Bunuel wrote:

How many three-digit numbers contain three primes that sum to an even number?

A. 27

B. 28

C. 54

D. 55

E. 64

The four single digit prime numbers are 2,3,5 and 7.

a) If we take these numbers in groups of 3s (remember the sum should be even) :

1) 2,3,5 - 6 possible numbers

2) 2,5,7 - 6 possible numbers

3) 2,3,7 - 6 possible numbers

All the above combinations will give even numbers upon adding the three digits of the number.

Hence total 6 * 3 = 18 possibilities.

b) Now since we need '2' to be present out of the three digits to keep the sum even, keep '2' and repeat the remaining primes, i.e. 233, 255, 277

Each of these three numbers can be presented in 3 ways.

Now total possibilities = 18 + 9 = 27

c) Moreover 222 will also give an even number when the digits are summed up.

Therefore total possibilities = 27+1 = 28

Answer : B