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
OG QR question 83
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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.
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.