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# What is the remainder when the positive integer n is divided by 5 ?

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What is the remainder when the positive integer n is divided by 5 ?  [#permalink]

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26 Apr 2019, 02:28
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What is the remainder when the positive integer n is divided by 5 ?

(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.

DS07502.01
OG2020 NEW QUESTION

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Re: What is the remainder when the positive integer n is divided by 5 ?  [#permalink]

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26 Apr 2019, 04:28
1
From S1:

n = 3*4+1
n = 13
Sufficient.
When 13 is divided by 5, the remainder is 3.

From S2:

n/4 = 1
n can be 1, 5, 9....
Insufficient.

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Re: What is the remainder when the positive integer n is divided by 5 ?  [#permalink]

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27 Apr 2019, 07:02
Bunuel wrote:
What is the remainder when the positive integer n is divided by 5 ?

(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.

DS07502.01
OG2020 NEW QUESTION

from given info
#1
When n is divided by 3, the quotient is 4 and the remainder is 1.
n= 13 , remainder divided by 5 ; 3
sufficient
#2
When n is divided by 4, the remainder is 1
n=5,15,25 , we get remainder 0
and for all other values remainder as 1 for n = 9, 21
insufficeint
IMO A
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Re: What is the remainder when the positive integer n is divided by 5 ?  [#permalink]

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27 Apr 2019, 07:09
Bunuel wrote:
What is the remainder when the positive integer n is divided by 5 ?

(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.

DS07502.01
OG2020 NEW QUESTION

We know that $$n$$ is a positive integer. The original question: $$n \bmod 5=?$$

1) We know that $$n=3\cdot 4+1=13$$, so $$n \bmod 5=3$$. Thus, the answer to the original question is a unique value. $$\implies$$ Sufficient

2) We know that $$n=4q+1$$ and can test possible cases. If $$n=1$$, then $$n \bmod 5=1$$. However, if $$n=5$$, then $$n \bmod 5=0$$. Thus, we can't get a unique value to answer the original question. $$\implies$$ Insufficient

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What is the remainder when the positive integer n is divided by 5 ?  [#permalink]

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30 Apr 2019, 08:10
Quote:
What is the remainder when the positive integer n is divided by 5 ?

(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.

This question primarily hinges on our understanding of the relationship between dividend, divisor, quotient, and remainder. If we can either solve for n, or solve for the units digit of n, we will have sufficiency (as divisibility by 5 depends entirely on the units digit). Now we're ready to take a look at our statements!

Statement (1) tells us that "When n is divided by 3, the quotient is 4 and the remainder is 1." If we set this up mathematically using our understanding that the dividend = (divisor)*(quotient) + remainder, we can solve for "n," as n = 3*4 + 1, or 13. If we know "n," we certainly know the remainder when we divide "n" by 5 - in this case, 3. (Sufficient)

With Statement (2), we know that n/4 gives us a remainder of 1, so we know that n = "some multiple of 4, plus 1." However, we can quickly disprove sufficiency, as we could have 4+1 = 5, giving us a remainder of 0, or 8+1 = 9, giving us a remainder of 4. As soon as we can pick permissible values that give us different values for this value Data Sufficiency quesiton, we have disproven sufficiency. (Not Sufficient)

In this case, taking a moment to preempt what we need to have sufficiency, and recognizing that if we're given enough information to solve for "n," we have sufficiency, and that if we are able to quickly choose permissible values for "n" that give us different answers to our value DS question, we can efficiently disprove sufficiency, we are left with (A).
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Re: What is the remainder when the positive integer n is divided by 5 ?  [#permalink]

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30 Apr 2019, 09:39
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Bunuel wrote:
What is the remainder when the positive integer n is divided by 5 ?

(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.

Target question: What is the remainder when the positive integer n is divided by 5 ?

Statement 1: When n is divided by 3, the quotient is 4 and the remainder is 1.
There's a nice rule that says, "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
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

So, from statement 1, we can write: n = (3)(4) + 1 = 13
If n = 13, then we get a remainder of 3 when we divide 13 by 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: When n is divided by 4, the remainder is 1.
We have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Some possible values of n are: 1, 5, 9, 13, 17, . . . etc.
Case a: If n = 1, then we get a remainder of 1 when we divide 1 by 5.
Case b: If n = 5, then we get a remainder of 0 when we divide 5 by 5.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Re: What is the remainder when the positive integer n is divided by 5 ?  [#permalink]

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06 May 2019, 20:15
Bunuel wrote:
What is the remainder when the positive integer n is divided by 5 ?

(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.

DS07502.01
OG2020 NEW QUESTION

Statement One Alone:

When n is divided by 3, the quotient is 4 and the remainder is 1.

We see that n must be 3 x 4 + 1 = 13 and 13/5 = 2 remainder 3.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

When n is divided by 4, the remainder is 1.

Thus, n can be values such as 1, 5, 9, 13…

1/5 = 0 remainder 1, however, 5/5 = 1 remainder 0.

Statement two alone is sufficient to answer the question.

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Re: What is the remainder when the positive integer n is divided by 5 ?  [#permalink]

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16 May 2019, 14:38
Hi All,

We're told that N is a positive integers. We're asked for the remainder when N is divided by 5. This question can be solved with a mix of Arithmetic and TESTing VALUES.

(1) When N is divided by 3, the quotient is 4 and the remainder is 1.

Fact 1 gives us remarkably specific information....
N/3 = 4r1
This outcome can only occur when N = 13, since 13/3 = 4r1. No other value of N fits this information, so we have 13/5 = 2r3 and the answer to the question must be 3.
Fact 1 is SUFFICIENT

(2) When N is divided by 4, the remainder is 1.

Fact 2 isn't quite as 'restrictive' as Fact 1 is. There are lots of different values of N that will fit here:
IF...
N = 1, then 1/4 = 0r1 and the answer to the question is 1/5 = 0r1.... 1
N = 5, then 5/4 = 1r1 and the answer to the question is 5/5 = 1r0.... 0
Fact 2 is INSUFFICIENT

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Re: What is the remainder when the positive integer n is divided by 5 ?   [#permalink] 16 May 2019, 14:38
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