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If 9 is a factor of 2x, which of the following may not be an

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If 9 is a factor of 2x, which of the following may not be an [#permalink] New post 06 Mar 2007, 20:24
If 9 is a factor of 2x, which of the following may not be an integer?
a)6x/54 +2x/3
B)(4x-18)/9
C) (2x+27)/9
D)(81-4xsqr)/81
E)(2x-3)/3
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 [#permalink] New post 06 Mar 2007, 23:54
(A) for me :)

We have : 2*x = 9*k where k is an integer

A) 6x/54 +2x/3
= 3*(2*x)/54 + 2*x/3
= 3*(9*k)/54 + 9*k/3
= 3*k/6 + 3*k
= k/2 + 3k : may or may not be an integer :)

For a verification :)

B) (4x-18)/9
= (18*k - 18)/9
= 2k - 2 >>>>> OK

C) (2x+27)/9
= (9*k + 27) / 9
= k + 3 >>>> OK

D) (81-4xsqr)/81
= I dont know the meaning u want to put ;)

E) (2x-3)/3
= (9*k - 3)/3
= 3*k - 1 >>> OK
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 [#permalink] New post 07 Mar 2007, 09:11
(A) is the answer

In (D),

(81-4xsqr)/81 can be written as

=> 81/81 - 4*x^2/81

=> 1 - (2x * 2x)/81

as 9 is a factor of 2x, 2nd part is also an integer.
  [#permalink] 07 Mar 2007, 09:11
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If 9 is a factor of 2x, which of the following may not be an

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