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# When positive integer n is divisible by 3, the remainder is

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Manager
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When positive integer n is divisible by 3, the remainder is [#permalink]

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30 Jan 2008, 02:04
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When positive integer “n” is divisible by 3, the remainder is 2; and when positive integer “t” is divided by 5, the remainder is 3. What is the remainder when the product “nt” is divided by 15?

1) n-2 is divisible by 5.
2) t is divisible by 3.

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-positive-integer-n-is-divided-by-3-the-remainder-is-86155.html
[Reveal] Spoiler: OA

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Senior Manager
Joined: 26 Jan 2008
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Kudos [?]: 117 [0], given: 16

Re: GMAT prep : DS - Remainder [#permalink]

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30 Jan 2008, 02:39
GHIBI wrote:
When positive integer “n” is divisible by 3, the remainder is 2; and when positive integer “t” is divided by 5, the remainder is 3. What is the remainder when the product “nt” is divided by 15?

1) n-2 is divisible by 5.
2) t is divisible by 3.

Could you please explain in detail?
Thank you.

1) and 2) alone are insufficient

The answer should be (C). The remainder will come to 6

n = 3k + 2
t = 5m + 3

Also (n-2) is divisible by 5
=> 3k is divisible by 5
=> k is divisible by 5

Similarly, m is divisible by 3

nt = (3k + 2) * (5m + 3)
=> nt = 15km + 9k + 10m + 6

when divided by 15, you get
nt = 15(km + 3k/5 + 5m/3) + 6
since k is divisible by 5 and m is divisible by 3, the first 3 terms are not relevant to the remainder, leaving 6 as the answer.
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Kudos [?]: 117 [0], given: 16

CEO
Joined: 17 Nov 2007
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Kudos [?]: 4473 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: GMAT prep : DS - Remainder [#permalink]

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30 Jan 2008, 02:48
E

Thanks for the excellent question! +1
It is my weak point.

a wild solution:

n can be {2,5,8,11,14,17}
t can be {3,8,13,18}

1. n can be {2,17}.
nt=2*3 has reminder 6, nt=2*8 has reminder 1
insuff.

2. t can be {3,18}.
nt=2*3 has reminder 6, nt=8*3 has reminder 9
insuff.

1&2. n can be {2,17}, t can be {3,18}.
nt=2*3 has reminder 6, nt=17*18 has reminder 2
insuff.

eschn3am and maratikus, please, help to find the fast and clear 1-min way!
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Kudos [?]: 4473 [0], given: 360

Senior Manager
Joined: 26 Jan 2008
Posts: 263

Kudos [?]: 117 [1], given: 16

Re: GMAT prep : DS - Remainder [#permalink]

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30 Jan 2008, 03:49
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walker wrote:
E

Thanks for the excellent question! +1
It is my weak point.

a wild solution:

n can be {2,5,8,11,14,17}
t can be {3,8,13,18}

1. n can be {2,17}.
nt=2*3 has reminder 6, nt=2*8 has reminder 1
insuff.

2. t can be {3,18}.
nt=2*3 has reminder 6, nt=8*3 has reminder 9
insuff.

1&2. n can be {2,17}, t can be {3,18}.
nt=2*3 has reminder 6, nt=17*18 has reminder 2
insuff.

eschn3am and maratikus, please, help to find the fast and clear 1-min way!

Won't the remainder for 17*18 be 6, as opposed to 2?
_________________

Kudos [?]: 117 [1], given: 16

CEO
Joined: 17 Nov 2007
Posts: 3585

Kudos [?]: 4473 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: GMAT prep : DS - Remainder [#permalink]

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30 Jan 2008, 03:53
incognito1 wrote:
Won't the remainder for 17*18 be 6, as opposed to 2?

Thanks. You are right. A stupid mistake.
+1
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Kudos [?]: 4473 [0], given: 360

Director
Joined: 12 Jul 2007
Posts: 857

Kudos [?]: 326 [0], given: 0

Re: GMAT prep : DS - Remainder [#permalink]

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30 Jan 2008, 05:22
GHIBI wrote:
When positive integer “n” is divisible by 3, the remainder is 2; and when positive integer “t” is divided by 5, the remainder is 3. What is the remainder when the product “nt” is divided by 15?

1) n-2 is divisible by 5.
2) t is divisible by 3.

Could you please explain in detail?
Thank you.

n: 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38
t: 8, 13, 18, 23, 28, 33, 38

1. n: 17, 32
2. t: 18, 33

1. 17*3*3*2/3*5 = 17*3*2/5 = remainder 2
2. 17*3*11/3*5 = 17*11/5 = 187/5 = remainder 2
3. 16*2*2*3*3/3*5 = 16*2*2*3/5 = 192/5 = remainder 2
4. 16*2*3*11/3*5 = 16*2*11/5 = 352/5 = remainder 2

Answer C

Kudos [?]: 326 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3585

Kudos [?]: 4473 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: GMAT prep : DS - Remainder [#permalink]

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30 Jan 2008, 13:03
Can anyone provide fast "mod" - approach to the problem?
Thanks.
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Director
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Re: GMAT prep : DS - Remainder [#permalink]

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31 Jan 2008, 15:03
Look for a fast answer approach as well. These types of problems kick my a\$\$.

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Director
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Re: GMAT prep : DS - Remainder [#permalink]

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31 Jan 2008, 15:09
incognito1, can you break this down some more...

nt = (3k + 2) * (5m + 3)
=> nt = 15km + 9k + 10m + 6

when divided by 15, you get
nt = 15(km + 3k/5 + 5m/3) + 6
since k is divisible by 5 and m is divisible by 3, the first 3 terms are not relevant to the remainder, leaving 6 as the answer.

Kudos [?]: 370 [0], given: 0

Director
Joined: 01 May 2007
Posts: 794

Kudos [?]: 370 [0], given: 0

Re: GMAT prep : DS - Remainder [#permalink]

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31 Jan 2008, 15:24
I think there is a math error in the yellow.

incognito1 wrote:
GHIBI wrote:
When positive integer “n” is divisible by 3, the remainder is 2; and when positive integer “t” is divided by 5, the remainder is 3. What is the remainder when the product “nt” is divided by 15?

1) n-2 is divisible by 5.
2) t is divisible by 3.

Could you please explain in detail?
Thank you.

1) and 2) alone are insufficient

The answer should be (C). The remainder will come to 6

n = 3k + 2
t = 5m + 3

Also (n-2) is divisible by 5
=> 3k is divisible by 5
=> k is divisible by 5

Similarly, m is divisible by 3

nt = (3k + 2) * (5m + 3)
=> nt = 15km + 9k + 10m + 6

when divided by 15, you get
nt = 15(km + 3k/5 + 5m/3) + 6
since k is divisible by 5 and m is divisible by 3, the first 3 terms are not relevant to the remainder, leaving 6 as the answer.

Kudos [?]: 370 [0], given: 0

Senior Manager
Joined: 26 Jan 2008
Posts: 263

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Re: GMAT prep : DS - Remainder [#permalink]

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31 Jan 2008, 17:38
jimmyjamesdonkey wrote:
I think there is a math error in the yellow.

incognito1 wrote:
GHIBI wrote:
When positive integer “n” is divisible by 3, the remainder is 2; and when positive integer “t” is divided by 5, the remainder is 3. What is the remainder when the product “nt” is divided by 15?

1) n-2 is divisible by 5.
2) t is divisible by 3.

Could you please explain in detail?
Thank you.

1) and 2) alone are insufficient

The answer should be (C). The remainder will come to 6

n = 3k + 2
t = 5m + 3

Also (n-2) is divisible by 5
=> 3k is divisible by 5
=> k is divisible by 5

Similarly, m is divisible by 3

nt = (3k + 2) * (5m + 3)
=> nt = 15km + 9k + 10m + 6

when divided by 15, you get
nt = 15(km + 3k/5 + 5m/3) + 6
since k is divisible by 5 and m is divisible by 3, the first 3 terms are not relevant to the remainder, leaving 6 as the answer.

Jimmy you're right - it should be 2m/3 instead of 5m/3, but shouldn't affect the overall solution
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Re: GMAT prep : DS - Remainder [#permalink]

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01 Feb 2008, 04:58
GHIBI wrote:
When positive integer “n” is divisible by 3, the remainder is 2; and when positive integer “t” is divided by 5, the remainder is 3. What is the remainder when the product “nt” is divided by 15?

1) n-2 is divisible by 5.
2) t is divisible by 3.

Could you please explain in detail?
Thank you.

I remember I was exposed to this question and found the link: 7-p397597?t=55775&hilit=divisible#p397597
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Re: GMAT prep : DS - Remainder   [#permalink] 01 Feb 2008, 04:58
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# When positive integer n is divisible by 3, the remainder is

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