How many positive even integers less than 100 contain digits 4 or 7?
A. 16
B. 17
C. 18
D. 19
E. 20
B. 17
C. 18
D. 19
E. 20
There are 2 one-digit numbers {4 and 7 }. One of them is even.
For the two-digit numbers (a and b):
Numbers that have 4 or 7 for the first digit (4b, 7b).
Since even numbers must end by even digit, b could be {0, 2, 4, 6 or 8}. There are 2 × 5 = 10 such numbers.
Since even numbers must end by even digit, b could be {0, 2, 4, 6 or 8}. There are 2 × 5 = 10 such numbers.
Numbers that have 4 as the second digit (a4). These are all even.
The first digit, a, can be anything except 0. So there are 1 × 9 = 9 numbers.
Numbers that have 7 as the second digit (a4, b7) and these are all odd.
Note, that we’ve counted twice the two-digit numbers that have 4 as the second digit and 4 or 7 as the first (44, 74).
Therefore we have 1 + 10 + 9–2 = 18 possible variants overall.
C
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