': $9 \times 12 + 450 - 8208 - 18$
- Replace '-' with '÷': $9 \times 12 + 450 - 8208 \div 18$
So, the transformed equation becomes:
$9 \times 12 + 450 - 8208 \div 18 = ?$
Solving the Transformed Equation
Now, we solve the transformed equation using the order of operations (BODMAS/PEMDAS): Brackets, Orders, Division/Multiplication (from left to right), Addition/Subtraction (from left to right).
-
Division: First, perform the division operation.
$8208 \div 18$
To calculate $8208 \div 18$:
$8208 \div 18 = 456$
The equation now is: $9 \times 12 + 450 - 456 = ?$ -
Multiplication: Next, perform the multiplication.
$9 \times 12 = 108$
The equation now is: $108 + 450 - 456 = ?$ -
Addition: Perform the addition.
$108 + 450 = 558$
The equation now is: $558 - 456 = ?$ -
Subtraction: Finally, perform the subtraction.
$558 - 456 = 102$
Therefore, the result of the equation after the symbol substitutions is 102.
Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’, and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying, etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
