If A denotes '+', B denotes '×', C denotes '-', and D denotes '÷', then what will come in place of '?' in the following equation? (51 D 17) A (21 B 9) C 78 A (16 D 4) = ?
118
Understanding the Operator Substitution Problem
This problem requires us to substitute specific mathematical operators for given letters and then evaluate the resulting expression following the standard order of operations (BODMAS/PEMDAS).
Operator Substitutions
The question provides the following substitutions:
- A denotes '+' (Addition)
- B denotes '×' (Multiplication)
- C denotes '-' (Subtraction)
- D denotes '÷' (Division)
The Given Expression
The expression we need to evaluate is:
(51 D 17) A (21 B 9) C 78 A (16 D 4) = ?
Substituting the Operators
Now, let's replace the letters with their corresponding mathematical operators:
$(51 \div 17) + (21 \times 9) - 78 + (16 \div 4) = ?$
Step-by-Step Evaluation using BODMAS/PEMDAS
We follow the BODMAS/PEMDAS rule which dictates the order of operations:
- B/P: Brackets/Parentheses
- O/E: Orders/Exponents
- D/M: Division/Multiplication (from left to right)
- A/S: Addition/Subtraction (from left to right)
Step 1: Evaluate expressions within Parentheses
First, calculate the values inside the parentheses:
- $(51 \div 17) = 3$
- $(21 \times 9) = 189$
- $(16 \div 4) = 4$
The expression now becomes:
$3 + 189 - 78 + 4 = ?$
Step 2: Perform Addition and Subtraction from Left to Right
Now, we perform addition and subtraction operations as they appear from left to right:
- $3 + 189 = 192$
- $192 - 78 = 114$
- $114 + 4 = 118$
So, the final value of the expression is 118.
Summary of Evaluation
Here is a summary of the steps:
| Step | Expression | Operation | Result |
|---|---|---|---|
| Initial Expression | (51 D 17) A (21 B 9) C 78 A (16 D 4) | Substitution | $(51 \div 17) + (21 \times 9) - 78 + (16 \div 4)$ |
| Evaluate Parentheses 1 | $(51 \div 17)$ | Division | 3 |
| Evaluate Parentheses 2 | $(21 \times 9)$ | Multiplication | 189 |
| Evaluate Parentheses 3 | $(16 \div 4)$ | Division | 4 |
| Expression after Parentheses | $3 + 189 - 78 + 4$ | Simplification | $3 + 189 - 78 + 4$ |
| Addition 1 | $3 + 189$ | Addition | 192 |
| Subtraction | $192 - 78$ | Subtraction | 114 |
| Addition 2 | $114 + 4$ | Addition | 118 |
| Final Result | $?$ | Evaluation Complete | 118 |
The value that comes in place of '?' is 118.
Revision Table: Key Concepts in Operator Substitution
| Concept | Description |
|---|---|
| Operator Substitution | Replacing given symbols or letters with standard mathematical operators (+, -, ×, ÷). |
| Mathematical Expression | A combination of numbers, variables, and mathematical operators. |
| Order of Operations (BODMAS/PEMDAS) | Rules defining the sequence for evaluating a mathematical expression to ensure a unique result. Brackets/Parentheses, Orders/Exponents, Division/Multiplication, Addition/Subtraction. |
Additional Information: Solving Mathematical Expressions
Solving mathematical expressions involving multiple operations requires careful application of the order of operations. Failing to follow the correct order can lead to an incorrect result. Parentheses are always evaluated first. Then, exponents or orders are calculated. After that, multiplication and division are performed from left to right. Finally, addition and subtraction are performed from left to right. Practice with different types of expressions and substitutions is key to mastering these problems.
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) = ?
