BTGmoderatorDC wrote: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
The following codes will yield a valid transpose:
01, 02, 03 --> tranposes 10, 20, 30
10, 11, 12, 13 --> transposes 01, 11, 21, 31
20, 21, 22 --> transposes 02, 12, 22
30, 31 --> tranposes 03, 13
Total ways = 12
Since 12 of the 31 codes will yield a valid transpose, the number that will NOT yield a valid transpose = 31-12 = 19
The correct answer is
D.
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