9 and 2
\(9 ÷ 3 + 2 - 4 = 6\)
Interchanging Numbers 9 and 2
The goal is to interchange the numbers 9 and 2 in each given equation and determine which equation becomes incorrect after the swap.
Option 1 Analysis: \(9 \div 3 + 2 - 4 = 6\)
- Original Equation: \(9 \div 3 + 2 - 4 = 6\)
- Interchange 9 and 2: \(2 \div 3 + 9 - 4 = 6\)
- Evaluate the swapped equation using BODMAS (Division, Addition, Subtraction):
- \(2 \div 3 = 2/3 \approx 0.67\)
- \(0.67 + 9 = 9.67\)
- \(9.67 - 4 = 5.67\)
- The resulting equation is \(5.67 = 6\), which is incorrect.
Option 2 Analysis: \(9 - 2 + 7 = 0\)
- Original Equation: \(9 - 2 + 7 = 0\)
- Interchange 9 and 2: \(2 - 9 + 7 = 0\)
- Evaluate:
- \(2 - 9 = -7\)
- \(-7 + 7 = 0\)
- The resulting equation is \(0 = 0\), which is correct.
Option 3 Analysis: \(2+9 \times 3-4=11\)
- Original Equation: \(2+9 \times 3-4=11\)
- Interchange 9 and 2: \(9 + 2 \times 3 - 4 = 11\)
- Evaluate using BODMAS (Multiplication first):
- \(2 \times 3 = 6\)
- \(9 + 6 - 4 = 15 - 4 = 11\)
- The resulting equation is \(11 = 11\), which is correct.
Option 4 Analysis: \(9+4 \times 2-6=32\)
- Original Equation: \(9+4 \times 2-6=32\)
- Interchange 9 and 2: \(2 + 4 \times 9 - 6 = 32\)
- Evaluate using BODMAS (Multiplication first):
- \(4 \times 9 = 36\)
- \(2 + 36 - 6 = 38 - 6 = 32\)
- The resulting equation is \(32 = 32\), which is correct.
Conclusion
After interchanging the numbers 9 and 2, only the equation in Option 1 becomes mathematically incorrect.
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.)
