What will come in the place of the question mark (?) in the following equation if ‘+’ and '-' are interchanged and ‘×' and '÷' are interchanged? 11 ÷ 42 × 3 - 69 + 25 = ?
198
Understanding Operator Interchange in Equations
This problem requires us to solve a mathematical equation after interchanging certain operators. The rules given are:
- The addition sign (+) is interchanged with the subtraction sign (-).
- The multiplication sign (×) is interchanged with the division sign (÷).
We need to apply these rules to the given equation and then solve it following the standard order of operations, commonly known as BODMAS or PEMDAS.
Applying the Interchange Rules
The original equation is:
\(11 \div 42 \times 3 - 69 + 25 = ?\)
Applying the given interchange rules:
- ‘÷’ becomes ‘×’
- ‘×’ becomes ‘÷’
- ‘-’ becomes ‘+’
- ‘+’ becomes ‘-’
So, the new equation after interchanging the operators is:
\(11 \times 42 \div 3 + 69 - 25 = ?\)
Solving the Modified Equation using BODMAS/PEMDAS
Now, let's solve the modified equation \(11 \times 42 \div 3 + 69 - 25\) following the order of operations:
BODMAS/PEMDAS Order:
- Brackets (Parentheses)
- Orders (Exponents/Powers/Roots)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
In our equation, we only have multiplication, division, addition, and subtraction. We perform multiplication and division first, from left to right.
Step 1: Perform the multiplication \(11 \times 42\)
\(11 \times 42 = 462\)
The equation becomes:
\(462 \div 3 + 69 - 25\)
Step 2: Perform the division \(462 \div 3\)
\(462 \div 3 = 154\)
The equation becomes:
\(154 + 69 - 25\)
Now, we perform addition and subtraction from left to right.
Step 3: Perform the addition \(154 + 69\)
\(154 + 69 = 223\)
The equation becomes:
\(223 - 25\)
Step 4: Perform the subtraction \(223 - 25\)
\(223 - 25 = 198\)
Final Answer for the Operator Interchange Problem
After applying the operator interchanges and solving the modified equation using the correct order of operations, we find that the value of the equation is 198.
Thus, the number that will come in the place of the question mark (?) is 198.
Revision Table: Operator Rules & Order
| Rule Applied | Original Operator | New Operator |
|---|---|---|
| Interchange 1 | + | - |
| Interchange 1 | - | + |
| Interchange 2 | × | ÷ |
| Interchange 2 | ÷ | × |
| Order of Operations (BODMAS/PEMDAS) | Action |
|---|---|
| B/P | Brackets/Parentheses first |
| O/E | Orders/Exponents (powers, roots) next |
| D/M | Division and Multiplication (left to right) |
| A/S | Addition and Subtraction (left to right) |
Additional Information: Understanding BODMAS/PEMDAS
The BODMAS or PEMDAS rule is crucial for solving mathematical expressions correctly, especially when multiple operations are involved. It provides a standard order to follow to ensure everyone arrives at the same correct answer for a given expression.
- B/P (Brackets/Parentheses): Solve any operations inside brackets first. If there are nested brackets, work from the innermost outwards.
- O/E (Orders/Exponents): Evaluate any powers, roots, or orders next.
- D/M (Division and Multiplication): Perform all division and multiplication operations from left to right in the expression. These operations have the same priority.
- A/S (Addition and Subtraction): Finally, perform all addition and subtraction operations from left to right. These operations also have the same priority.
Following this specific order prevents ambiguity and errors in calculations. In operator interchange problems, you first apply the interchange rules to get the new expression and then use BODMAS/PEMDAS to evaluate it.
Important Questions from Logical Puzzle
Seven persons P, Q, R, S, T, U and V like different watches namely W1, W2, W3, W4, W5, W6 and W7 (not necessarily in the same order). P and R do not like odd numbered watch. T likes W5. U does not like W2 or W3 or W6 or W7. P likes prime numbered watch. Q likes W4. S likes W2 or W7. Which of the following statement(s) is/are correct ?
I. S likes W7.
II. R likes W2.
III. U likes W1.
IV. V likes W3.
If ‘+’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘–’ and ‘–’ means ‘+’, then
16 + 18 × 3 ÷ 6 = ?
In a certain code language, ‘Today is last match’ is written as ‘Sa Te Mo Pt’, ‘Last king like your team’ is written as ‘De Ra Mo Lo Zs’, ‘Our team won today match’ is written as ‘Te Ra Pt Ae We’. What is the code for ‘Our won is Last’ in that code language?
In a certain code language, ‘LETTER’ is written as ‘ZLZYIO’. What is the code for ‘ACTION’ in that code language?
If A denotes ‘+’, B denotes ‘×’, C denotes ‘-’, and D denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
34 A 15 B 3 C 11 B 2 A (51 D 17) = ?
