2002 AMC 10A Problem 15

Question

The digits

1,

2,

3,

4,

5,

6,

7,

and

9

are used to form four two-digit prime numbers, with each digit used exactly once. What is the sum of these four primes?

150

160

170

180

190

A two-digit prime cannot end in

2,

4,

5,

or

6

Those four digits must therefore be the tens digits

A two-digit prime cannot end in

2,

4,

5,

or

6,

so these four are the tens digits and

1,

3,

7,

and

9

are the units digits.

The sum is

10(2+4+5+6)

+(1+3+7+9)

=170+20=190.

One valid set is

\{23,47,59,61\}.

Thus, the correct answer is E.

Problem 15 in other years