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?
- A.
Three
- B.
Two
- C.
One
- 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.
Digit 6 (even): 6 × 2 − 3 = 9
Digit 3 (odd): 3 × 2 + 1 = 7
Digit 1 (odd): 1 × 2 + 1 = 3
Digit 4 (even): 4 × 2 − 3 = 5
Digit 3 (odd): 3 × 2 + 1 = 7
Digit 2 (even): 2 × 2 − 3 = 1
Digit 1 (odd): 1 × 2 + 1 = 3
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.