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Brandon spends his afternoon picking apples from an orchard.  He notices that if he groups the apples he picked by fives, six, or sevens, then he ends up with $1$ left over.  If he groups by eights, he has $1$ left over.  If Brandon knows that he picked between $1000$ and $2000$ apples, how many did he pick?

 Jul 4, 2024
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Brandon spends his afternoon picking apples from an orchard.  He notices that if he groups the apples he picked by fives, six, or sevens, then he ends up with $1$ left over.  If he groups by eights, he has $1$ left over.  If Brandon knows that he picked between $1000$ and $2000$ apples, how many did he pick?   

 

I multiplied 5 • 6 • 7 • 8 and got 1680.  Then I added 1 to it.   

 

                                              Brandon picked 1681 apples   

 

check answer   

                                              1681 / 5  =  335 R 1   

                                              1681 / 6  =  280 R 1   

                                              1681 / 7  =  240 R 1   

                                              1681 / 8  =  210 R 1   

.

 Jul 4, 2024

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