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Question 1163970: Find all sets of four consecutive even integers whose sum is between 595 and 606
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Using algebra to solve the problem might be a good exercise in formal mathematics.... But this problem is far more easily solved by logical reasoning and a bit of basic arithmetic.
600/4 = 150; so the four even numbers should be close to 150. Find the sequences that satisfy the condition by trial and error.
144+146+148+150 = 588 too small
The sum of the "next" sequence of 4 even numbers will be 8 greater than that (because each of the four numbers in the sequence is increased by 2). So we can get the sums of the "next" sequences of four even numbers without adding the numbers themselves.
146+...+152 = 588+8 = 596 good
148+...+154 = 596+8 = 604 good
Obviously the "next" sequence, starting with 150, will have a sum that is too large.
ANSWER: There are two sets that satisfy the conditions:
146+148+150+152 = 596
148+150+152+154 = 604
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