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:

The remainder when N is divided by 18 is 16. Given that N is [#permalink]
26 Apr 2013, 02:28

1

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

27% (03:40) correct
73% (02:22) wrong based on 55 sessions

The remainder when N is divided by 18 is 16. Given that N is a multiple of 28, how many integers between 0 and 18 inclusive could be the remainder when N/4 is divided by 18?

Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]
27 Apr 2013, 01:10

4

This post received KUDOS

1

This post was BOOKMARKED

So, my solution. Just a little bit different from the previous.

The remainder when N is divided by 18 is 16 means that N=18q+16 for some integer q. N is a multiple of 28 means that N=28s for some integer s.

We need to find the remainder when \frac{N}{4} is divided by 18.

On one hand \frac{N}{4}=7s, on the other hand \frac{N}{4}=\frac{9q}{2}+4. Since 7s=\frac{9q}{2}+4 and s is an integer, q must be even.

So, \frac{N}{4}=9k+4 for some integer k. Ifk is even (k=2n for some integer n) the remainder when \frac{N}{4} is divided by 18 is 4 (\frac{N}{4}=9*2n+4=18n+4). If k is odd (k=2n+1 for some integer n) the remainder when \frac{N}{4} is divided by 18 is 13 (\frac{N}{4}=9(2n+1)+4=18n+13).

So, there two possible values for the remainder 4 and 13. The answer is B. _________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: The remainder when N is divided by 18 is 16 [#permalink]
26 Apr 2013, 03:18

2

This post received KUDOS

The remainder when N is divided by 18 is 16, translated : N=18k+16 \frac{N}{4} is divided by 18 means what is the remainder of \frac{N}{4*18}? Given that N is a multiple of 28, translated: N=28m

\frac{N}{4*18} with N=28m is \frac{28m}{4*18} or \frac{7m}{18} and its "form" can be written as 7m=18q+R ( or 14m=36q+2R, this will be useful later)

Going back to the first equation N=18k+16 = 28m=18k+16 = 14m=9k+8. From the equation before is its "useful" form 14m=36q+2R so puttin them together 9k+8=36q+2Rall the numbers k,q,R must be integer

8-2R=36q-9k if q and r are 0 8-2R=0 so R=4value #1 the other possible value of R (because must be positive, it's a reminder) will be in the case 9k>36q The difference 36q-9k can be (36-45) = -9 but 8-2R=-9 means R=17/2 no integer difference -18 => R = 5 value #2 difference -27 => R = 33/2 no integer difference -36 => R=21 out of range 0,18 We can stop here bigger differences mean R out of 0,18 range

2 values, B (I am not sure of my method though, the Master Mind could help here and +1 to the question! it took me 10 minutes to came up with a solution!) _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: The remainder when N is divided by 18 is 16 [#permalink]
26 Apr 2013, 03:46

Zarrolou wrote:

The remainder when N is divided by 18 is 16, translated : N=18k+16 \frac{N}{4} is divided by 18 means what is the remainder of \frac{N}{4*18}? Given that N is a multiple of 28, translated: N=28m

\frac{N}{4*18} with N=28m is \frac{28m}{4*18} or \frac{7m}{18} and its "form" can be written as 7m=18q+R ( or 14m=36q+2R, this will be useful later)

Going back to the first equation N=18k+16 = 28m=18k+16 = 14m=9k+8. From the equation before is its "useful" form 14m=36q+2R so puttin them together 9k+8=36q+2Rall the numbers k,q,R must be integer

8-2R=36q-9k if q and r are 0 8-2R=0 so R=4value #1 the other possible value of R (because must be positive, it's a reminder) will be in the case 9k>36q The difference 36q-9k can be (36-45) = -9 but 8-2R=-9 means R=17/2 no integer difference -18 => R = 5 value #2 difference -27 => R = 33/2 no integer difference -36 => R=21 out of range 0,18 We can stop here bigger differences mean R out of 0,18 range

2 values, B (I am not sure of my method though, the Master Mind could help here and +1 to the question! it took me 10 minutes to came up with a solution!)

Thank you so much for solution and kudos!

It took me some time to find the nice solution. I will post how I see the solution later here. I'm just waiting for possible other comments. _________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: The remainder when N is divided by 18 is 16 [#permalink]
26 Apr 2013, 04:49

1

This post was BOOKMARKED

The remainder when N is divided by 18 is 16. Given that N is a multiple of 28, how many integers between 0 and 18 inclusive could be the remainder when \frac{N}{4} is divided by 18?

Let N = 28x so 28x = 18y + 16 or 18z - 2 both are equivalent . so 28x = 18z -2 according to statement mentioned .

Now remainder when N/4 is divided by 18 let remainder be R Let N/4 = 18q + R Substituting N = 28x = 18z-2 we get 18z -2 = 72q + 4R therefore R = (18(z - 4q)-2)/4 = (9(z - 4q ) - 2 ) /2 = (9*someinteger - 1) /2 If a number is divided by 18 so remainder is between 1 and 17 . Substituting integer values we get : (9*1 -1)/2 = 4 possible remainder (9*2 -1 )/2 = 8.5 not possible (9*3 -1 )/2 = 13 possible (9*4 -1 )/2 = 17.5 not possible

Thus we get only 2 possible values for remainder i.e 4 and 13 hence answer is 2 .

Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]
29 Jul 2014, 00:30

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________