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

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When a positive integer n is divided by 7, what is the remainder?  [#permalink]

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New post 28 Sep 2016, 04:00
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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

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When a positive integer n is divided by 7, what is the remainder?  [#permalink]

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New post 28 Sep 2016, 06:52
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MathRevolution wrote:
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


This is how I tried

We have let n be positive integer

n = 7q+x and here x is the reminder.

Stat 1: n-294 = 7q+3

n = 7q+297

now when n is divided by 7 then we get 3 as reminder (297/7 = 3 reminder)...Sufficient.

Stat 2: n-3 = 7q => n = 7q+3.

Now n divided by 7 , we get 3 as reminder...Sufficient.

Option D.
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Re: When a positive integer n is divided by 7, what is the remainder?  [#permalink]

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New post 28 Sep 2016, 13:36
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MathRevolution wrote:
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

Answer =

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Re: When a positive integer n is divided by 7, what is the remainder?  [#permalink]

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New post 30 Sep 2016, 07:45
==> 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

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Re: When a positive integer n is divided by 7, what is the remainder?  [#permalink]

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New post 22 Jan 2019, 15:49
MathRevolution wrote:
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


First 7k=multiple of 7 for k>=0

(1) Sufficient

n-294=7k+3
n=7k+(42)(7)+3
n=7(k+42)+3 --> multiple of 7, plus 3. The reminder is 3

(2) Sufficient

n-3=7k
n=7k+3 --> multiple of 7, plus 3. The reminder is 3

Answer (D)
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Re: When a positive integer n is divided by 7, what is the remainder?   [#permalink] 22 Jan 2019, 15:49
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