It is currently 20 Oct 2017, 13:13

### GMAT Club Daily Prep

#### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The remainder when N is divided by 18 is 16. Given that N is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Tutor
Joined: 20 Apr 2012
Posts: 100

Kudos [?]: 328 [2], given: 36

Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

26 Apr 2013, 03:28
2
This post received
KUDOS
20
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

36% (03:18) correct 64% (02:57) wrong based on 193 sessions

### HideShow timer Statistics

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?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Just nice problem from http://www.mualphatheta.org/National_Co ... Tests.aspx
I know some ways how to solve it quickly. May be someone knows nicer way of solution. Thanks:)
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 328 [2], given: 36

Tutor
Joined: 20 Apr 2012
Posts: 100

Kudos [?]: 328 [9], given: 36

Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

27 Apr 2013, 02:10
9
This post received
KUDOS
9
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 $$k$$.
If$$k$$ 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:)

Kudos [?]: 328 [9], given: 36

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2327 [3], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: The remainder when N is divided by 18 is 16 [#permalink]

### Show Tags

26 Apr 2013, 04:18
3
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 $$9k+8=36q+2R$$ all the numbers k,q,R must be integer

$$8-2R=36q-9k$$
if q and r are 0 $$8-2R=0$$ so $$R=4$$ value #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.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2327 [3], given: 219

Intern
Status: Application process
Joined: 23 Jan 2013
Posts: 32

Kudos [?]: 15 [2], given: 12

Location: India
GMAT 1: 600 Q50 V22
GMAT 2: 650 Q49 V28
GPA: 3.39
WE: Information Technology (Computer Software)
Re: The remainder when N is divided by 18 is 16 [#permalink]

### Show Tags

26 Apr 2013, 05:49
2
This post received
KUDOS
2
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 .

Kudos [?]: 15 [2], given: 12

Senior Manager
Joined: 29 Jun 2017
Posts: 345

Kudos [?]: 66 [2], given: 64

WE: Engineering (Transportation)
Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

18 Aug 2017, 04:21
2
This post received
KUDOS
pratik1709 wrote:
Not sure about this big formule!!! but I got as per below logic.

We are been asked to find ... rem(N/(4*18))....

rem(n/18)=16... so hence (rem(n(4*18))=rem (16/4)=0... We can 0 remider only with two cases.. either 0 or 18.. so answer B is correct choice.

...............................

I guess your remainder values are wrong, see my solution and the remainder will be 13 and 4 which will come alternate as the N is increased in series./

Kudos for right answer
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 66 [2], given: 64

Senior Manager
Joined: 29 Jun 2017
Posts: 345

Kudos [?]: 66 [1], given: 64

WE: Engineering (Transportation)
Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

18 Aug 2017, 03:36
1
This post received
KUDOS
Answer is B

N= 18i + 16, and N is multiple of 28
N can have values, = 196,376,556,736 .. and so on
N/4 is 49,94,139,184.....
remainder when divided by 18 gives ... 13,4,13,4 resp.

Therefore only 2 values possible

Answer is B

Kodos for right answer..
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 66 [1], given: 64

Director
Joined: 07 Dec 2014
Posts: 815

Kudos [?]: 248 [1], given: 12

The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

18 Aug 2017, 18:40
1
This post received
KUDOS
smyarga wrote:
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?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

N=28x
N=18y+16
28x=18y+16➡
7x-4.5y=4
x=7
y=10
least value of N=28*7=196
N/4=196/4=49
49/18 gives a remainder of 13
LCM of 18 and 28=4*7*9=252
196+252=448=next value of N
N/4=112
112/18 leaves a remainder of 4
(N/4)/18 leaves two cycling remainders, 13 and 4
2
B

Kudos [?]: 248 [1], given: 12

Tutor
Joined: 20 Apr 2012
Posts: 100

Kudos [?]: 328 [0], given: 36

Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Re: The remainder when N is divided by 18 is 16 [#permalink]

### Show Tags

26 Apr 2013, 04:46
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 $$9k+8=36q+2R$$ all the numbers k,q,R must be integer

$$8-2R=36q-9k$$
if q and r are 0 $$8-2R=0$$ so $$R=4$$ value #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:)

Kudos [?]: 328 [0], given: 36

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16635

Kudos [?]: 273 [0], given: 0

Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

29 Jul 2014, 01:30
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.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16635

Kudos [?]: 273 [0], given: 0

Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

11 Oct 2015, 06:01
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.
_________________

Kudos [?]: 273 [0], given: 0

Manager
Joined: 04 Feb 2017
Posts: 57

Kudos [?]: 7 [0], given: 45

Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

18 Aug 2017, 04:17
Not sure about this big formule!!! but I got as per below logic.

We are been asked to find ... rem(N/(4*18))....

rem(n/18)=16... so hence (rem(n(4*18))=rem (16/4)=0... We can 0 remider only with two cases.. either 0 or 18.. so answer B is correct choice.

Kudos [?]: 7 [0], given: 45

Manager
Joined: 04 May 2014
Posts: 127

Kudos [?]: 9 [0], given: 69

Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

19 Aug 2017, 06:30
Is this a GMAT question?

Kudos [?]: 9 [0], given: 69

Intern
Joined: 25 Jan 2013
Posts: 26

Kudos [?]: 3 [0], given: 1888

Concentration: General Management, Entrepreneurship
Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

19 Aug 2017, 09:20
smyarga wrote:
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?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Just nice problem from http://www.mualphatheta.org/National_Co ... Tests.aspx
I know some ways how to solve it quickly. May be someone knows nicer way of solution. Thanks:)

I am not sure of my method. Experts do let me know.
Anyways,

N= 18p+ 16 R
Since N is multiple of 28, make it multiple. Divide by 4 (so its N/4 and divide by 18)

N = (18*28p + 16*28R)/(4*18)

N= 7p + 56/9R. Only 9 and 18 will make full remainder R. So, 2 values.

Kudos [?]: 3 [0], given: 1888

Senior Manager
Joined: 29 Jun 2017
Posts: 345

Kudos [?]: 66 [0], given: 64

WE: Engineering (Transportation)
Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

20 Aug 2017, 11:29
gps5441 wrote:
Is this a GMAT question?

Yes , it can be asked above or around 700 level difficulty level.
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 66 [0], given: 64

Intern
Joined: 03 Aug 2017
Posts: 7

Kudos [?]: 0 [0], given: 14

Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

20 Sep 2017, 06:52
gracie wrote:
smyarga wrote:
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?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

N=28x
N=18y+16
28x=18y+16➡
7x-4.5y=4
x=7
y=10
least value of N=28*7=196
N/4=196/4=49
49/18 gives a remainder of 13
LCM of 18 and 28=4*7*9=252
196+252=448=next value of N
N/4=112
112/18 leaves a remainder of 4
(N/4)/18 leaves two cycling remainders, 13 and 4
2
B

Hey, can you please explain the cycling remainders bit? I got the answer till ' remainder as 4'. Therefore I selected 1 as the answer. can you please explain?

Kudos [?]: 0 [0], given: 14

Senior Manager
Joined: 29 Jun 2017
Posts: 345

Kudos [?]: 66 [0], given: 64

WE: Engineering (Transportation)
Re: The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

20 Sep 2017, 07:24
akshay94raja wrote:
gracie wrote:
smyarga wrote:
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?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

N=28x
N=18y+16
28x=18y+16➡
7x-4.5y=4
x=7
y=10
least value of N=28*7=196
N/4=196/4=49
49/18 gives a remainder of 13
LCM of 18 and 28=4*7*9=252
196+252=448=next value of N
N/4=112
112/18 leaves a remainder of 4
(N/4)/18 leaves two cycling remainders, 13 and 4
2
B

Hey, can you please explain the cycling remainders bit? I got the answer till ' remainder as 4'. Therefore I selected 1 as the answer. can you please explain?

HOPE IT HELPS

N= 18i + 16, and N is multiple of 28
N can have values, = 196,376,556,736 .. and so on
N/4 is 49,94,139,184.....
remainder when divided by 18 gives ... 13,4,13,4 resp.

Therefore only 2 values possible

Answer is B
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 66 [0], given: 64

Intern
Joined: 11 Nov 2016
Posts: 4

Kudos [?]: [0], given: 3

The remainder when N is divided by 18 is 16. Given that N is [#permalink]

### Show Tags

20 Sep 2017, 07:50
X, I be integers,

28X = 18I + 16

28X/4 => (18I+16)/4 => (9/2)I + 4

here (9/2)I leaves the remainder

For all even values of I,

(9/2)I leaves 0 as remainder

For all odd values of I.

(9/2) I leaves 1 as remainder

so we have 2 different remainders between 0 and 18 inclusive

Kudos [?]: [0], given: 3

The remainder when N is divided by 18 is 16. Given that N is   [#permalink] 20 Sep 2017, 07:50
Display posts from previous: Sort by

# The remainder when N is divided by 18 is 16. Given that N is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.