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# If a certain positive integer is divided by 9, the remainder

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Director
Joined: 29 Nov 2012
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If a certain positive integer is divided by 9, the remainder [#permalink]

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19 Jan 2013, 00:28
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If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?

(1) If the integer is divided by 45, the remainder is 30
(2) The integer is divisible by 2

[Reveal] Spoiler:
info we have n=9k+3

statement 1 n=45k+30 >>> 5(9k+6)

how is this sufficient?

9k+6 and 9k+3 are not the same.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 19 Jan 2013, 05:21, edited 1 time in total.
Edited the question and the tags.
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Re: If a certain positive integer is divided by 9, the remainder [#permalink]

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19 Jan 2013, 00:46
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fozzzy wrote:
If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?
1. If the integer is divided by 45, the remainder is 30
2. The integer is divisible by 2

info we have n=9k+3

statement 1 n=45k+30 >>> 5(9k+6)

how is this sufficient?

9k+6 and 9k+3 are not the same.

Actually n is 45L + 30 , not 45k + 30.

45L + 30 = 15(3L + 2). Since L is an integer, this value is divisible by 5. The remainder will be 0. We do not even need the first part of the question statement. A alone is sufficient to answer the question.
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Re: If a certain positive integer is divided by 9, the remainder [#permalink]

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19 Jan 2013, 00:58
but don't we need to test values that satisfy both equations?
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Re: If a certain positive integer is divided by 9, the remainder [#permalink]

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19 Jan 2013, 01:50
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Statement A openly tells us that the number is a multiple of 5. So regardless of what the number is, when we divide that number by 5, the remainder is going to be 0. We do not have to find the number itself.
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Re: If a certain positive integer is divided by 9, the remainder [#permalink]

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19 Jan 2013, 01:56
MacFauz wrote:
Statement A openly tells us that the number is a multiple of 5. So regardless of what the number is, when we divide that number by 5, the remainder is going to be 0. We do not have to find the number itself.

I realize my mistake, I misinterpreted the question. Thanks!
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Re: If a certain positive integer is divided by 9, the remainder [#permalink]

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19 Jan 2013, 05:20
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If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?

Given that $$x=9q+3$$. x could be: 3, 12, 21, 30, 39, 42, ...

(1) If the integer is divided by 45, the remainder is 30 --> $$x=45p+30=5(9p+6)$$. So, x is a multiple of 5, which means that the remainder when x is divided by 5 is 0. Sufficient.

(2) The integer is divisible by 2 --> x is even. If x is 12, then the remainder is 2 but if x is 30, then the remainder is 0. Not sufficient.

As for your doubt: the values of x which satisfies both equations are: 30, 75, 120, ...

Hope it helps.
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Re: If a certain positive integer is divided by 9, the remainder [#permalink]

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02 Sep 2015, 14:21
Bunuel wrote:
If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?

Given that $$x=9q+3$$. x could be: 3, 12, 21, 30, 39, 42, ...

(1) If the integer is divided by 45, the remainder is 30 --> $$x=45p+30=5(9p+6)$$. So, x is a multiple of 5, which means that the remainder when x is divided by 5 is 0. Sufficient.

(2) The integer is divisible by 2 --> x is even. If x is 12, then the remainder is 2 but if x is 30, then the remainder is 0. Not sufficient.

As for your doubt: the values of x which satisfies both equations are: 30, 75, 120, ...

Hope it helps.

Hi Bunuel,

One question. With statement 1, are the following inferences all valid?
- N is divisible by 5 since --> n = 5 (9q + 6)
- N is also divisible by 3 since --> n = 3 (15q + 10)
- N is therefore also divisible by 15 since --> n = 15 (3q + 2)

I know this goes beyond the scope of answering this question. I just wanna check if my reasoning is correct for future problems such as this one.

Thanks,
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Re: If a certain positive integer is divided by 9, the remainder [#permalink]

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30 Apr 2017, 18:00
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Re: If a certain positive integer is divided by 9, the remainder   [#permalink] 30 Apr 2017, 18:00
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