Carcass wrote:
If x and y are different prime numbers less than ten, what must be true about the sum of x and y?
A. the sum is even
B. the sum is odd
C. the sum is less than ten
D. the sum is greater than ten
E. the sum is less than 13
APPROACH #1:
The prime numbers less than 10 are: 2, 3, 5 and 7
So, the greatest possible sum of x and y = 5 + 7 = 12, and all other sums are less than 12
Answer: E
APPROACH #2: Use the process of elimination to find the right answer
A. the sum is even
If x = 2 and y = 3, then the sum is odd.
ELIMINATE A.
B. the sum is odd
If x = 5 and y = 3, then the sum is even.
ELIMINATE B.
C. the sum is less than ten
If x = 5 and y = 7, then the sum is greater than 10.
ELIMINATE C.
D. the sum is greater than ten
If x = 2 and y = 3, then the sum is less than 10.
ELIMINATE D.
By the process of elimination, the correct answer is E