kaplan test question

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ayushiiitm: Master | Next Rank: 500 Posts; Posts: 216; Joined: Wed Jul 23, 2008 2:35 am; Location: Pune, India; Thanked: 5 times; GMAT Score:700

by ayushiiitm » Sat Jul 24, 2010 7:50 am

it is given that 9 is a factor of 2x

so why 6x/54 is not considered to be an integer

My approach was:

9 has 2 3's

so since 2x is divisible by 9, x must have 2 3's

hence 6x will have (2*3*3*3) which makes up for prime factors of 54 (2*3*3*3)

hence 6x must be divisible by 54

Please point out flaw in my thinking

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Source: Beat The GMAT — Problem Solving | Sat Jul 24, 2010 7:50 am

4GMAT_Mumbai: Master | Next Rank: 500 Posts; Posts: 161; Joined: Mon Apr 05, 2010 9:06 am; Location: Mumbai; Thanked: 37 times

by 4GMAT_Mumbai » Sat Jul 24, 2010 7:56 am

Why assume that x is an integer?

x could have been 4.5.

9 is thus a factor of 2x.

6x = 27 (and hence, not divisible by 54).

Hope this helps. Thanks.

Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai

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ayushiiitm: Master | Next Rank: 500 Posts; Posts: 216; Joined: Wed Jul 23, 2008 2:35 am; Location: Pune, India; Thanked: 5 times; GMAT Score:700

by ayushiiitm » Sun Jul 25, 2010 12:19 pm

Thanks Got it

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dinesh19aug: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Thu Feb 21, 2008 9:05 am; Thanked: 7 times

by dinesh19aug » Sun Jul 25, 2010 8:50 pm

Ans is A

A) 6x/54 + 2x/3 ==> 2x is multiple of 9 has 2x/3 will be integer.
6x/54 ===> 3*2x/54 ===> If 2x =9, then this is a fraction hence A

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frank1: Legendary Member; Posts: 537; Joined: Fri Jan 22, 2010 10:06 pmFollowed by: 1 member; Thanked: 14 times

by frank1 » Mon Jul 26, 2010 3:39 am

what am i missing here?
which may not be integer?

Ok if x=2.5 as said here...
it gives
d) (81-4 (2.5)^2)/81=0.69
which is not an integer

doesnt that answer/satifies the above question
it says 'may' or may be not

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BastiG: Master | Next Rank: 500 Posts; Posts: 146; Joined: Sun Jun 13, 2010 5:05 am; Thanked: 7 times

by BastiG » Mon Jul 26, 2010 10:51 am

x should be at least 4,5 and then it works.

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KapTeacherEli: GMAT Instructor; Posts: 578; Joined: Tue Aug 25, 2009 6:00 pmFollowed by: 62 members; Thanked: 136 times

by KapTeacherEli » Tue Jul 27, 2010 5:46 pm

BastiG wrote:x should be at least 4,5 and then it works.

Got it!

4.5 is 9/2, so we have 81 - 4 * [(9/2)^2] all over 81. Square the fraction (PEMDAS!) and we get 81 - 4 * (81/4). The fours cancel, and we get 0/81 = 0, which is an integer.

Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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