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MathematicsArithmetic
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Find the value of 50тИТ[30тИТ(80├╖4тИТ(10тИТ12├╖4)├╖7)]50 - [30 - (80 \div 4 - (10^{-12} \div 4) \div 7)]50тИТ[30тИТ(80├╖4тИТ(10тИТ12├╖4)├╖7)].

A

21

B

23

C

25

D

27

Correct Answer

тЪЩя╕П TE тАв Technical BODMAS RuleMathematicsArithmetic
Option A

21

Quick Summary:

Work from the innermost parentheses outward; perform the operations inside the smallest brackets first, keeping track of the signs to prevent errors.

ЁЯУРMAMath SolutionBODMAS Rule
ЁЯУЛ Given

A mathematical expression: 50 - [30 - (80 / 4 - (10тИТ12(10^{-12}(10тИТ12 / 4) / 7)]

ЁЯФв Formula Used

BODMAS:┬аBracket,┬аOf,┬аDivision,┬аMultiplication,┬аAddition,┬аSubtraction\text{BODMAS: Bracket, Of, Division, Multiplication, Addition, Subtraction}BODMAS:┬аBracket,┬аOf,┬аDivision,┬аMultiplication,┬аAddition,┬аSubtraction

тЪб Exam Hall Shortcut / Speed Trick

Work from the innermost parentheses outward; perform the operations inside the smallest brackets first, keeping track of the signs to prevent errors.

тЪая╕П Common Student Trap / Pitfall

A common mistake is incorrectly evaluating the order inside the innermost parentheses, specifically performing subtraction before division (i.e., (10тБ╗┬╣┬▓)/4 instead of 10-(12/4)).

ЁЯУК Diagram / Illustration
BODMAS Calculation: 50 - [30 - (80 ├╖ 4 - (10 - 12 ├╖ 4) ├╖ 7)] 1 Innermost Parenthesis (10 - 12 ├╖ 4) = (10 - 3) = 7 2 Middle Bracket (80 ├╖ 4 - 7 ├╖ 7) = (20 - 1) = 19 3 Square Bracket [30 - 19] = 11 4 Final Result 50 - 11 = 39 Final Value: 39
ЁЯФв Step-by-Step Solution
1

Solve innermost parenthesis

Evaluate the innermost parenthesis by first performing the division inside it: 12├╖4=312 \div 4 = 312├╖4=3, then subtract: 10тИТ3=710^{-3} = 710тИТ3=7.

10тИТ12├╖4=10тИТ3=710^{-12} \div 4 = 10^{-3} = 710тИТ12├╖4=10тИТ3=7

2

Simplify the next level of brackets

Substitute the result back into the middle bracket: (80├╖4тИТ7├╖7)(80 \div 4 - 7 \div 7)(80├╖4тИТ7├╖7). First, 80├╖4=2080 \div 4 = 2080├╖4=20 and 7├╖7=17 \div 7 = 17├╖7=1. Then, subtract: 20тИТ1=1920 - 1 = 1920тИТ1=19.

80├╖4тИТ7├╖7=20тИТ1=1980 \div 4 - 7 \div 7 = 20 - 1 = 1980├╖4тИТ7├╖7=20тИТ1=19

3

Calculate the outer square bracket

Substitute 19 into the outer bracket: 30тИТ19=1130 - 19 = 1130тИТ19=11.

30тИТ19=1130 - 19 = 1130тИТ19=11

4

Final subtraction

Subtract the result of the brackets from 50: 50тИТ11=3950 - 11 = 3950тИТ11=39.

50тИТ11=3950 - 11 = 3950тИТ11=39

тЬЕ

There appears to be a mismatch between the standard BODMAS evaluation and the provided option. Following the correct order of operations, the result is 39. Given the options provided, if forced to check the expression logic 50тИТ[30тИТ(20тИТ1)]=50тИТ11=3950 - [30 - (20 - 1)] = 50 - 11 = 3950тИТ[30тИТ(20тИТ1)]=50тИТ11=39.

Core Concepts Used
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Order of operations (BODMAS) Algebraic simplification Parentheses management
ЁЯТб EXAM TIP

This topic is foundational for Data Interpretation and number series questions where strict order of operations is required to get the correct tabular value.

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