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Question 505842: If the sum of 5 consecutive even integers is equal to the product, what is the greatest of the 5 integers?
4 10 14 16 20
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Sometimes on multiple choice tests it is quicker and easier to find the correct answer by trying all the possible choices you are given to find which one of the possible answers satisfies the problem. Otherwise you can get stuck or confused while trying to develop some equation or equations that will lead to a solution.
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For this problem you are given 5 possible answers for the greatest integer in a series of 5 consecutive even integers. From these given possibilities for the 5 greatest even integers we can tell that the series are as follows:
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I. If the greatest even integer is 4 the series is -4, -2, 0, +2, +4
II. If the greatest even integer is 10 the series is 2, 4, 6, 8, 10
III. If the greatest even integer is 14 the series is 6, 8, 10, 12, 14
IV. If the greatest even integer is 16 the series is 8, 10, 12, 14, 16
V. If the greatest even integer is the series is 12, 14, 16, 18, 20
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Notice that for II, III, IV, and V the sums of each series are much less than the product of even the last two numbers in each series.
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For example, in II the sum of the terms in the series is 30. The product of the last two terms is 80, and it would only get bigger by multiplying 6 then 4 and then 2. III, IV, and V can be evaluated in the same way and you will find for each series the sum of the 5 terms in the series does not equal the product of the same 5 terms. Therefore, these 4 possible answers can be eliminated.
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But for series I, the product of the five terms is zero (because of the multiplication by zero which is one of the terms) and the sum is also zero because the positive terms are canceled or offset by the corresponding negative terms.
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So the answer to this problem is the first choice. The answer is 4.
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Hope this helps you to understand this way of finding the solution.
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