If $'\div'$ stands for 'addition', '+' stands for 'subtraction', '×' stands for 'division' and '-' stands for 'multiplication', then which of the following equations will NOT be correct?
Symbol Substitution and Equation Verification
This problem requires substituting given symbols with arithmetic operations and then verifying the correctness of different equations using the order of operations (PEMDAS/BODMAS).
Symbol Mapping
The provided symbol substitutions are:
- The symbol '$÷$' stands for addition ($+$).
- The symbol '$+$' stands for subtraction ($-$).
- The symbol '$×$' stands for division ($÷$).
- The symbol '$-$' stands for multiplication ($×$).
Evaluating Each Option
Option 1: $36 ÷ 4 - 3 × 6 + 16 = 22$
After substituting the symbols, the expression becomes:
$36 + 4 \times 3 \div 6 - 16$
Evaluating using the order of operations:
1. Multiplication: $4 \times 3 = 12$. Expression: $36 + 12 \div 6 - 16$.
2. Division: $12 \div 6 = 2$. Expression: $36 + 2 - 16$.
3. Addition: $36 + 2 = 38$. Expression: $38 - 16$.
4. Subtraction: $38 - 16 = 22$.
Result: $22 = 22$. This equation is correct.
Option 2: $36 - 4 × 3 + 6 ÷ 16 = 60$
After substituting the symbols, the expression becomes:
$36 \times 4 \div 3 + 6 + 16$
Evaluating using the order of operations:
1. Multiplication: $36 \times 4 = 144$. Expression: $144 \div 3 + 6 + 16$.
2. Division: $144 \div 3 = 48$. Expression: $48 + 6 + 16$.
3. Addition: $48 + 6 = 54$. Expression: $54 + 16$.
4. Addition: $54 + 16 = 70$.
Result: $70 \neq 60$. This equation is NOT correct.
Option 3: $36 × 4 + 3 - 6 ÷ 16 = 7$
After substituting the symbols, the expression becomes:
$36 \div 4 - 3 \times 6 + 16$
Evaluating using the order of operations:
1. Division: $36 \div 4 = 9$. Expression: $9 - 3 \times 6 + 16$.
2. Multiplication: $3 \times 6 = 18$. Expression: $9 - 18 + 16$.
3. Subtraction: $9 - 18 = -9$. Expression: $-9 + 16$.
4. Addition: $-9 + 16 = 7$.
Result: $7 = 7$. This equation is correct.
Option 4: $36 + 4 ÷ 3 × 6 - 16 = 40$
After substituting the symbols, the expression becomes:
$36 - 4 + 3 \div 6 \times 16$
Evaluating using the order of operations:
1. Division: $3 \div 6 = 0.5$. Expression: $36 - 4 + 0.5 \times 16$.
2. Multiplication: $0.5 \times 16 = 8$. Expression: $36 - 4 + 8$.
3. Subtraction: $36 - 4 = 32$. Expression: $32 + 8$.
4. Addition: $32 + 8 = 40$.
Result: $40 = 40$. This equation is correct.
Conclusion
The analysis shows that the equation in Option 2 yields a result of $70$, which contradicts the given value of $60$. Therefore, Option 2 is the equation that will NOT be correct.
Similar Questions
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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.)
