UKMT - Grey Kangaroo - 2022 - 6 | Exact Science

6

How many positive integers between 100 and 300 have only odd digits?

A 25 B 50 C 75 D 100 E 150

Answer

A

SOLUTIOn

For each digit to be odd, the first digit has to be 1, the second digit can be any one of 1, 3, 5, 7 or 9 and so can the third digit. Hence the number of positive integers between 100 and 300 with only odd digits is 1 × 5 × 5 = 25.

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