Factor Question

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mlaboda: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sun Jan 25, 2009 2:34 pm; Thanked: 1 times

by mlaboda » Thu Apr 23, 2009 4:45 am

Thank you ahead of time for your help!

x is divisible by 144. if x^(1/3) is an integer, then which of the following is x^(1/3) definitely divisible by? (Choose all that apply)

A. 4
B. 8
C. 9
D. 12

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Source: Beat The GMAT — Problem Solving | Thu Apr 23, 2009 4:45 am

Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

Re: Factor Question

by Vemuri » Thu Apr 23, 2009 6:18 am

mlaboda wrote:Thank you ahead of time for your help!

x is divisible by 144. if x^(1/3) is an integer, then which of the following is x^(1/3) definitely divisible by? (Choose all that apply)

A. 4
B. 8
C. 9
D. 12

x^(1/3) must definitely be divisible by 4 & 12.

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rossmj: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Feb 26, 2009 12:50 pm; Location: Chicago; Thanked: 3 times

by rossmj » Thu Apr 23, 2009 6:43 am

If x is divisible by 144 then its prime factorization must contain at least (3^2)(2^4). If the cube root of x is an integer then it must contain at least 3 or a multiple of 3 of each of its prime factors. Therefore it must contain at least (3^3)(2^6) the cube root of this leaves us with 3(2^2). Manhattan Gmat does a great job explaining this in its Number Properties book.

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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Thu Apr 23, 2009 7:35 am

It took me less than 10 seconds to solve this

if x^(1/3) is an integer

Now look for the Option which is having an Integral Cube root

Only (B) that is 8 has cube-root = 2(integer)

rest don't satisfy this condition

Hope this helps

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rossmj: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Feb 26, 2009 12:50 pm; Location: Chicago; Thanked: 3 times

by rossmj » Thu Apr 23, 2009 7:46 am

gmat740, the correct answer is 4 and 12 not 8. After taking the cube root of X we are left with 3(2^2)=12 we can also divide by 4 because we have 2 2s. We want factors of x^1/3. I think you probably read the question a little too quickly but there are 2 answers which is a possiblity mentioned in the question.

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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Thu Apr 23, 2009 8:01 am

Thanks for correcting me!
I read the question way too fast.

I took x to be multiple of 144 although the question ask you just the reverse.

You see,just a careless mistake can land you up with wrong answer

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Sun Apr 26, 2009 2:16 pm

This is a "tongue twister" of a question (maybe brain twister).

4 and 12 for me as well.

Good question.

rgds

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