If A means '+', B means '×', C means '−', and D means '÷', then what is the meaning of '?' in the following equation. What will come in place of ? (90 C 9) D 9 B 9 A 9 = ?
90
The question asks us to decode a mathematical expression where symbols represent standard arithmetic operations and then evaluate the expression to find the missing value, denoted by '?'.
Understanding the Symbol Code
We are given a specific code where symbols correspond to mathematical operators:
- A means '+' (Addition)
- B means '×' (Multiplication)
- C means '−' (Subtraction)
- D means '÷' (Division)
Decoding the Expression
The given expression is:
(90 C 9) D 9 B 9 A 9 = ?
Let's replace the symbols with their corresponding mathematical operators according to the code:
- 'C' is replaced by '−'
- 'D' is replaced by '÷'
- 'B' is replaced by '×'
- 'A' is replaced by '+'
Substituting these operators into the expression, we get:
\((90 - 9) \div 9 \times 9 + 9 = ?\)
Evaluating the Expression Using Order of Operations
To solve this mathematical expression, we must follow the standard order of operations (often remembered by acronyms like BODMAS or PEMDAS).
- Brackets first
- Orders (powers and square roots)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's evaluate the expression step by step:
Step 1: Solve the operation inside the Brackets.
\(90 - 9 = 81\)
The expression becomes:
\(81 \div 9 \times 9 + 9\)
Step 2: Perform Division and Multiplication from left to right.
First, perform the division:
\(81 \div 9 = 9\)
The expression becomes:
\(9 \times 9 + 9\)
Next, perform the multiplication:
\(9 \times 9 = 81\)
The expression becomes:
\(81 + 9\)
Step 3: Perform Addition and Subtraction from left to right.
Finally, perform the addition:
\(81 + 9 = 90\)
So, the value of the expression \((90 - 9) \div 9 \times 9 + 9\) is 90.
Conclusion
The meaning of '?' in the given equation is 90. This involves decoding the symbols and applying the correct order of operations to evaluate the resulting mathematical expression.
| Original Symbol | Mathematical Operator |
|---|---|
| A | + |
| B | × |
| C | − |
| D | ÷ |
| Step | Expression | Operation | Result |
|---|---|---|---|
| Original | (90 C 9) D 9 B 9 A 9 | Symbol Decoding | \((90 - 9) \div 9 \times 9 + 9\) |
| 1 | \((90 - 9) \div 9 \times 9 + 9\) | Brackets | \(81 \div 9 \times 9 + 9\) |
| 2a | \(81 \div 9 \times 9 + 9\) | Division | \(9 \times 9 + 9\) |
| 2b | \(9 \times 9 + 9\) | Multiplication | \(81 + 9\) |
| 3 | \(81 + 9\) | Addition | \(90\) |
Revision Table: Mathematical Operators and Order
| Operation Type | Operators | Order Rule (BODMAS/PEMDAS) |
|---|---|---|
| Grouping | Brackets ( ), { }, [ ] | Solve first |
| Powers & Roots | Indices (\(x^n\)), Square Roots (\(\sqrt{x}\)) | Solve next |
| Multiplication & Division | ×, ÷ | Solve from left to right |
| Addition & Subtraction | +, − | Solve from left to right |
Additional Information: Decoding and Evaluation Puzzles
Puzzles like this, where symbols represent operations, are common in logical reasoning and quantitative aptitude tests. They require careful attention to the given code and strict application of the order of operations. These puzzles test not just mathematical skills but also pattern recognition and logical deduction.
It's important to remember that multiplication and division have equal priority, and you should perform them in the order they appear from left to right. The same rule applies to addition and subtraction.
Similar Questions
If '+' means 'divided by', '-' means 'add', '×' means 'minus' and '÷' means 'multiplied by', then what will be the value of the following expression:
[{(18 × 16) - (5 ÷ 2)} + (5 - 1)] ÷ 1
Which two numbers from amongst the given options should be interchanged to make the given equation correct?
126 ÷ 23 – 138 ÷ ( 5 × 4 – 6) + 4 = 1
If A denotes '+', B denotes '×', C denotes '-’, and D denotes '÷', then what will be the value of the following expression?
124 C 5 B 23 A 56 D 8 = ?
Which of the following interchange of signs would make the given equation correct?
320 × 4 − 16 ÷ 4 + 2 = 18
Which two numbers from amongst the given options should be interchanged to make the given equation correct?
(63 ÷ 9 + 17) ÷ 11 = 15 – 195 ÷ 17 – 2
Which two symbols from amongst the given options should be interchanged to make the given equation correct?
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If A denotes ‘+’, B denotes ‘×’, C denotes ‘−’, and D denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
(9 A 9 C 55 D 5) B ? = 10 B 3 A 5
Which two numbers from amongst the given options should be interchanged to make the given equation correct?
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Which two numbers from amongst the given options should be interchanged to make the given equation correct?
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In the given question, the statement is followed by two conclusions. Which of the two conclusions is/are true?
Statement: B = T < E ≤ G > F = H > Q
Conclusions:
I. G > Q
II. G > B
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?
21 A 34 C 6 B (72 D 9) A 13 B 1 + (56 D 4) = ?
