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Difficulty: MediumSimplification and BODMAS Rule
What is the simplified numerical value of the following mathematical expression when evaluated strictly according to the VBODMAS rule?
40% of 150−[16+{20÷(8.5−3.1+1.4‾)}]40\% \text{ of } 150 - \left[ 16 + \left\{ 20 \div \left( 8.5 - \overline{3.1 + 1.4} \right) \right\} \right]
  1. 39Answer
  2. B
    51
  3. C
    49
  4. D
    40

Answer

39
Evaluating strictly by VBODMAS priority: first the vinculum yields 4.5, then the round bracket gives 8.5 - 4.5 = 4, then division yields 20 ÷ 4 = 5, followed by square bracket addition 16 + 5 = 21. Finally, subtracting 21 from 40% of 150 (which is 60) gives 60 - 21 = 39.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{3.1 + 1.4} = 4.5
The vinculum has the highest priority and must be evaluated first.
2
Evaluate the terms inside the round brackets
8.5 - 4.5 = 4
The next priority is resolving the innermost parentheses.
3
Perform division inside the curly brackets
20÷4=520 \div 4 = 5
Inside curly brackets, division takes precedence over addition.
4
Evaluate the terms inside the square brackets
16 + 5 = 21
Resolve the outer square bracket by adding the terms.
5
Calculate the percentage term
40\% \text{ of } 150 = \frac{40}{100} \times 150 = 60
'Of' represents multiplication in percentage operations.
6
Perform final subtraction
60 - 21 = 39
Subtract the total bracket value from the percentage calculation.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
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Topics

Simplification and BODMAS Rule

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