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
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its 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.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its 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.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
