SOLUTION: Let X be a four-digit positive integer such that the unit digit of X is prime and the product of all digits of X is also prime. How many such integers are possible? (1) 4

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Question 1011744: Let X be a four-digit positive integer such that the unit digit of X is prime and the product of all digits of X is also prime. How many such integers are possible?
(1) 4 (2) 8 (3) 12 (4) 24 (5) None of the above
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Since the units digit is prime, all the other digits must be 1s,
because if any of them weren't 1 the product would not be prime. 

The units digit can only be 2,3,5, or 7, since they are the only
digits that are prime,  so there are four,

1112, 1113, 1115, 1117.  

Edwin