SOLUTION: 1) When is the sum of any three consecutive numbers odd? when is it even? 2)I am a 2-digit prime number. the sum of my digits is 5, and the difference between them is 3. What nu

Question 94158: 1) When is the sum of any three consecutive numbers odd? when is it even?
2)I am a 2-digit prime number. the sum of my digits is 5, and the difference between them is 3. What number am I?
Please help me answer these questions
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
1) The sum of three consecutive numbers is odd when the first of these three numbers is even. (8+9+10 = 27)
The sum of three consecutive numbers is even when the first of these three numbers is odd. (15+16+17 = 48)
2) Let x = the tens digit and y = the units digit, then:
x+y = 5
x-y = 3 or x = y+3 Substitute into the above equation.
y+3+y = 5
2y+3 = 5
2y = 2
y = 1 This is the units digit.
x = y+3
x = 1+3 = 4 This is the tens digit.
The number is 41, a prime number.

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