Question

If '+' stands for division, '$\div$' stands for multiplication, 'x' stands for subtraction and '-' stands for addition, then which of the following is the correct equation?

• A. $18 \div 6 - 7 + 5 \times 2 = 2/3$
• B. $18 + 6 \div 7 \times 5 - 2 = 18$
• C. $18 \times 6 + 7 \div 5 - 2 = 16$
• D. $18 \div 6 \times 7 + 5 - 2 = 22$

Answer 1

The Correct Option is D

Concept:
The symbols do not have their usual meanings. Replace each symbol according to the given instructions: \[ + \rightarrow \div \] \[ \div \rightarrow \times \] \[ \times \rightarrow - \] \[ - \rightarrow + \] After substitution, apply the BODMAS rule and check which equation is correct.

Step 1: Check Option (A).
Given: \[ 18 \div 6 - 7 + 5 \times 2 = \frac{2}{3} \] Replacing the symbols: \[ 18 \times 6 + 7 \div 5 - 2 \] Applying BODMAS: \[ 108+\frac{7}{5}-2 = 106+\frac{7}{5} = 107.4 \] Since \[ 107.4 \ne \frac{2}{3}, \] Option (A) is incorrect. 

Step 2: Check Option (B).
Given: \[ 18 + 6 \div 7 \times 5 - 2 = 18 \] Replacing the symbols: \[ 18 \div 6 \times 7 - 5 + 2 \] Applying BODMAS: \[ 3\times7-5+2 \] \[ 21-5+2 \] \[ 18 \] Thus, \[ 18=18. \] So this equation is correct. 

Step 3: Verify the remaining options.
Option (C): \[ 18 \times 6 + 7 \div 5 - 2 \] becomes \[ 18-6\div7\times5+2 \] \[ 18-\frac{30}{7}+2 = 15.714\ldots \ne16. \] Hence incorrect. 

Option (D): \[ 18 \div 6 \times 7 + 5 - 2 \] becomes \[ 18\times6-7\div5+2 \] \[ 108-\frac{7}{5}+2 = 108.6 \ne22. \] Hence incorrect. 

Step 4: Conclusion.
Only Option (B) satisfies the equation after replacing the symbols. 

Final Answer: \[ \boxed{18 + 6 \div 7 \times 5 - 2 = 18} \] Hence, the correct option is \[ \boxed{\text{(B)}}. \]