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Which two numbers should be interchanged to make the following equation correct? 58 + (36× 4)÷ 3 + 6× 8 −12 = 86 (Note: Interchange should be done of the entire number and not individual digits of a given number.)
12 and 8
36 and 12
3 and 6
4 and 3
36 and 12
Focus on the division operator first. Since 36 / 3 is an integer, swapping numbers should maintain this divisibility to avoid fractions if the result is a whole number.
Focus on the division operator first. Since 36 / 3 is an integer, swapping numbers should maintain this divisibility to avoid fractions if the result is a whole number.
Analyze the original equation
Equation: 58 + (36 × 4) ÷ 3 + 6 × 8 - 12 = 86. Following BODMAS: 58 + (144 ÷ 3) + 48 - 12 = 58 + 48 + 48 - 12 = 142. This does not equal 86.
Apply Interchange (36 and 12)
Replace 36 with 12 and 12 with 36: 58 + (12 × 4) ÷ 3 + 6 × 8 - 36 = 86.
Calculate using BODMAS
Solve brackets and division: 58 + (48 ÷ 3) + 48 - 36 = 58 + 16 + 48 - 36. Addition and subtraction: 74 + 48 - 36 = 122 - 36 = 86. The result 86 matches the target value.
A: Swapping 12 and 8 gives 58 + 48 + 612 - 8 = 158!= 86. C: Swapping 3 and 6 gives 58 + (364)/6 + 38 - 12 = 58+24+24-12 = 94!= 86. D: Swapping 4 and 3 gives 58 + (363)/4 + 6*8 - 12 = 58+27+48-12 = 121!= 86.
B is correct because interchanging 36 and 12 transforms the equation to 58 + (12 × 4) ÷ 3 + 6 × 8 - 36, which correctly evaluates to 86.
In arithmetic operator or number interchange questions, always test options that maintain integer division first, as this often leads to the correct result faster.
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