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If N is a positive integer, what is the remainder when N is divided by

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Bunuel
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If N is a positive integer, what is the remainder when N is divided by [#permalink] New post   20 Mar 2021, 12:37
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If N is a positive integer, what is the remainder when N is divided by 3?

(1) N + 3 is divisible by 5
(2) N is divisible by 4
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E
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Re: If N is a positive integer, what is the remainder when N is divided by [#permalink] New post   20 Mar 2021, 16:52
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Bunuel wrote:
If N is a positive integer, what is the remainder when N is divided by 3?

(1) N + 3 is divisible by 5
(2) N is divisible by 4


Statement 1:

We may write N as \(N + 3 = 5*i\) where \(i\) is any positive integer. Then \(N = 5*i - 3\) is not always a multiple of 3, so it might be divisible by 3 or not. Insufficient.

Statement 2:

Insufficient.

Combined:

Combined we have \(N = 5*i - 3 = 4*j\). We may plug in a couple \(i\)'s that make N a multiple of 4, and see which N's we can take. \(i = 3\) gives \(N = 12\). The next possible \(i\) is \(i = 7\) which gives \(N = 32\). We can see there are different remainders after dividing by 3. Insufficient.

Ans: E
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Re: If N is a positive integer, what is the remainder when N is divided by [#permalink] New post   20 Mar 2021, 19:26
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Bunuel wrote:
If N is a positive integer, what is the remainder when N is divided by 3?

(1) N + 3 is divisible by 5
(2) N is divisible by 4


(1) N + 3 is divisible by 5
So N will be an integer with units digit as 2 or 7.
N could be be 2, 7, 12, 17, 22, 27, 32....
If 12 or 27, remainder is 0 when divided by 3.
If 2 or 32, remainder is 2.
Insufficient

(2) N is divisible by 4
N could be 0, 4, 8, 12...
Again 12 is divisible by 3, while 4 will leave a remainder of 1.
Insufficient

Combined
12 and 32 are common in the statements.
Both will give different remainders when divided by 3.
Sufficient

E
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Re: If N is a positive integer, what is the remainder when N is divided by [#permalink] New post   21 Mar 2021, 12:20
Question: N>0; n/3, r=?

St1: N+3 = 5k + 0
k=1 n=2, 2/3 gives remainder 2
k=2 n=7 7/3 gives remainder 1
k=3 n=12 12/3 gives remander 0
NS

St2: n=4k +0
k=1 n=4 4/3 -> r=1
k=2 n=8 8/3 -> r=2
NS

Combining not sufficient

Answer E
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gmatclubot
Re: If N is a positive integer, what is the remainder when N is divided by [#permalink]
21 Mar 2021, 12:20
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Bunuel
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