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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 21*4 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

 May 13, 2023
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set the integers equal to x, x+1, x+2, x+3, x+4, x+5, x+6

sum of all integers = 7x+21

21*4 = 84

7x + 21 = 84(x+6)

7x + 21 = 84x + 504

-483 = 77x

x is not an integer, thus there is no solution. However, as I interpreted * to signal multiplication, but the word "times" is written out immediately afterwards, I believe the question is incorrectly formatted.

 May 13, 2023

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