In the number 63143214, each odd digit is doubled and 1 is added, and each…

2026

In the number 63143214, each odd digit is doubled and 1 is added, and each even digit is doubled and 3 is subtracted. How many digits repeat in the new number?

  1. A.

    Three

  2. B.

    Two

  3. C.

    One

  4. D.

    Four

Attempted by 9 students.

Show answer & explanation

Correct answer: A

When a digit-transformation rule depends on parity — doubling and adding 1 for each odd digit, doubling and subtracting 3 for each even digit — the number of repeating digits in the result is found by transforming every digit first, then tallying how many times each resulting digit occurs. A digit counts as repeating only when it appears more than once in the transformed number.

  1. Digit 6 (even): 6 × 2 − 3 = 9

  2. Digit 3 (odd): 3 × 2 + 1 = 7

  3. Digit 1 (odd): 1 × 2 + 1 = 3

  4. Digit 4 (even): 4 × 2 − 3 = 5

  5. Digit 3 (odd): 3 × 2 + 1 = 7

  6. Digit 2 (even): 2 × 2 − 3 = 1

  7. Digit 1 (odd): 1 × 2 + 1 = 3

  8. Digit 4 (even): 4 × 2 − 3 = 5

Transformed number: 97357135

Digit

Frequency in transformed number

9

1

7

2

3

2

5

2

1

1

Reading the transformed number 97357135 digit by digit confirms three matching pairs — 7 with 7, 3 with 3, and 5 with 5 — while 9 and 1 each appear only once, so exactly three digits repeat.

Hence, three digits repeat in the new number.

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