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If 1 is added to each odd digit and 2 is subtracted from each even digit in the number 7381564, how many digits will appear more than once in the new number thus formed?
Three
One
None
Two
Three
Map the odd/even rules first, then count the frequency of each digit in the resulting sequence by scanning left to right.
Map the odd/even rules first, then count the frequency of each digit in the resulting sequence by scanning left to right.
Apply Transformation Rules
Original digits: 7, 3, 8, 1, 5, 6, 4. Rules: Odd тЖТ Add 1, Even тЖТ Subtract 2. 7(O) тЖТ 8, 3(O) тЖТ 4, 8(E) тЖТ 6, 1(O) тЖТ 2, 5(O) тЖТ 6, 6(E) тЖТ 4, 4(E) тЖТ 2.
Construct Transformed Number
The new number is 8 4 6 2 6 4 2.
Count Frequencies
Counting digits: 8 appears 1 time; 4 appears 2 times; 6 appears 2 times; 2 appears 2 times. The digits 4, 6, and 2 appear more than once.
B: Incorrect, 1 is too low as there are three digits repeating. C: Incorrect, None implies zero repeats, but 4, 6, and 2 repeat. D: Incorrect, 2 is less than the actual count of three.
A is correct because the transformation results in the sequence 8, 4, 6, 2, 6, 4, 2 where digits 4, 6, and 2 each appear twice, totaling three such digits.
Always list out the transformed digits explicitly to avoid missing duplicates in longer sequences.
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