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When a positive integer n is divided by 7, what is the remainder?

1) When n-294 is divided by 7, the remainder is 3 2) n-3 is divisible by 7

Target question:What is the remainder when positive integer n is divided by 7?

Statement 1: When n-294 is divided by 7, the remainder is 3 ASIDE: There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2

The statement tells us that when n - 294 is divided by 7, the remainder is 3 So, using the above rule, we can say that: n - 294 = 7k + 3, for some integer k. Take n - 294 = 7k + 3 and... ...add 294 to both sides to get: n = 7k + 294 + 3 [you'll see why I wrote the right side this way] Since 294 = (7)(42), we can write: n = 7(k + 42) + 3 This tells us that n is 3 GREATER THAN some multiple of 7. So, if we divide n by 7, the remainder will be 3 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n-3 is divisible by 7 In other words, n-3 = 7j for some integer j. If we add 3 to both sides we get: n = 7j + 3 This tells us that n is 3 GREATER THAN some multiple of 7. So, if we divide n by 7, the remainder will be 3 Since we can answer the target question with certainty, statement 2 is SUFFICIENT

==> In the original condition, the answer is highly likely to be D since there is 1 variable(n), and it becomes 1)=2) so the remainder of both is 3, hence unique, and suffi. The answer is D. Answer: D

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Re: When a positive integer n is divided by 7, what is the remainder? [#permalink]

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17 Nov 2017, 03:11

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