题目信息
A certain online form requires a 2-digit code for the day of the month to be entered into one of its fields, such as 04 for the 4th day of the month. The code is valid if it is 01, 02, 03, …, 31 and not valid otherwise. The transpose of a code xy is yx. For example, 40 is the transpose of 04. If N is the number of valid codes having a transpose that is not valid, what is the value of N ?
A:12
B:13
C:18
D:19
E:20
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正确答案：
D:19
Arithmetic Operations with integers
It will be quicker to count the number of valid codes whose transposes are valid codes, and then subtract the result from 31 (the number of valid codes) to obtain the value of N.
Three such codes begin with 0: 01, 02, 03. The rest are such that their transposes are invalid codes.
Four such codes begin with 1: 10, 11, 12, 13. The rest are such that their transposes are invalid codes.
Three such codes begin with 2: 20, 21, 22. The rest are such that their transposes are invalid codes.
Two such codes begin with 3: 30, 31. The rest are invalid codes.
Therefore, the total number of valid codes whose transposes are valid codes is 3 + 4 + 3 + 2 = 12, and hence the total number of valid codes whose transposes are not valid is 31 − 12 = 19.
The correct answer is D.
It will be quicker to count the number of valid codes whose transposes are valid codes, and then subtract the result from 31 (the number of valid codes) to obtain the value of N.
Three such codes begin with 0: 01, 02, 03. The rest are such that their transposes are invalid codes.
Four such codes begin with 1: 10, 11, 12, 13. The rest are such that their transposes are invalid codes.
Three such codes begin with 2: 20, 21, 22. The rest are such that their transposes are invalid codes.
Two such codes begin with 3: 30, 31. The rest are invalid codes.
Therefore, the total number of valid codes whose transposes are valid codes is 3 + 4 + 3 + 2 = 12, and hence the total number of valid codes whose transposes are not valid is 31 − 12 = 19.
The correct answer is D.
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