divisibility...

Expert replies

topspin360: Master | Next Rank: 500 Posts; Posts: 103; Joined: Sat Jun 02, 2012 9:46 pm; Thanked: 1 times

by topspin360 » Sat Jul 21, 2012 1:57 pm

I used to break down these type of problems through prime factorization. If the overall numerator can have a 9 (ie two 3's), then it is divisible by 9. but it didn't work in this scenario... just looking for a comprehensive thought process on how to go about this problem.

Is x^2 * y^4 an integer divisible by 9 ?

(1) x is an integer divisible by 3

(2) xy is an integer divisible by 9

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

Like this post

Source: Beat The GMAT — Problem Solving | Sat Jul 21, 2012 1:57 pm

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 Jul 21, 2012 2:13 pm

topspin360 wrote:I used to break down these type of problems through prime factorization. If the overall numerator can have a 9 (ie two 3's), then it is divisible by 9. but it didn't work in this scenario... just looking for a comprehensive thought process on how to go about this problem.

Is x^2 * y^4 an integer divisible by 9 ?

(1) x is an integer divisible by 3

(2) xy is an integer divisible by 9

It's important to note how a problem is restricted and how it ISN'T.
There are NO conditions given in the question stem.
Thus, we must consider NONINTEGER values.

If x=18 and y=1/2, both statements are satisfied.
In this case, xÂ²yâ�´ = 18Â²(1/2)â�´, which is NOT divisible by 9.

If x=18 and y=9, both statements are satisfied.
In this case, xÂ²yâ�´ = 18Â²9â�´, which IS divisible by 9.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.

Last edited by GMATGuruNY on Sun Jul 22, 2012 4:05 am, edited 1 time in total.

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

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jul 21, 2012 8:39 pm

Deleted.

Last edited by Anurag@Gurome on Sat Jul 21, 2012 9:18 pm, edited 1 time in total.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Like this post

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

by eagleeye » Sat Jul 21, 2012 9:14 pm

For those of you who are math buffs, here's a mathematical proof of Insufficiency when both statements are taken together.

1. x=3m (where m is an integer)

2. xy=9n (where n is an integer)

Combining the two, (3m)*y=9n => y = 3n/m.

Hence x^2*y^4 = (3m)^2*(3n/m)^4 = 3^6*(n^2/m)^2.

Since n^2/m can be anything ranging from an integer to an even fraction depending upon m and n, The two together are insufficient.

E is correct. Cheers

Last edited by eagleeye on Sat Jul 21, 2012 9:27 pm, edited 1 time in total.

Like this post

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jul 21, 2012 9:20 pm

eagleeye wrote:If x is an integer and and so is xy, y doesn't have to be an integer.

Thanks for pointing it out. Deleted my post.

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