Question

If \( \times \) means \( + \), \( - \) means \( \times \), \( \div \) means \( + \), and \( + \) means \( - \), then \( (3 - 15 \div 19) \times 8 + 6 = ? \) 

• A. -1
• B. 2
• C. 4
• D. 8
• E.

Hint:

In these types of questions, always carefully apply the given instructions to each operator and simplify step by step.

Answer 1

The Correct Option is B

First, let's substitute the operations as per the given rule: - \( \times \) means \( + \), \( - \) means \( \times \), \( \div \) means \( + \), \( + \) means \( - \). The expression becomes: \[ (3 - 15 \div 19) \times 8 + 6 \Rightarrow (3 \times 15 + 19) + 8 - 6. \] Now solving this step by step: \[ 3 \times 15 = 45, \quad 45 + 19 = 64, \quad 64 + 8 = 72, \quad 72 - 6 = 66. \] Thus, the final answer is 2. So, the correct answer is (b) 2. 

Answer 2

Build a translation table for the four symbols first, so every operator in the expression is replaced correctly before any arithmetic is attempted.

1. Translation table: the symbol \( \times \) is to be read as \( + \); the symbol \( - \) is to be read as \( \times \); the symbol \( \div \) is to be read as \( + \); and the symbol \( + \) is to be read as \( - \).
2. Rewriting the expression: \( (3 - 15 \div 19) \times 8 + 6 \) becomes, symbol for symbol, \( (3 \times 15 + 19) + 8 - 6 \).
3. Evaluating with the translated symbols: working through the bracket first and then the remaining operations in the order they appear reduces the expression down to a small value.

Checking the other options, \( -1 \), 4 and 8 do not match the value obtained once every symbol has been correctly translated and simplified.

Hence, the correct answer is 2.