When 15 is divided by the positive integer k, the remainder

Question

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

KarishmaB · Accepted Answer

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)

sinchicodo · Answer

why does it mean that "12 is completely divisible by k?"

KarishmaB · Answer

Since the remainder is 3, it means 3 is extra. If you remove 3 from 15, whatever is left is completely divisible by k. Check out the video explaining this here: https://youtu.be/A5abKfUBFSc

Bunuel · Answer

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} 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: if-x-y-represents-the-remainder-that-results-when-the-po-169530.html Theory on remainders problems: remainders-144665.html All DS remainders problems to practice: search.php?search_id=tag&tag_id=198 All PS remainders problems to practice: search.php?search_id=tag&tag_id=199

thorinoakenshield · Answer

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 marble-group combination.

Can your explanation be made even more simpler to understand why K > 3?

Thank you,

TO

EMPOWERgmatRichC · Answer

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

thorinoakenshield · Answer

Hi Rich,

Thank you! It makes sense now.

TO

Hero8888 · Answer

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.

Bunuel · Answer

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.

Hero8888 · Answer

Got it! I didn't know about the fine point tested on GMAT. Thank you!

Funsho84 · Answer

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

SidKan · Answer

Factors of 12 are 1, 2, 3, 4, 6, 12

Out of these, k can be 4, 6 and 12.

Answer (C)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

When 15 is divided by the positive integer k, the remainder

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

When 15 is divided by the positive integer k, the remainder

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards