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value of r?

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by sanju09 » Wed Apr 08, 2009 4:40 am
If n is a positive integer and r is the remainder when 4 + 7 n is divided by 3, what is the value of r?

(1) n + 1 is divisible by 3.

(2) n > 20.



OA A
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by mals24 » Wed Apr 08, 2009 5:03 am
question can be solved in 2 ways

1. Plug in values

St 1. n+1 is divisible by 3

Let n = 2, 5 or 8

when n = 2
4 + 7n = 18; r = 0

when n = 5
4 + 7n = 39; r = 0

when n = 8
4 + 7n = 60; r = 0
SUFF

St 2: n>20
Insuff

Answer is A

2. Algebraically

St 1: n+1 is divisible by 3

n+1 = 3b (where 'b' is a number which when multiplied with 3 gives n+1)
n = 3b-1

Substitute in 4+7n
= 4+7(3b-1)
= 4+21b-7
= 21b-3
= 3(7b-1) --> when divided by 3 gives r = 0

Answer is A
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