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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:

84% (00:22) correct 15% (00:54) wrong based on 38 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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Kudos [?]: 1651 [2] , given: 396

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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Kudos [?]: 1109 [2] , given: 7

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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Joined: 10 Sep 2017
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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!
GMAT Club Legend
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GRE 1: Q167 V156
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Kudos [?]: 1651 [2] , given: 396

Re: n is a positive integer. [#permalink]  20 Sep 2017, 03:01
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Expert's post
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 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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# n is a positive integer.

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