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kaplan test question

by ayushiiitm » Sat Jul 24, 2010 7:50 am
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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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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.
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by ayushiiitm » Sun Jul 25, 2010 12:19 pm
Thanks Got it
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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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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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by BastiG » Mon Jul 26, 2010 10:51 am
x should be at least 4,5 and then it works.
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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.
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www.kaptest.com/gmat

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