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# If the sum of three different prime numbers is an even number, what is

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Joined: 02 Sep 2009
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If the sum of three different prime numbers is an even number, what is  [#permalink]

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12 Oct 2017, 23:06
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If the sum of three different prime numbers is an even number, what is the smallest of the three?

A. 2
B. 3
C. 5
D. 7
E. It cannot be determined from the information given.

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If the sum of three different prime numbers is an even number, what is  [#permalink]

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13 Oct 2017, 03:58
Bunuel wrote:
If the sum of three different prime numbers is an even number, what is the smallest of the three?

A. 2
B. 3
C. 5
D. 7
E. It cannot be determined from the information given.

If adding three prime numbers, the only way to guarantee an even result is if one of the prime numbers is 2. All other primes are odd.

If all three terms are odd, the sum is odd. If two terms are odd, and one is even, the sum is even. That "Even" must be 2.

2 + 3 + 5 = 10
3 + 5 + 7 = 15
2 + 11 + 19 = 32
7 + 13 + 17 = 37

With addition, an even number of odd terms sums to an even result.*

If there are two, four, or any even number of odd terms, the sum is even.

O + O = E, or

(O + O) + (O + 0) = E + E = E

Then ANY number of evens, added to even, sums to an even result.

Three primes that sum to an even number must therefore be some combination of

(O + O) + E, where
E = 2, the only even prime

1) (O + O) = E, then
2) E + E = E

Answer

*If odd is 2n + 1, then a pair of those terms, added, will pair the "plus 1s." That pairing eliminates the +1 which makes the term odd in the first place, i.e., (+1 +1) = 2
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Re: If the sum of three different prime numbers is an even number, what is  [#permalink]

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13 Oct 2017, 05:13
Ans is A => 2

sum of two prime numbers is always even if 2 is not one of them eg 3+5 =8 , and if 2 is one of them then sum is odd => 2+3 =5

Now there are three prime number whose sum is even => 2 is one of them so that the sum of other two prime number which is even since 2 is not one of them will be prime, when added to 2 gives => even

2+ Even = even

2 is answer.
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Re: If the sum of three different prime numbers is an even number, what is  [#permalink]

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16 Oct 2017, 16:09
Bunuel wrote:
If the sum of three different prime numbers is an even number, what is the smallest of the three?

A. 2
B. 3
C. 5
D. 7
E. It cannot be determined from the information given.

In order for the sum of 3 numbers to be even, we either need to sum 3 even numbers or 1 even number and 2 odds. Since there is only one even prime number, 2, the smallest number in the sum must be 2.

Answer: A
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Re: If the sum of three different prime numbers is an even number, what is  [#permalink]

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28 Jan 2019, 17:24
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Re: If the sum of three different prime numbers is an even number, what is   [#permalink] 28 Jan 2019, 17:24
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# If the sum of three different prime numbers is an even number, what is

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