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Delta Key Calculator Pattern

XAT 2023 · Quantitative Ability & Data Interpretation · Easy · Sequences and Series

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Suppose Haruka has a special key Δ\Delta in her calculator called delta key:

Rule 1: If the display shows a one-digit number, pressing delta key Δ\Delta replaces the displayed number with twice its value. Rule 2: If the display shows a two-digits number, pressing delta key Δ\Delta replaces the displayed number with the number sum of two digits.

Suppose Haruka enters the value 1 and then presses delta key Δ\Delta repeatedly. After pressing the key for 68 times, what will be the displayed number?

  1. A.

    7

  2. B.

    4

  3. C.

    10

  4. D.

    2

  5. E.

    8

Answer

A

Explanation

Starting at 1: Press 1: 1×2=21 \times 2 = 2 Press 2: 2×2=42 \times 2 = 4 Press 3: 4×2=84 \times 2 = 8 Press 4: 8×2=168 \times 2 = 16 Press 5: 1+6=71 + 6 = 7 Press 6: 7×2=147 \times 2 = 14 Press 7: 1+4=51 + 4 = 5 Press 8: 5×2=105 \times 2 = 10 Press 9: 1+0=11 + 0 = 1 The cycle repeats every 9 presses. 68=9×7+568 = 9 \times 7 + 5. So after 68 presses, the result corresponds to the 5th press, which is 7.

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