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How many positive integers less than 2*10^4 are there in

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How many positive integers less than 2*10^4 are there in [#permalink] New post 29 Oct 2017, 01:14
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Question Stats:

40% (02:19) correct 60% (01:59) wrong based on 10 sessions
How many positive integers less than 2*10^4 are there in which each digit is a prime number?

(A) 256
(B) 326
(C) 340
(D) 625
(E) 775

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[Reveal] Spoiler: OA
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Re: How many positive integers less than 2*10^4 are there in [#permalink] New post 30 Oct 2017, 08:59
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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
Re: How many positive integers less than 2*10^4 are there in   [#permalink] 30 Oct 2017, 08:59
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How many positive integers less than 2*10^4 are there in

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