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If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?

1) n+1 is divisible by 3

2) n > 20

A.

1: n+1 = 3k, where k is an integer. so if n is divided by 3, the reminder is 2. then when 7n is divided by 3, reminder is 2. so 2+4 is 6. then r 0. 2: n > 20 tells nothing. nsf.

everything is correct, just wanted to add that (4+7n)/3=4/3+7n/3=4/3+2

If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?

1) n+1 is divisible by 3

2) n > 20

alternatively:

1: n + 1 = 3k where k is an integer. 4 + 7n = 1+1+1+1+n+n+n+n+3n = 4(1+n) + 3n

in the above expression, 4(1+n) is divisible by 3, r is 0 for this one. 3n is less than 3(n+1) or (3n + 3) by 3. if n+1 is divisible by 3, then (3n+3) is also divisibly by 3. also divisibly by 3 is any addition or substraction of any value that is multiple of 3.

so (3n + 3) - 3 = 3n, whcih is also divisibly by 3. so r = 0.

2: n > 20 doesnot tell much about its divisibility by 3.
_________________

If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?

1) n+1 is divisible by 3

2) n > 20

A.

1: n+1 = 3k, where k is an integer. so if n is divided by 3, the reminder is 2. then when 7n is divided by 3, reminder is 2. so 2+4 is 6. then r 0. 2: n > 20 tells nothing. nsf.

everything is correct, just wanted to add that (4+7n)/3 = 4/3 + 7n/3 = 4/3 + 2

check again the highlighted part, whcih is not correct and should be (4/3 + 2/3), above.
_________________