Hi All,
We're told that we have four INTEGERS. We're asked if the sum of those four integers is EVEN. This is a YES/NO question and can be solved with either Number Property rules or TESTing VALUES.
(1) Two of the integers are ODD and two are EVEN.
Fact 1 gives us enough information to deal with some specific Number Properties.
Adding two ODD numbers will give us a sum that is EVEN (for example, 3+5 = 8)
Adding two EVEN numbers will give us a sum that is EVEN (for example, 2+4 = 6)
Thus, adding two ODDs and two EVENs will give us EVEN+EVEN = EVEN. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
(2) The average (arithmetic mean) of the four integers is an integer.
Fact 2 references the 'Average Formula', so we should think in those terms. If we refer to the values as A, B, C and D, we can set up an average as:
(A+B+C+D)/4 = Integer
(A+B+C+D) = (4)(Integer)
From this equation, we know that the sum of the four integers will be 4 times an integer. Multiplying ANY integer by an EVEN number will give us a product that is EVEN. For example:
4(-1) = -4
4(0) = 0
4(1) = 4
4(2) = 8
4(3) = 12
Etc.
Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer:
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Rich
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