Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 28 Jan 2006
Posts: 116

Is n/18 an integer? [#permalink]
Show Tags
29 Aug 2006, 14:07
6
This post received KUDOS
46
This post was BOOKMARKED
Question Stats:
25% (01:11) correct 75% (00:53) wrong based on 1141 sessions
HideShow timer Statistics
Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer. SOLUTION IS HERE: isn18aninteger3441520.html#p1341451
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
All the best!!
shinewine



VP
Joined: 02 Jun 2006
Posts: 1240

7
This post received KUDOS
4
This post was BOOKMARKED
Q: n = 18 x k where k = integer.
S1: n = 18xm/5 where m = integer.
Therefore, n/18 = m/5 Not sufficient.
S2: n= 18 x s/ 3 where s = integer.
=> n/18 = s/3; Not sufficient.
S1 & S2:
n/18 = m/5
n/18 = s/3
or m/5 = s/3
or 3m = 5s
Which means m & s are multiples of both 5 and 3.
Therefore n/18 is an integer.
Answer: C



VP
Joined: 02 Jun 2006
Posts: 1240

If n/18= 0 and n/18 = 1/5,
In one case, we get
5n/18 = 0 integer. n/18 => integer...
5n/18 =1 integer, n/18 => not integer...
I don't understand how its A?
X & Y wrote: Getting A
St 1: Suff St 2: Insuff



Manager
Joined: 09 Aug 2005
Posts: 72

I've used just common sense here, since I'm not getting anywhere with traditional ways.
(A) St 1 is sufficient. Because, since 18 = 3*3*2, 5 and 18 have no factors in common.
Which means for 5n/18 to be an integer, n must be a multiple of 18!
Hence sufficient.
(B) is not sufficient because 3 and 18 have common factors, so n may be a multiple of 18, the only thing certain here is that it will be a multiple of 6. Therefore not sufficient.
MG



GMAT Instructor
Joined: 04 Jul 2006
Posts: 1253
Location: Madrid

We don't know that n is an integer!



VP
Joined: 02 Jun 2006
Posts: 1240

1
This post was BOOKMARKED
Kevin,
Can you elaborate a little bit? I think I am losing my mind....can't seem to figure this out for some reason? Are you getting A too?
kevincan wrote: We don't know that n is an integer!



Manager
Joined: 09 Aug 2005
Posts: 72

Ah so then I'm wrong....
i.e. N can be 18/5 to begin with... thats true.
But Haas, going back to your solution, if N is a multiple of both 5 and 3, how can you be sure it is a multiple of 18??
It only proves it can be a multiple of 15. It still may or may not be a multiple of 18.
Does that mean hte answer is E?
MG



VP
Joined: 28 Mar 2006
Posts: 1330

Re: DS : MGMAT3 [#permalink]
Show Tags
29 Aug 2006, 20:20
shinewine wrote: Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer.
n/18 can be x/5 in 1 and x/3 in 2 where x is some number
taking both into consideration we get nothing
E it is



Manager
Joined: 12 May 2006
Posts: 116
Location: Philadelphia

1
This post was BOOKMARKED
I believe it is A...
I think it was said before
stmnt1 5 shares no common factors with 18. This means that N must be a direct factor of 18. Suff
stmnt2 Insuff for reasons explained above.



GMAT Instructor
Joined: 04 Jul 2006
Posts: 1253
Location: Madrid

6
This post received KUDOS
4
This post was BOOKMARKED
(1) If 5n/18 is an integer, call it k, we know that n/18=k/5, which may or may not be an integer. NOT SUFF
(2) Similarly, if 3n/18 is an integer, call it m, we know that n/18= m/3, which may or may not be an integer NOT SUFF
(1) and (2): For some integers k and m, k/5=m/3 => 3k=5m =>k=5m/3.
Thus m is a multiple of 3, so n/18=m/3 is an integer SUFF



Director
Joined: 13 Nov 2003
Posts: 779
Location: BULGARIA

(1) If 5n/18 is an integer, call it k, we know that n/18=k/5, which may or may not be an integer. NOT SUFF
If (5n/18)=k=>5n=18k=>n=(18k/5) since both n and k are INTEGERS then k is multiple of 5 and respectively n is a multiple of 18 and an INTEGER so A) is SUFF byitself,



Director
Joined: 28 Dec 2005
Posts: 729

rdw28 wrote: Kevincan,
There is no way possible that 5n/18 could be an integer if n were not an integer.
There is: consider n/18 = 1/5. Then 5 (n/18) = 5. (1/5) = 1.



Current Student
Joined: 28 Dec 2004
Posts: 3293
Location: New York City
Schools: Wharton'11 HBS'12

Re: DS : MGMAT3 [#permalink]
Show Tags
30 Aug 2006, 10:19
5
This post received KUDOS
2
This post was BOOKMARKED
shinewine wrote: Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer.
lets see..the stem says nothing about N being an integer...soo
1) 5 N/18  integer...well N can be an integer multiple of 18 or it can be 18M/5 where M is an integer not divisible by 5...Insuff
2) simplify this to N/6, so N has prime factors 2 and 3, we still dont know if it has enuff 3s or not...but we noe for sure that N is not a fraction...
combining them we now now that N is not a fraction and that its a mutliple of 18....
C it is...
Answer woud be A if we are told in the stem that N is an integer..



Intern
Joined: 29 Dec 2012
Posts: 17

Re: DS : MGMAT3 [#permalink]
Show Tags
30 Nov 2013, 15:17
5n/18=integer If we consider n=18M/5 Where M can be number which is not divisible by 5 .. If we consider this case, then 5(18M/5)/18=integer is not fulfilling sinceM is not integer , to fulfill this M must be integer hence N is integer..
Thus A should be OA.



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 620

Re: Is n/18 an integer? [#permalink]
Show Tags
01 Dec 2013, 00:30
2
This post received KUDOS
1
This post was BOOKMARKED
shinewine wrote: Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer. From F.S 1, we know that \(\frac{5n}{18}\) is an integer. For\(\frac{n}{18} = 1\), we have a YES. Again, for \(\frac{n}{18} = \frac{1}{5}\) , we have a NO.Insufficient. From F.S 2, we know that\(\frac{3n}{18}\) is an integer. For \(\frac{n}{18} = 1\), we have a YES,but for \(\frac{n}{18} = \frac{1}{3}\) , we have a NO.Insufficient. Taking both together, we know that from F.S 1, either\(\frac{n}{18} = \frac{k}{5}\) or \(\frac{n}{18} = p\) , where k,p are integers and k and 5 are coprimes. But, for \(\frac{n}{18} = \frac{k}{5}\), \(\frac{3*n}{18} = \frac{3*k}{5}\) and it will not be an integer. Thus, \(\frac{n}{18} = p\) can the only be form possible. C.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Director
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: Is n/18 an integer? [#permalink]
Show Tags
03 Dec 2013, 01:07
7
This post received KUDOS
4
This post was BOOKMARKED
shinewine wrote: Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer. We need to find whether n is a multiple of 18 or n= 18I for some integer I St 1: 5n/18= Integer or n = 18*Integer/ 5 Now if Integer = 2, then n =7.2 and n/18 is not an integer but integer = 5 then n = 18 and 18/18 is an integer Possible values of n = 3.6,7.2,10.8,14.4,18......So A and D ruled out St 2: we see that n is a multiple of 6 so possible values of n =6,12,18......If n= 6 then n/18 is not an integer but if n=18 then n/18 is an integer. So option B ruled out Combining we get possible values of n =18,36,54 and so on
Hence Ans C
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Intern
Joined: 06 Feb 2014
Posts: 3

Re: Is n/18 an integer? [#permalink]
Show Tags
11 Feb 2014, 12:53
1
This post received KUDOS
From 1: 5n/18 = a (an integer) => n/18 = a/5 (we cannot be sure if this is an interger) From 2: 3n/18 = b (an integer) => n/18 = b/3 (we cannot be sure if this is an interger) Combining 1&2: 2*(statement 2)  (statement 1) => 6n/18  5n/18 = 18*2*b  18*a => n/18 = 18(2ba) {this we know for sure is an integer} Thus, Option C



Intern
Joined: 13 Feb 2014
Posts: 3

Re: Is n/18 an integer? [#permalink]
Show Tags
13 Feb 2014, 20:12
3
This post received KUDOS
1
This post was BOOKMARKED
It's C, but I think this is as clear as it can be explained:
S1: \(\frac{5n}{18}=K1\) (Letting K1 be an integer)
Then, isolating n we get \(n=\frac{18K1}{5}\)
Going back to the original question if n is divisible by 18, based on this answer is "Maybe" (provided that K1 is a multiple of 5)
Insufficient.
S2: \(\frac{3n}{18}=K2\) (Letting K2 be an integer)
Then, isolating n we get \(n=\frac{18K2}{3}\), reducing \(n=6K2\)
Going back to the original question if n is divisible by 18, based on this answer is "Maybe" (Provided that K2 is a multiple of 3)
Insufficient.
S1 & S2: We will make the expressions for n equal:
\(\frac{18K1}{5}=6K2\), simplifying \(K2=\frac{3K1}{5}\) The key here is understanding that K1 and K2 MUST be integers. As such, the "Maybes" of S1 and S2 are proven to be true. From the expression above, K2 is a multiple of 3 and K1 is a multiple of 5.
This is perhaps an extended explanation, but I think is clear enough.



Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 518
Location: India

Re: Is n/18 an integer? [#permalink]
Show Tags
13 Feb 2014, 23:30
1
This post received KUDOS
3
This post was BOOKMARKED
shinewine wrote: Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is an integer. Statement I is insufficient: n = 36 (YES) n = 18/5 (NO) Statement II is insufficient: n = 36 (YES) n = 6 (NO) Combining is sufficient: Since 5 and 3 are co primes to each other n will have to be a multiple of 18 for 5n/18 and 3n/18 to be an integer. Answer is C
_________________
Register for CrackVerbal MBA Achiever's Summit here  http://crackverbal.com/mbasummit2018
Enroll for our GMAT Trial Course here  http://gmatonline.crackverbal.com/
For more info on GMAT and MBA, follow us on @AskCrackVerbal



Manager
Joined: 28 Aug 2013
Posts: 92
Location: India
Concentration: Operations, Marketing
GMAT Date: 08282014
GPA: 3.86
WE: Supply Chain Management (Manufacturing)

Re: Is n/18 an integer? [#permalink]
Show Tags
08 Mar 2014, 07:40
3
This post was BOOKMARKED
ndiaz17 wrote: It's C, but I think this is as clear as it can be explained:
S1: \(\frac{5n}{18}=K1\) (Letting K1 be an integer)
Then, isolating n we get \(n=\frac{18K1}{5}\)
Going back to the original question if n is divisible by 18, based on this answer is "Maybe" (provided that K1 is a multiple of 5)
Insufficient.
S2: \(\frac{3n}{18}=K2\) (Letting K2 be an integer)
Then, isolating n we get \(n=\frac{18K2}{3}\), reducing \(n=6K2\)
Going back to the original question if n is divisible by 18, based on this answer is "Maybe" (Provided that K2 is a multiple of 3)
Insufficient.
S1 & S2: We will make the expressions for n equal:
\(\frac{18K1}{5}=6K2\), simplifying \(K2=\frac{3K1}{5}\) The key here is understanding that K1 and K2 MUST be integers. As such, the "Maybes" of S1 and S2 are proven to be true. From the expression above, K2 is a multiple of 3 and K1 is a multiple of 5.
This is perhaps an extended explanation, but I think is clear enough. Umm...I am having 1 query ...very simple I don't want to get into such complex solution my only query is ... S 1 : tells 5n/18 is an integer  5 is prime, hence it must be clear that "n" will be divisible by 18 , in that case n/18 will be an integer . then why some folks are not mentioning A wrong ?? Is i am missing any logic plz explain ?
_________________
Gprep1 540 > Kaplan 580>Veritas 640>MGMAT 590 >MGMAT 2 640 > MGMAT 3 640 > MGMAT 4 650 >MGMAT 5 680  >GMAT prep 1 570
Give your best shot...rest leave upto Mahadev, he is the extractor of all negativity in the world !!




Re: Is n/18 an integer?
[#permalink]
08 Mar 2014, 07:40



Go to page
1 2
Next
[ 37 posts ]



