Re: How many positive integers less than 2*10^4 are there in
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30 Oct 2017, 08:59
The upper bound of our set is 2*10^4 = 20,000. Thus, the highest number in the set is 19,999. The problem is that for a 5-digit number to be less than 20,000, the ten-hundredths digit must be 1 and 1 is not a prime number. Thus, we must move down our boundary to 9,999, 4-digit number.
Then, the prime numbers made of one digit are 2, 3, 5, 7. Thus they are 4. Thus, 4-digit numbers made of prime number digits are 4*4*4*4 = 256 because each digit can assume four values and they can be repeated. Then, 3-digit numbers are 4*4*4 = 64, 2-digit numbers are 4*4 = 16 and 1-digit number are 4.
Summing up, we get 256+64+16+4 = 340. Answer C