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Printimc
number theory intermediate
Problem
Using the digits 1, 2, 3, 4, 5, 6, 7, and 9, form 4 two-digit prime numbers, using each digit only once. What is the sum of the 4 prime numbers?
(A)
(B)
(C)
(D)
(E)
Solution
Since a multiple-digit prime number is not divisible by either 2 or 5, it must end with 1, 3, 7, or 9 in the units place. The remaining digits given must therefore appear in the tens place. Hence our answer is . (Note that we did not need to actually construct the primes. If we had to, one way to match the tens and ones digits to form four primes is , , , and .) (You could also guess the numbers, if you have a lot of spare time.)
Final answer
E