Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Join a free 1-hour webinar and learn how to create the ultimate study plan, and be accepted to the upcoming Round 2 deadlines. Save your spot today! Monday, September 23rd at 8 AM PST

When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

25 Oct 2010, 11:08

1

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

81% (01:49) correct 19% (01:49) wrong based on 151 sessions

HideShow timer Statistics

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

Re: When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

25 Oct 2010, 11:24

2

shrive555 wrote:

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

2 3 4 5 6

Any algebraic approach to this question

Cant think of a straight approach but here is how I solved it: K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer) so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 40) Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5 so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 40)

17 is the only common number in both the sets. Hence k = 17. so 3 is the answer.

Re: When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

26 Oct 2010, 15:52

1

I dont think there is any easy algebraic way to solve this, the best approach is to enumerate out the possibilities and eliminate to get the answer as highlighted in the solution above. That is why you are given the constraint of the answer being less than 40, to make this search & elimination easier.
_________________

Re: When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

15 Mar 2018, 05:26

1

shrive555 wrote:

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

A. 2 B. 3 C. 4 D. 5 E. 6

If we list out the numbers < 40, than 17 is the only common number for both 5 and 6 that gives the remainder 2 & 5 respectively.

Therefore, 17/ 7 gives remainder 3

(B)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

Re: When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

08 Apr 2018, 07:18

1

Cant think of a straight approach but here is how I solved it: K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer) so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 40) Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5 so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 40)

17 is the only common number in both the sets. Hence k = 17. so 3 is the answer.

Re: When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

26 Oct 2010, 21:48

shrouded1 wrote:

I dont think there is any easy algebraic way to solve this, the best approach is to enumerate out the possibilities and eliminate to get the answer as highlighted in the solution above. That is why you are given the constraint of the answer being less than 40, to make this search & elimination easier.

Thanks. i guess that's a good clue. the constraint of 40.
_________________

Re: When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

19 Mar 2018, 06:37

shrive555 wrote:

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

A. 2 B. 3 C. 4 D. 5 E. 6

We are given that k < 40. Since when positive integer k is divided by 5, the remainder is 2:

k = 5Q + 2

So k can be 2, 7, 12, 17, 22, 27, 32, or 37.

Since, when k is divided by 6, the remainder is 5:

k = 6Q + 5

So k can be 5, 11, 17, 23, 29, or 35.

Thus, we see that k must be 17, and 17/7 = 2 remainder 3.

When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

Updated on: 18 Sep 2018, 14:25

shrive555 wrote:

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

A. 2 B. 3 C. 4 D. 5 E. 6

k=5q+2 k=6p+5 5q+2=6p+5➡ 5q/3=2p+1 because 2p+1 is odd, q must be odd multiple of 3 least value of q that will make p an integer is 3 k=5*3+2=17 17/7 gives a remainder of 3 B

Originally posted by gracie on 08 Apr 2018, 11:46.
Last edited by gracie on 18 Sep 2018, 14:25, edited 1 time in total.

Re: When positive integer k is divided by 5, the remainder is 2. When k is
[#permalink]

Show Tags

28 Apr 2019, 07:58

Top Contributor

shrive555 wrote:

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

A. 2 B. 3 C. 4 D. 5 E. 6

When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

When positive integer k is divided by 5, the remainder is 2 The possible values of k are: 2, 7, 12, 17, 22, 27, 32, 37, 42, . . .

When k is divided by 6, the remainder is 5. The possible values of k are: 5, 11, 17, 23, 29, 35, 41. . . .

Since 17 is the only number (less than 40) that both lists share, it must be the case that k = 17

What is the remainder when k is divided by 7? 17 divided by 7 = 2 with remainder 3