How many two-digit numbers have both of their digits odd?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
How many odd digits are there?
2The strategy
Both positions must hold an odd digit. Count how many odd digits are available for the first position and how many for the second, and remember that neither choice uses the other up.
3The full solution
The odd digits are 1, 3, 5, 7 and 9 - five of them. Five choices for each position gives 5 x 5 = 25.
Solution— no shortcut on this one
The odd digits are 1, 3, 5, 7 and 9, so there are five. The first digit must be one of those five, and so must the second - and using one for the first position does not stop it being used again for the second. So the count is 5 x 5 = 25. Note that no odd digit is 0, so the leading-zero problem never arises here. The transferable idea: check whether a choice uses anything up before deciding what to multiply by.
Why this is on the test: Both digits odd is a much stronger condition than the number being odd, and choice D is exactly that confusion.