divisibility...

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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.

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, x²y� = 18²(1/2)�, which is NOT divisible by 9.

If x=18 and y=9, both statements are satisfied.
In this case, x²y� = 18²9�, 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.

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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.

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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.

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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.

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