NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 14:55 It is currently 23 Apr 2024, 14:55
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If 9 is a factor of 2x, then which of the following may not

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
Questor
Manager
Manager
Joined: 30 Oct 2004
Posts: 80
Own Kudos [?]: 201 [26]
Given Kudos: 0
Send PM
If 9 is a factor of 2x, then which of the following may not [#permalink] New post   25 Dec 2004, 13:56
4
Kudos
22
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

53% (02:07) correct 47% (02:11) wrong based on 526 sessions
Hide Show 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. (4x-18)/9

C. (2x+27)/9

D. (81-4x^2)/81

E. (2x-3)/3

The answer and my question are posted below.
ShowHide Answer
Official Answer
A
User avatar
Questor
Manager
Manager
Joined: 30 Oct 2004
Posts: 80
Own Kudos [?]: 201 [0]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   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?
User avatar
NM
Intern
Intern
Joined: 19 Aug 2004
Posts: 25
Own Kudos [?]: 26 [3]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   25 Dec 2004, 17:25
3
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.
User avatar
gayathri
Senior Manager
Senior Manager
Joined: 07 Nov 2004
Posts: 367
Own Kudos [?]: 468 [0]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   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. (4x-18)/9 = 4x/9 -18/9 = 2.2x/9 - 2 = 2n -2 = integer

c. (2x+27)/9 = 2x/9 + 27/9 = n+3 = integer

d. (81-4x^2)/81 = 81/81 - (2x/9)^2 = 1-n^2 = integer

e. (2x-3)/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.
User avatar
NM
Intern
Intern
Joined: 19 Aug 2004
Posts: 25
Own Kudos [?]: 26 [1]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   26 Dec 2004, 15:21
1
Bookmarks
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.
User avatar
patrickpui
Manager
Manager
Joined: 02 Dec 2004
Posts: 98
Own Kudos [?]: 48 [0]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   27 Dec 2004, 11:18
my choice is D. the tricky part of the question is that D is written as (81-4x^2)/81 . With the (x-y), we must solve the (81-4x^2) before doing the division with 81. The result is often a fraction.
User avatar
gayathri
Senior Manager
Senior Manager
Joined: 07 Nov 2004
Posts: 367
Own Kudos [?]: 468 [4]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   28 Dec 2004, 17:11
4
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.
User avatar
rxs0005
Senior Manager
Senior Manager
Joined: 07 Jun 2004
Posts: 438
Own Kudos [?]: 2828 [0]
Given Kudos: 22
Location: PA
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   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
User avatar
Questor
Manager
Manager
Joined: 30 Oct 2004
Posts: 80
Own Kudos [?]: 201 [1]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   28 Dec 2004, 22:56
1
Bookmarks
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.
User avatar
gayathri
Senior Manager
Senior Manager
Joined: 07 Nov 2004
Posts: 367
Own Kudos [?]: 468 [2]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   31 Dec 2004, 18:17
2
Kudos
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. (4x-18)/9 = (4(4.5)-18)/9 = (18-18)/9 = 0 (an integer)

c. (2x+27)/9 = (9+27)/9 = 4 (an integer)

d. (81-4x^2)/81 = (81 - 4(4.5)^2)/81 = (81-81)/81 = 0 (an integer)

e. (2x-3)/3 = (9-3)/3 = 2 (an integer)
User avatar
FN
Current Student
Joined: 28 Dec 2004
Posts: 1581
Own Kudos [?]: 642 [0]
Given Kudos: 2
Location: New York City
Concentration: Social Enterprise
Schools:Wharton'11 HBS'12
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   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
User avatar
twixt
Senior Manager
Senior Manager
Joined: 31 Aug 2004
Posts: 289
Own Kudos [?]: 344 [0]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   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...
User avatar
ggurface
Manager
Manager
Joined: 09 Aug 2015
Posts: 73
Own Kudos [?]: 77 [1]
Given Kudos: 7
Schools: Schulich Jan '18 (A)
GMAT 1: 770 Q51 V44
GPA: 2.3
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   11 Aug 2015, 13:21
1
Kudos
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
avatar
kham71
Intern
Intern
Joined: 31 Oct 2015
Posts: 19
Own Kudos [?]: 31 [0]
Given Kudos: 53
Send PM
If 9 is a factor of 2x, then which of the following may not [#permalink] New post   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.
avatar
B
mikeyg51
Intern
Intern
Joined: 07 Jun 2016
Posts: 24
Own Kudos [?]: 8 [0]
Given Kudos: 106
Schools: Ross Weekend"19 UNC Kenan-Flagler Booth PT '19 Kelley Online MBA"19
GPA: 3.8
WE:Supply Chain Management (Manufacturing)
Send PM
GMAT ToolKit User
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   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
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11664 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   11 Feb 2018, 13:14
2
Kudos
Expert Reply
Hi All,

Tougher GMAT questions are sometimes designed to test the thoroughness of your thinking. This prompt NEVER stated that X was an integer; it even goes so far as to state that 9 is a factor of 2X (not that 9 is a factor of X). When a prompt is built around some quirky language or 'design elements', it's often worthwhile to ask yourself what you really KNOW and what you don't know. As has been pointed out in several of the explanations, thinking about X=4.5 is the easiest way to get to the correct answer (even though 4.5 isn't the easiest value that fits the given description).

GMAT assassins aren't born, they're made,
Rich
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32627
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If 9 is a factor of 2x, then which of the following may not [#permalink] New post   10 Nov 2022, 11:49
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 Club Bot
gmatclubot
Re: If 9 is a factor of 2x, then which of the following may not [#permalink]
10 Nov 2022, 11:49
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions