Which two signs should be interchanged to make the following equation correct?
$56-74\times17+391\div23 = 1297$
Question Type: Arithmetic Reasoning
Step-by-step Solution:
The given equation is: \(56 - 74 \times 17 + 391 \div 23 = 1297\)
Let's evaluate the equation using the standard order of operations (BODMAS/PEMDAS):
- Division: \(391 \div 23 = 17\)
- Multiplication: \(74 \times 17 = 1258\)
- Subtraction and Addition: \(56 - 1258 + 17 = -1185\)
The result is -1185, which is not equal to 1297. We need to interchange two signs to make the equation correct.
Let's try interchanging the '+' and '-' signs:
\(56 + 74 \times 17 - 391 \div 23 = ?\)
- Division: \(391 \div 23 = 17\)
- Multiplication: \(74 \times 17 = 1258\)
- Addition and Subtraction: \(56 + 1258 - 17 = 1297\)
The equation now holds true: \(1297 = 1297\)
Why other options are incorrect:
- Option 1 (\(\div\) and \(\times\)): Interchanging these would significantly alter the result and not lead to 1297.
- Option 3 (\(\times\) and \(-)\): This would result in a large negative number.
- Option 4 (\(\div\) and +): This would also result in a value far from 1297.
Core Logic/Pattern: The core logic is to systematically try interchanging the arithmetic operators to find a combination that satisfies the equation. The order of operations must be carefully followed.
Therefore, the correct answer is to interchange the '+' and '-' signs.
Important Questions from Bodmas Rule
Solve: {7.88 × 2 + 2.4 × 5 - 242.4 ÷ 4 + [9.2 × 4 - 2.46 of 3 + (36.3 ÷ 3 - 1.42 × 2)]}
What will come in the place of question mark (?) in the given expression?
(420 ÷ 12 × 35 + 452- 152) = ?2
What will come in place of the question mark ‘?’ in the following question?
(44 of 15) – [(450 × 240 ÷ 60 – 40) ÷ 80 × 25 + 50] – 10 = ?Simplify: 92 - 18 ( 9 + 36 ÷ 3 × 12 - 27 × 3) + 51
Simplify the following expression.
\(\rm \frac{3}{5}\ of\ \left\{\left(48\div\overline{36\div9}\times\frac{1}{6}\right)+\frac{1}{3}\right\}=?\)
