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
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
