If 'A' denotes 'addition', 'B' denotes 'multiplication', 'C' denotes 'subtraction', and 'D' denotes 'division', then what will be the value of the following expression? 50 D (2 B 5) A 3 B(15 A 12) C 2 B(18 C 15) = ?
80
Evaluating Mathematical Expressions with Symbol Substitution
This problem requires us to substitute specific mathematical operations for given letters in an expression and then evaluate the resulting numerical expression following the standard order of operations.
The given mappings are:
- 'A' denotes 'addition' ($+$)
- 'B' denotes 'multiplication' ($\times$)
- 'C' denotes 'subtraction' ($-$)
- 'D' denotes 'division' ($\div$)
The expression to evaluate is:
50 D (2 B 5) A 3 B (15 A 12) C 2 B (18 C 15)
Step 1: Substitute the Symbols with Operations
Replace each letter with its corresponding mathematical operation:
50 $\div$ (2 $\times$ 5) $+$ 3 $\times$ (15 $+$ 12) $-$ 2 $\times$ (18 $-$ 15)
Step 2: Evaluate the Expression using Order of Operations (BODMAS/PEMDAS)
We follow the order of operations: Brackets first, then Orders (powers and roots), then Division and Multiplication (from left to right), and finally Addition and Subtraction (from left to right).
Evaluate Expressions inside Brackets:
- (2 $\times$ 5) = 10
- (15 $+$ 12) = 27
- (18 $-$ 15) = 3
Substituting these values back into the expression, we get:
50 $\div$ 10 $+$ 3 $\times$ 27 $-$ 2 $\times$ 3
Perform Division and Multiplication (from left to right):
- 50 $\div$ 10 = 5
- 3 $\times$ 27 = 81
- 2 $\times$ 3 = 6
The expression now becomes:
5 $+$ 81 $-$ 6
Perform Addition and Subtraction (from left to right):
- 5 $+$ 81 = 86
- 86 $-$ 6 = 80
The final value of the expression is 80.
Result of the Expression Evaluation
After substituting the operations and following the order of operations, the value of the expression 50 D (2 B 5) A 3 B(15 A 12) C 2 B(18 C 15) is 80.
Revision Table: Symbol Mapping
| Letter | Operation Denoted | Symbol |
|---|---|---|
| A | Addition | $+$ |
| B | Multiplication | $\times$ |
| C | Subtraction | $-$ |
| D | Division | $\div$ |
Additional Information: Order of Operations
The order of operations is a rule used in mathematics to clarify which procedures should be performed first in a given mathematical expression. Common mnemonics include BODMAS and PEMDAS.
- BODMAS: Brackets, Orders (powers, square roots, etc.), Division, Multiplication, Addition, Subtraction.
- PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Division and Multiplication have the same priority and are performed from left to right. Similarly, Addition and Subtraction have the same priority and are performed from left to right.
In this problem, correctly applying the order of operations after substituting the symbols was crucial to arrive at the correct result.
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) = ?
