If '$' means 'addition', '@' means 'subtraction', '#' means 'multiplication', and '&' means 'division'. What will be the value of the following expression? 54 & 6 # 2 $ 8 @ 4
Expression Evaluation with Symbol Substitution
The question asks to evaluate an arithmetic expression where symbols represent mathematical operations. We need to substitute the symbols with their corresponding operators and then solve the expression using the order of operations (BODMAS/PEMDAS).
Symbol Mapping
First, let's define the mapping provided:
- $ means addition ($+$)
- $@$ means subtraction ($-$)
- $#$ means multiplication ($*$)
- $&$ means division ($/$)
Expression Transformation
The given expression is: $54 & 6 # 2 $ 8 @ 4$
Substituting the symbols with their operators, we get:
$54 / 6 * 2 + 8 - 4$
Calculation using BODMAS/PEMDAS
We follow the order of operations (Division, Multiplication, Addition, Subtraction):
- Division: Calculate $54 / 6$. $54 \div 6 = 9$ The expression becomes: $9 * 2 + 8 - 4$
- Multiplication: Calculate $9 * 2$. $9 \times 2 = 18$ The expression becomes: $18 + 8 - 4$
- Addition: Calculate $18 + 8$. $18 + 8 = 26$ The expression becomes: $26 - 4$
- Subtraction: Calculate $26 - 4$. $26 - 4 = 22$
Final Result
The value of the expression $54 & 6 # 2 $ 8 @ 4$ is 22.
Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
