finding the non integer

Expert replies

Amrabdelnaby: Master | Next Rank: 500 Posts; Posts: 137; Joined: Fri Nov 13, 2015 11:01 amFollowed by: 2 members; Thanked: 1 times

by Amrabdelnaby » Sat Dec 26, 2015 8:17 am

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

Here is my thought process:

If 9 is a factor of 2x then 9 is hiding in the prime factorization of 2x

2x: 2 x 3 x 3 x.... other unknown numbers that could even be 1

Hence X: 3 x 3 x ...... other numbers that could be even 1

Hence X is a 9 or a multiple of 9

When I plugged in 9 in the answer choices all answers yielded to integers.

I am confused!

please help

Like this post

Source: Beat The GMAT — Problem Solving | Sat Dec 26, 2015 8:17 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Dec 26, 2015 8:33 am

Amrabdelnaby wrote: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

Here is my thought process:

If 9 is a factor of 2x then 9 is hiding in the prime factorization of 2x

2x: 2 x 3 x 3 x.... other unknown numbers that could even be 1

Hence X: 3 x 3 x ...... other numbers that could be even 1

Hence X is a 9 or a multiple of 9

When I plugged in 9 in the answer choices all answers yielded to integers.

I am confused!

please help

Test the SMALLEST POSSIBLE CASE.
If 2x=9, then x=9/2.
Plugging X=9/2 into the answer choices, we get:
A) 6x/54 + 2x/3 = (6 * 9/2)/54 + (2 * 9/2)/3 = 1/2 + 3 = 3.5.

The correct answer is A.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Amrabdelnaby: Master | Next Rank: 500 Posts; Posts: 137; Joined: Fri Nov 13, 2015 11:01 amFollowed by: 2 members; Thanked: 1 times

by Amrabdelnaby » Sat Dec 26, 2015 9:17 am

Thanks Mitch,

i actually assumed that x is an integer and then thought that if 9 is a factor if 2x then 9 is hiding in the prime factorization of 2x.

hence prime factorization of 2x would be: 2 . 3 . 3 and some other numbers

and prime factorization of x would be : 3 . 3 . and some other numbers

Didn't think about assuming that x itself could be 4.5!

However, when should I use the prime factorization technique then? only when told that x is an integer?

GMATGuruNY wrote:
Amrabdelnaby wrote: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

Here is my thought process:

If 9 is a factor of 2x then 9 is hiding in the prime factorization of 2x

2x: 2 x 3 x 3 x.... other unknown numbers that could even be 1

Hence X: 3 x 3 x ...... other numbers that could be even 1

Hence X is a 9 or a multiple of 9

When I plugged in 9 in the answer choices all answers yielded to integers.

I am confused!

please help
Test the SMALLEST POSSIBLE CASE.
If 2x=9, then x=9/2.
Plugging X=9/2 into the answer choices, we get:
A) 6x/54 + 2x/3 = (6 * 9/2)/54 + (2 * 9/2)/3 = 1/2 + 3 = 3.5.

The correct answer is A.

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Dec 26, 2015 10:13 am

Hi amrabdelnaby,

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 Mitch pointed out in his explanation, 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

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review