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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # How many positive integers less than 2*10^4 are there in  Question banks Downloads My Bookmarks Reviews Important topics
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Senior Manager Joined: 20 May 2014
Posts: 282
Followers: 18

Kudos [?]: 50 , given: 220

How many positive integers less than 2*10^4 are there in [#permalink] 00:00

Question Stats: 36% (02:19) correct 63% (02:02) wrong based on 11 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

Kudos for correct solution.
[Reveal] Spoiler: OA Director Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 344  , given: 66

Re: How many positive integers less than 2*10^4 are there in [#permalink]
1
KUDOS
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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