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Find the missing rule in the pattern: Input -> Intermediate Value -> Output. The second step is adding 5. Examples: 2->11, 4->17, 6->23. Options: A) +4, B) +8, C) x2, D) x3

Mathematics

ScanSolve AI Answer

Answer

D

Step-by-step solution

3 steps
  1. Analyze the given pattern to find the intermediate values.

    The pattern is: Input →Missing RuleIntermediate Value→+5Output\xrightarrow{\text{Missing Rule}} \text{Intermediate Value} \xrightarrow{+5} \text{Output}.
    We can find the intermediate value by reversing the "+5" operation, which means subtracting 5 from the output.

    • For input 2, the output is 11. Intermediate Value for 2: 11−5=611 - 5 = 6. So, 2→Missing Rule62 \xrightarrow{\text{Missing Rule}} 6.

    • For input 4, the output is 17. Intermediate Value for 4: 17−5=1217 - 5 = 12. So, 4→Missing Rule124 \xrightarrow{\text{Missing Rule}} 12.

    • For input 6, the output is 23. Intermediate Value for 6: 23−5=1823 - 5 = 18. So, 6→Missing Rule186 \xrightarrow{\text{Missing Rule}} 18.

  2. Determine the missing rule based on the input and intermediate values.

    We observe the following transformations:

    2→62 \to 6 4→124 \to 12 6→186 \to 18

    In each case, the intermediate value is obtained by multiplying the input value by 3.

    2×3=62 \times 3 = 6 4×3=124 \times 3 = 12 6×3=186 \times 3 = 18

    Therefore, the missing rule is ×3\times 3.

  3. Select the correct option.

    Comparing our finding with the given options:
    A) +4
    B) +8
    C) ×2\times 2
    D) ×3\times 3
    The correct option is D.

    The final answer is D) ×3\boxed{\text{D) } \times 3}.

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