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13 Oct 2017, 00:06
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
89% (00:37) correct
11%
(00:44)
wrong
based on 139
sessions
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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.
A. 2
B. 3
C. 5
D. 7
E. It cannot be determined from the information given.
13 Oct 2017, 04:58
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Bunuel
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
13 Oct 2017, 06:13
Kudos
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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.
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.
