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When 15 is divided by the positive integer k, the remainder [#permalink]
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When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true? A) 1 B) 2 C) 3 D) 4 E) 5
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Originally posted by sinchicodo on 08 Apr 2014, 22:27.
Last edited by Bunuel on 09 Apr 2014, 02:01, edited 2 times in total.
Renamed the topic, edited the question and added the OA.



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Re: When 15 is divided by the positive integer k? remainder is ? [#permalink]
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08 Apr 2014, 22:42
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sinchicodo wrote: When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
A) 1 B) 2 C) 3 D) 4 E) 5 When 15 is divided by k, remainder is 3 i.e. there are 3 balls leftover after grouping. so k must be greater than 3. It also means that 12 is completely divisible by k. Factors of 12 are 1, 2, 3, 4, 6, 12 Out of these, k can be 4, 6 and 12. Answer (C)
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Re: When 15 is divided by the positive integer k? remainder is ? [#permalink]
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08 Apr 2014, 22:49
VeritasPrepKarishma wrote: sinchicodo wrote: When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
A) 1 B) 2 C) 3 D) 4 E) 5 When 15 is divided by k, remainder is 3 i.e. there are 3 balls leftover after grouping. so k must be greater than 3. It also means that 12 is completely divisible by k. Factors of 12 are 1, 2, 3, 4, 6, 12 Out of these, k can be 4, 6 and 12. Answer (C) why does it mean that "12 is completely divisible by k?"



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Re: When 15 is divided by the positive integer k? remainder is ? [#permalink]
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08 Apr 2014, 23:00
sinchicodo wrote: VeritasPrepKarishma wrote: sinchicodo wrote: When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
A) 1 B) 2 C) 3 D) 4 E) 5 When 15 is divided by k, remainder is 3 i.e. there are 3 balls leftover after grouping. so k must be greater than 3. It also means that 12 is completely divisible by k. Factors of 12 are 1, 2, 3, 4, 6, 12 Out of these, k can be 4, 6 and 12. Answer (C) why does it mean that "12 is completely divisible by k?" Since the remainder is 3, it means 3 is extra. If you remove 3 from 15, whatever is left is completely divisible by k. You should check out these posts for theory on divisibility and remainders: http://www.veritasprep.com/blog/2011/04 ... unraveled/http://www.veritasprep.com/blog/2011/04 ... yapplied/http://www.veritasprep.com/blog/2011/05 ... emainders/
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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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09 Apr 2014, 02:04
sinchicodo wrote: When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
A) 1 B) 2 C) 3 D) 4 E) 5 Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is nonnegative integer and always less than divisor). When 15 is divided by the positive integer k, the remainder is 3 > \(15=kq+3\), where \(k>3\). From above: \(15=kq+3\) > \(kq=12\) > k is a factor of 12 greater than 3, thus k can be 4, 6, or 12. Answer: C. Similar question to practice: ifxyrepresentstheremainderthatresultswhenthepo169530.html
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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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30 Jan 2015, 19:18
VeritasPrepKarishma wrote: sinchicodo wrote: When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
A) 1 B) 2 C) 3 D) 4 E) 5 When 15 is divided by k, remainder is 3 i.e. there are 3 balls leftover after grouping. so k must be greater than 3. It also means that 12 is completely divisible by k. Factors of 12 are 1, 2, 3, 4, 6, 12 Out of these, k can be 4, 6 and 12. Answer (C) Hi Karisma,
Thank you for the posts. I also read your Veritas blog on "grouping marbles" on this topic. However, I still cannot understand why K > 3. Based on grouping marbles analogy, for 15 marbles, I can have a remainder of 3 for:
2 groups: 6 marbles each 6 groups: 2 marbles each 4 groups: 3 marbles each 3 groups 4 marbles each 1 group: 12 marbles
or for Bunuel's formula 15 = KV + 3, where K can be a number for any of the above marblegroup combination.
Can your explanation be made even more simpler to understand why K > 3?
Thank you,
TO



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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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30 Jan 2015, 20:19
Hi thorinoakenshield, When dealing with a 'remainder' question, there's a relationship between what you 'divide by' and the 'possible remainders' If you're supposed to end up with a remainder of 3, then you CANNOT be dividing by 1, 2 or 3 (since dividing by any of those numbers CANNOT yield a reminder of 3): For example: 17/1 = 17r0 17/2 = 8r1 17/3 = 5r2 To have a remainder of 3, we need to divide by a number that is GREATER than 3.... eg 7/4 = 1r3 When combined with the possibilities that Karishma defined (1,2,3,4,6,12), the ONLY values that fit both restrictions are 4, 6 and 12.... 15/4 = 3r3 15/6 = 2r3 15/12 = 1r3 GMAT assassins aren't born, they're made, Rich
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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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30 Jan 2015, 20:52
EMPOWERgmatRichC wrote: Hi thorinoakenshield,
When dealing with a 'remainder' question, there's a relationship between what you 'divide by' and the 'possible remainders'
If you're supposed to end up with a remainder of 3, then you CANNOT be dividing by 1, 2 or 3 (since dividing by any of those numbers CANNOT yield a reminder of 3):
For example:
17/1 = 17r0
17/2 = 8r1
17/3 = 5r2
To have a remainder of 3, we need to divide by a number that is GREATER than 3....
eg 7/4 = 1r3
When combined with the possibilities that Karishma defined (1,2,3,4,6,12), the ONLY values that fit both restrictions are 4, 6 and 12....
15/4 = 3r3 15/6 = 2r3 15/12 = 1r3
GMAT assassins aren't born, they're made, Rich Hi Rich,
Thank you! It makes sense now.
TO



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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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02 Apr 2018, 08:05
Hi there, I think the question should have constraints such as k<15. Otherwise 15/20 = 3/4  leaves us the remainder of 3, so K is unlimited.



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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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02 Apr 2018, 08:39



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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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02 Apr 2018, 09:32
Bunuel wrote: Hero8888 wrote: Hi there, I think the question should have constraints such as k<15. Otherwise 15/20 = 3/4  leaves us the remainder of 3, so K is unlimited. 15 divided by 20 does not give the remainder of 3 as stated in the stem. As far as remainders are concerned, 15/20 is not the same as 3/4, you cannot reduce like this: 15 divided by 20 gives the remainder of 15 but 3 divided by 4 gives the remainder of 3. Got it! I didn't know about the fine point tested on GMAT. Thank you!



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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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02 Apr 2018, 13:16
15/k = q +3 15=kq+3 12=kq
prime factors for 12 = 2*2*3
Different values that fit: 2*2, 2*3, 4*3 > 4,6,12
answer C



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Re: When 15 is divided by the positive integer k, the remainder [#permalink]
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08 Apr 2018, 06:57
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Factors of 12 are 1, 2, 3, 4, 6, 12
Out of these, k can be 4, 6 and 12.
Answer (C)




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