grotten wrote:
If the sum of a set of ten different positive prime numbers is an even number, which of the following prime numbers CANNOT be in the set?
A. 2
B. 3
C. 5
D. 7
E. 11
Some important rules:
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN
4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVENThe key concept here is that 2 is the only EVEN prime number. All other primes are ODD.
Since the set contains 10
different prime numbers , there are only two possible cases:
case 1) 2 is in the set of primes
case 2) 2 is NOT in the set of primes
case 1: If 2 IS in the set, then the set contains 9 ODD primes and 1 EVEN prime
In this case, the sum of the 10 primes will be ODD.
However, the question tells us that the sum is EVEN.
So, it CANNOT be the case that 2 is in the set of numbers.
Answer: A
Cheers,
Brent
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