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English and Logical Reasoning Prep Guide
Exam
English and Logical Reasoning Prep Guide
Subject
Logical Reasoning
Chapter
Mathematical Operations

English and Logical Reasoning Prep Guide · Logical Reasoning · Mathematical Operations

Which two numbers should be interchanged to make the given equation...

Which two numbers should be interchanged to make the given equation correct? (21 \times 4+(84 \div 7) \times 2-15 \times 5+42=105) (Note: Interchange should be done of entire number and not individual digits of a given number.)

Options

  1. A4 and 2
  2. B84 and 42
  3. C4 and 5
  4. D7 and 21

Correct answer

B. 84 and 42

Step-by-step solution

Given equation: (21 \times 4+(84 \div 7) \times 2-15 \times 5+42=105) Let's check each option one by one. Option 1) 4 and 2 Given: (21 \times 4+(84 \div 7) \times 2-15 \times 5+42=105) After interchanging the numbers we get; (→21×2+(84÷7)×4−15×5+42=105→42+12×4−15×5+42=105→42+48−75+42=105→132−75=105→57≠105\begin{aligned} & \rightarrow 21 \times 2+(84 \div 7) \times 4-15 \times 5+42=105 \\ & \rightarrow 42+12 \times 4-15 \times 5+42=105 \\ & \rightarrow 42+48-75+42=105 \\ & \rightarrow 132-75=105 \\ & \rightarrow 57 \neq 105 \end{aligned}) Option 2) 84 and 42 Given: (21 \times 4+(84 \div 7) \times 2-15 \times 5+42=105) After interchanging the numbers we get; (→21×4+(42÷7)×2−15×5+84=105→21×4+6×2−15×5+84=105→84+12−75+84=105→180−75=105→105=105\begin{aligned} & \rightarrow 21 \times 4+(42 \div 7) \times 2-15 \times 5+84=105 \\ & \rightarrow 21 \times 4+6 \times 2-15 \times 5+84=105 \\ & \rightarrow 84+12-75+84=105 \\ & \rightarrow 180-75=105 \\ & \rightarrow \mathbf{1 0 5}=\mathbf{1 0 5} \end{aligned}) Option 3) 4 and 5 Given: (21 \times 4+(84 \div 7) \times 2-15 \times 5+42=105) After interchanging the numbers we get; (→21×5+(84÷7)×2−15×4+42=105→21×5+12×2−15×4+42=105→105+24−60+42=105→171−60=105→111≠105\begin{aligned} & \rightarrow 21 \times 5+(84 \div 7) \times 2-15 \times 4+42=105 \\ & \rightarrow \mathbf{2 1} \times 5+\mathbf{1 2} \times \mathbf{2}-\mathbf{1 5} \times \mathbf{4}+42=105 \\ & \rightarrow \mathbf{1 0 5}+\mathbf{2 4}-60+\mathbf{4 2}=105 \\ & \rightarrow 171-60=105 \\ & \rightarrow 111 \neq 105 \end{aligned}) Option 4) 7 and 21 Given: (21 \times 4+(84 \div 7) \times 2-15 \times 5+42=105) After interchanging the numbers we get; (→7×4+(84÷21)×2−15×5+42=105→7×4+4×2−15×5+42=105→28+8−75+42=105→78−75=105→3≠105\begin{aligned} & \rightarrow 7 \times 4+(84 \div 21) \times 2-15 \times 5+42=105 \\ & \rightarrow 7 \times 4+4 \times 2-15 \times 5+42=105 \\ & \rightarrow \mathbf{2 8 + 8}-75+42=105 \\ & \rightarrow 78-75=105 \\ & \rightarrow 3 \neq 105 \end{aligned}) Hence, the correct answer is "Option 2".
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