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OG QR question 83

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OG QR question 83

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If k and n are integers, is n divisible by 7?

1) n - 3 = 2k

2) 2k - 4 is divisible by 7.

In the explanation when adding both statements together, I don't see the equation can be expressed as:

n = 2k -4 + 7

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Senior | Next Rank: 100 Posts Default Avatar
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The book does a terrible job explaining the solution.

Basically you need to remember that if two numbers are each multiples of the same number, the sum will also be a multiple of that number.

1) n=2k+3, tells us what n is but doesn't tell us if it is evenly divisible by
7 - INSUF

2) tells us nothing about n - INSUF

1+2)

2k-4 is a multiple of 7 according to #2, and 7 by definition is a multiple of 7, so add the two to rearrange the equation and you get
2k-4+7=2k+3. 2k+3 must now be a multiple of 7 since it is a sum of two numbers that are a multiple of 7. Combine that with statment 1 and we now know that n is a multipe of 7.

FYI you could keep adding any multiples of 7 to 2k-4 and the sum would be a multiple of 7, but since statement 1 makes it only necessary to add 7.

Hope that helps.

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Junior | Next Rank: 30 Posts Default Avatar
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thanks. that makes perfect sense now.

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