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# n is a positive integer.

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n is a positive integer. [#permalink]  24 Feb 2017, 02:37
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Question Stats:

95% (00:17) correct 4% (00:47) wrong based on 24 sessions

n is a positive integer.

 Quantity A Quantity B The remainder when n is divided by 5 The remainder when n + 10 is divided by 5

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: n is a positive integer. [#permalink]  28 Feb 2017, 16:45
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Explanation

Let us rewrite n as 5k + r.

Quantity A becomes 5k + r

Quantity B becomes 5k + r + 10 or 5(k+2) +r

Dividing each by 5 Quantity by 5 and checking remainder

Quantity A: $$k + \frac{r}{5}$$

Quantity B: $$(k+2) +\frac{r}{5}$$

Quantity A has remainder r.

Quantity B has remainder r as well.

Hence both quantities are equal. Thus C is the right option.
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Re: n is a positive integer. [#permalink]  25 Mar 2017, 07:15
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Carcass wrote:

n is a positive integer.

 Quantity A Quantity B The remainder when n is divided by 5 The remainder when n + 10 is divided by 5

Sandy's solution is great, so I won't duplicate it.
Instead, let's solve the question by Plugging in Numbers

Let's see what happens when n = 5.
We get:
Quantity A: The remainder when 5 is divided by 5
Quantity B: The remainder when 5 + 10 is divided by 5

Evaluate to get:
Quantity A: 0
Quantity B: 0
The quantities are EQUAL

Let's see what happens when n = 6.
We get:
Quantity A: The remainder when 6 is divided by 5
Quantity B: The remainder when 6 + 10 is divided by 5

Evaluate to get:
Quantity A: 1
Quantity B: 1
The quantities are EQUAL

Let's see what happens when n = 7.
We get:
Quantity A: The remainder when 7 is divided by 5
Quantity B: The remainder when 7 + 10 is divided by 5

Evaluate to get:
Quantity A: 2
Quantity B: 2
The quantities are EQUAL

Let's see what happens when n = 8.
We get:
Quantity A: The remainder when 8 is divided by 5
Quantity B: The remainder when 8 + 10 is divided by 5

Evaluate to get:
Quantity A: 3
Quantity B: 3
The quantities are EQUAL

Let's see what happens when n = 9.
We get:
Quantity A: The remainder when 9 is divided by 5
Quantity B: The remainder when 9 + 10 is divided by 5

Evaluate to get:
Quantity A: 4
Quantity B: 4
The quantities are EQUAL

And so on.
At this point, it certainly looks like the correct answer is C.
So, let's take it.

[Reveal] Spoiler:
C

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Re: n is a positive integer. [#permalink]  19 Sep 2017, 08:46
What happens if n=1?

Does the math work out to (1/5) so remainder = 4?

Then B would be (11/5) so remainder = 6?

I thought this worked as I remember possibly seeing it on a manhatten prep test?

Thanks!
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Re: n is a positive integer. [#permalink]  20 Sep 2017, 03:01
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clausen8657 wrote:
What happens if n=1?

Does the math work out to (1/5) so remainder = 4?

Then B would be (11/5) so remainder = 6?

I thought this worked as I remember possibly seeing it on a manhatten prep test?

Thanks!

(1/5) remainder = 1 (0 * 5 + 1 =1)

(11/5) also remainder = 1 (2 * 5 + 1 =11)
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Re: n is a postive integer [#permalink]  26 Nov 2017, 12:25
Expert's post
Explanation

This is a classic question that is there to waste your time. Instead to delve into the calculation, observe how n is divided by five and n+10 is divided by five. Actually, they are the same if not for the 10 added. This does not change anything to the result of the two quantities. The remainder is always the same

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Re: n is a positive integer. [#permalink]  27 Nov 2018, 02:16
nice example
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Re: n is a positive integer. [#permalink]  27 Nov 2018, 11:29
**The remainder of any positive integer (n) to m, when n > m is between 0 and m-1

A: The remainder of n to 5 is between 0 and 4
B: The remainder when n+10 is divided by 5 is just the same as the remainder of n to 5, because 10’s remainder to 5 equals to 0.
If we have a+b and we want to calculate the remainder of a+b to c, the remainder will be remainder of a to c plus remainder of b to c, if the result of the summation is bigger than c, again the remainder of summation is calculated to c.

A and B are the same.
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Re: n is a positive integer.   [#permalink] 27 Nov 2018, 11:29
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