Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 30 Oct 2004
Posts: 132

If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
25 Dec 2004, 13:56
2
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
51% (02:56) correct
49% (01:37) wrong based on 401 sessions
HideShow timer Statistics
If 9 is a factor of 2x, then which of the following may not be an integer? A. 6x/54 + 2x/3 B. (4x18)/9 C. (2x+27)/9 D. (814x^2)/81 E. (2x3)/3 The answer and my question are posted below.
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 30 Oct 2004
Posts: 132

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
25 Dec 2004, 14:06
I got the right answer A after plugging in 18 for x.
While going through Kaplan's explanation, I couldn't understand the part about choice A.
"6x/54 + 2x/3 = 3/6 * 2x/9 + 2x/3.
Since 9 is a factor of 2x, 3 is also factor of 2x. So 2x/3 is an integer, as is 2x/9. But 3/6 = 1/2, so if 2x/9 is not even, the expression 3/6 * 2x/9 will not be even."
But, isn't 2x/9 always even? 9 is a factor of 2x, which means that we could have 2(9), 2(2)(9), 2(3)(9), and so forth. The 9 in the denominator cancels out the 9 in the numerator. So we are left with 2 * something. So 2x/9 is even.
Your thoughts?



Intern
Joined: 19 Aug 2004
Posts: 47

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
25 Dec 2004, 17:25
1
This post received KUDOS
The question tells us that 9 is a factor of 2x.
Therefore, 2x = 9k where k is any integer.
2x = 9k. Therefore 6x = 27k.
But 6 is an even number. Therefore k also has to be an even number. But if k necessarily has to be an even number, then 6x must be divisible by 54.
Therefore, we can say that 6x = 54m for some integer m....... (1)
Since 2x is divisible by 9, it is also divisible by 3........... (2)
By (1) and (2), we can see that 6x/54 + 2x/3 is an integer.
So, the answer is NOT choice A.



Director
Joined: 07 Nov 2004
Posts: 683

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
25 Dec 2004, 19:57
A.
Stem: 2x/9 = n where n is any integer.
a. 6x/54 + 2x/3 (lets look at other choices)
b. (4x18)/9 = 4x/9 18/9 = 2.2x/9  2 = 2n 2 = integer
c. (2x+27)/9 = 2x/9 + 27/9 = n+3 = integer
d. (814x^2)/81 = 81/81  (2x/9)^2 = 1n^2 = integer
e. (2x3)/3 = 2x/3  3/3 = 2x/3  1 = integer (since 2x is divisible by 9, it is also divisible by 3)
The only choice that's left is A.



Intern
Joined: 19 Aug 2004
Posts: 47

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
26 Dec 2004, 15:21
1
This post was BOOKMARKED
Questor,
If you plug in 18 for x, then 
(6 * 18)/54 + (2 * 18)/3 = 2 + 12 = 14 (which is an integer).
As my earlier post showed, choice A cannot be the correct answer.



Manager
Joined: 02 Dec 2004
Posts: 224

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
27 Dec 2004, 11:18
my choice is D. the tricky part of the question is that D is written as (814x^2)/81 . With the (xy), we must solve the (814x^2) before doing the division with 81. The result is often a fraction.



Director
Joined: 07 Nov 2004
Posts: 683

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
28 Dec 2004, 17:11
1
This post received KUDOS
NM, the question says "which of the following may not be an integer?"
May Not is the key word in the question.
Lets look at choice A:
6x/54 + 2x/3 = (3/6)(2x/9) + 2x/3 = (1/2)(2x/9) + 2x/3
So, as long as 2x/9 is a multiple of two it will be an integer. In your case you are using 2(18)/9 = 4, a multiple of two and hence the answer is an integer.
It does not say x is an integer, so if you pick x=13.5 (2x=27 is divisible by 9), we get
6x/54 + 2x/3 = 1.5 + 9 = 10.5, not an integer.



Director
Joined: 07 Jun 2004
Posts: 612
Location: PA

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
28 Dec 2004, 18:22
All
the answer to this is simple since 9 is a factor of 2x that means x can be and integer then its a multiple of 9 itself then choices A  E will hold good and we will always get an integer.
BUT the problem does not say that x is an intger so take x = 4.5 so 2x will be 9 and 9 is a factor of 9 plug in the choices A  E you will only get D as an decimal value not an integer
ANSWER IS D
rxs0005



Manager
Joined: 30 Oct 2004
Posts: 132

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
28 Dec 2004, 22:56
1
This post was BOOKMARKED
Hi. Thanks for the explanations, guys! I'll check the CD again to make sure that I didn't make any typos in my original.



Director
Joined: 07 Nov 2004
Posts: 683

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
31 Dec 2004, 18:17
rxs0005 wrote: All
the answer to this is simple since 9 is a factor of 2x that means x can be and integer then its a multiple of 9 itself then choices A  E will hold good and we will always get an integer.
BUT the problem does not say that x is an intger so take x = 4.5 so 2x will be 9 and 9 is a factor of 9 plug in the choices A  E you will only get D as an decimal value not an integer
ANSWER IS D
rxs0005
rxs0005, I dont see how you get D.
Lets use x=4.5 as you have suggested:
a. 6x/54 + 2x/3 = 6(4.5)/54 +9/3 = 3.5 (NOT an integer)
b. (4x18)/9 = (4(4.5)18)/9 = (1818)/9 = 0 (an integer)
c. (2x+27)/9 = (9+27)/9 = 4 (an integer)
d. (814x^2)/81 = (81  4(4.5)^2)/81 = (8181)/81 = 0 (an integer)
e. (2x3)/3 = (93)/3 = 2 (an integer)



Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
01 Jan 2005, 11:58
RX you are wrong. the answer is A, you have to think of in terms of prime facrtos
2X/9 is like 2X/3.3 right?
so lets look at answer choice A
6x/54 is not an integer!
6X = 2.3.X right?
54= 3.3.2.3
6x/54 = 2.3.x/3.3.2.3 as you can see, 2.3 in the numerator cancels out with the ones in the denominator, right? you are left with X/3.3 which is never stated to be an integer, remember 2x/3.3 is an integer not x/3.3!
rxs0005 wrote: All
the answer to this is simple since 9 is a factor of 2x that means x can be and integer then its a multiple of 9 itself then choices A  E will hold good and we will always get an integer.
BUT the problem does not say that x is an intger so take x = 4.5 so 2x will be 9 and 9 is a factor of 9 plug in the choices A  E you will only get D as an decimal value not an integer
ANSWER IS D
rxs0005



Director
Joined: 31 Aug 2004
Posts: 606

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
01 Jan 2005, 15:10
A it is.
What you learn is that 2x = 9N where N is equal to or greater than 1.
if 2x = 9, then A is not an integer, for BCDE 2x=9 yields to integer results...



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15995

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
15 Sep 2014, 23:13
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Current Student
Joined: 09 Aug 2015
Posts: 95
GPA: 2.3

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
11 Aug 2015, 13:21
If 9 is a factor of 2x => 2x = 9k, where k = 0, 1, etc
6x/54 + 2x/3 can be rewritten in terms of k as: 27k/54 + 9k/3
which is k/2 + 3k
the 3k will always be an integer, but the first term only works for even k.
alternatively, if you just plugged in k=1 => 2x=9 => x=4.5 you would have arrived at A aswell



Intern
Joined: 31 Oct 2015
Posts: 37

If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
29 Dec 2015, 05:43
The answer is A.
The questions provides that 2x is divisible by 9, so x is either a multiple of 9 or x = 9/2 = 4.5
If x = 4.5 then 6x/54 = (6*4.5)/ (6*9) = 1/2. Not an integer.
In all other cases when the equations are simplified, 2x is always the numerator and 9 or 3 always the denominator making the answer always an integer.



Intern
Joined: 07 Jun 2016
Posts: 47
GPA: 3.8
WE: Supply Chain Management (Manufacturing)

Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
Show Tags
09 Oct 2016, 10:14
gayathri wrote: NM, the question says "which of the following may not be an integer?"
May Not is the key word in the question. Lets look at choice A: 6x/54 + 2x/3 = (3/6)(2x/9) + 2x/3 = (1/2)(2x/9) + 2x/3
So, as long as 2x/9 is a multiple of two it will be an integer. In your case you are using 2(18)/9 = 4, a multiple of two and hence the answer is an integer.
It does not say x is an integer, so if you pick x=13.5 (2x=27 is divisible by 9), we get 6x/54 + 2x/3 = 1.5 + 9 = 10.5, not an integer. Thank you very much, I wrongly assumed (and i should be beat for it because I knew better!) that x is an integer...I should've picked a more uncommon value for x in which 2x/9 still holds true. Again, thank you




Re: If 9 is a factor of 2x, then which of the following may not
[#permalink]
09 Oct 2016, 10:14







