If x and y are prime numbers, which of the following CANNOT be the sum of x and y?
A. 5
B. 9
C. 13
D. 16
E. 23
A. 5
B. 9
C. 13
D. 16
E. 23
look at choices; they are a mixture of odd number and even numberoquiella wrote:If x and y are prime numbers, which of the following CANNOT be the sum of x and y?
A. 5
B. 9
C. 13
D. 16
E. 23
lets address the odd choices,
x + y = odd; only works when one of the term is odd and the other is even.
The only even term that is a prime is 2.
Lets substitute 2 for x into the choices
A. 2+y=5; y=3; y is odd and prime, so this choice is elimated
B. 2+y=9; y=7; y is odd and prime, so this choice is elimated
C. 2+y=13; y=11; y is odd and prime, so this choice is elimated
E. 2+y=23; y=21; y is odd but not prime, so this is the answer
We can stop here!
lets address the even choice,
x + y = even; works when both terms are even or both are odd
the only time 2 prime numbers adds to be even is if both numbers are 2; 2+2 is not 16,
therefore numbers are not both even, and are both odd
odd + odd = 16
if the first term is 3, the second term is 13, both are odd and prime so we can eliminate this choice
ans = [spoiler]e
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