Which of the numbers(not digits) should be interchanged in the below equation to make it mathematically correct?
$216 \div 9 \times 16 + 24 - 27 = 126$
The problem asks us to find which pair of numbers, when interchanged in the given equation, makes it mathematically correct. The equation is:
$216 ÷ 9 × 16 + 24 - 27 = 126$
We need to test each option by swapping the specified numbers and evaluating the left-hand side (LHS) of the equation using the standard order of operations (BODMAS/PEMDAS: Brackets, Orders/Exponents, Division and Multiplication from left to right, Addition and Subtraction from left to right).
Solving by Testing Options
Let's evaluate the LHS for each option:
Option 1: Interchange 16 and 9
The equation becomes: $216 ÷ 16 × 9 + 24 - 27$
- Division: $216 \div 16 = 13.5$
- Multiplication: $13.5 \times 9 = 121.5$
- Addition: $121.5 + 24 = 145.5$
- Subtraction: $145.5 - 27 = 118.5$
Result: $118.5 \neq 126$. This option is incorrect.
Option 2: Interchange 27 and 9
The equation becomes: $216 ÷ 27 × 16 + 24 - 9$
- Division: $216 \div 27 = 8$
- Multiplication: $8 \times 16 = 128$
- Addition: $128 + 24 = 152$
- Subtraction: $152 - 9 = 143$
Result: $143 \neq 126$. This option is incorrect.
Option 3: Interchange 24 and 27
The equation becomes: $216 ÷ 9 × 16 + 27 - 24$
- Division: $216 \div 9 = 24$
- Multiplication: $24 \times 16 = 384$
- Addition: $384 + 27 = 411$
- Subtraction: $411 - 24 = 387$
Result: $387 \neq 126$. This option is incorrect.
Option 4: Interchange 9 and 24
The equation becomes: $216 ÷ 24 × 16 + 9 - 27$
- Division: $216 \div 24 = 9$
- Multiplication: $9 \times 16 = 144$
- Addition: $144 + 9 = 153$
- Subtraction: $153 - 27 = 126$
Result: $126 = 126$. This option is correct.
By interchanging the numbers 9 and 24, the equation becomes mathematically correct.
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.)
