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

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Manager
Joined: 15 Nov 2006
Posts: 224
Location: Ohio
Followers: 1

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If 9 is a factor of 2x, which of the following may not be an [#permalink]  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
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

(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
Manager
Joined: 09 Jan 2007
Posts: 240
Followers: 1

Kudos [?]: 7 [0], given: 0

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.
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