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If n is a positive integer and r is the remainder when 4 + 7

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Source: — Data Sufficiency |

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by Ian Stewart » Thu May 30, 2019 5:53 am

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If, from Statement 1, n+1 is divisible by 3, then for some integer q, we know n+1 = 3q, and n = 3q - 1.

Substituting "3q-1" for "n" in the expression 4 + 7n, we have

4 + 7n = 4 + 7(3q - 1)
= 4 + 21q - 7
= 21q - 3
= 3(7q - 1)

and since we can factor out a 3, this number is divisible by 3, and we will get a remainder of 0 when we divide it by 3. So Statement 1 is sufficient. Statement 2 is not sufficient, since if n = 21, say, then the expression will not be divisible by 3, but we also know it can be divisible by 3 from our analysis of Statement 1. So the answer is A.
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