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If x is an even integer which of the following must be an

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If x is an even integer which of the following must be an [#permalink] New post 25 Nov 2007, 19:44
If x is an even integer which of the following must be an odd integer?

A: 3x/2
B: 3x/2 +1
C: 3x^2
D: 3x^2 /2
E: 3x^2 /2 +1
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it's B [#permalink] New post 26 Nov 2007, 08:43
Amnswer is B. Any number multiplied by even is even. Even + 1 is odd
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Re: Even and Odd [#permalink] New post 26 Nov 2007, 08:54
jenniferia2002 wrote:
If x is an even integer which of the following must be an odd integer?

A: 3x/2
B: 3x/2 +1
C: 3x^2
D: 3x^2 /2
E: 3x^2 /2 +1


A: 3x/2 ----------> 3*4/2=6 no
B: 3x/2 +1 -------> 3*2/2+1=4 no
C: 3x^2 -----------> 3*4=12 no
D: 3x^2 /2----------> 3*4/2=2 no
E: 3x^2 /2 +1--------> 3*4/2 + 1= 7 yes. this one is always odd.


E
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 [#permalink] New post 26 Nov 2007, 09:15
If x is an even integer which of the following must be an odd integer?

A: 3x/2
B: 3x/2 +1
C: 3x^2
D: 3x^2 /2
E: 3x^2 /2 +1

b ( 3x/2 = even , even+1 = odd)

E ( 3x^2 = eve, even / even = odd or even...insuff

B is ok
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 [#permalink] New post 26 Nov 2007, 10:46
(E) for me :)

x = 2*k where k is an integer

A: 3x/2
= 3*(2*k)/2
= 3*k..... if k is an odd, the result is an odd otherwise it's even... No

B: 3x/2 +1
= 3*(2*k)/2 + 1
= 3*k + 1..... if k is an even, the result is an odd otherwis it's even... No

C: 3x^2
= 3*(2*k)^2
= 3*4*k^2... Always an even because of the multiplilcation with 4... No

D: 3x^2 /2
= 3*(2*k)^2 / 2
= 3*4*k^2 /2
= 3*2*k^2... Always an even because of the multiplilcation with 2... No

E: 3x^2 /2 +1
= 3*(2*k)^2 / 2 + 1
= 3*4*k^2 /2 + 1
= 3*2*k^2 + 1 ... Always an odd as 3*2*k^2 is always an even because of the multiplilcation with 2... Yes
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Re: Even and Odd [#permalink] New post 26 Nov 2007, 17:19
jenniferia2002 wrote:
If x is an even integer which of the following must be an odd integer?

A: 3x/2
B: 3x/2 +1
C: 3x^2
D: 3x^2 /2
E: 3x^2 /2 +1



A:3x/2 X can be 2. 3(2)/2=3 or 3(4)/2=6 No.
B: (3*2)/2 +1 6/2+1 dsnt equal odd 3+1=4...
C: Always Even.
D: 3*4/2= 6 even so dsnt have to be odd.

E: 3x^2/2 will always be Even so E+O= O

E it is.
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Re: Even and Odd [#permalink] New post 26 Nov 2007, 17:25
jenniferia2002 wrote:
If x is an even integer which of the following must be an odd integer?

A: 3x/2
B: 3x/2 +1
C: 3x^2
D: 3x^2 /2
E: 3x^2 /2 +1


another for E,

used ellimination method
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Re: Even and Odd [#permalink] New post 26 Nov 2007, 17:32
jenniferia2002 wrote:
If x is an even integer which of the following must be an odd integer?

A: 3x/2
B: 3x/2 +1
C: 3x^2
D: 3x^2 /2
E: 3x^2 /2 +1



E. 3x/2 in B could be odd or even but 3x^2 /2 in E must be even. so any even plus 1 is always odd.
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Re: Even and Odd [#permalink] New post 26 Nov 2007, 18:28
jenniferia2002 wrote:
If x is an even integer which of the following must be an odd integer?

A: 3x/2
B: 3x/2 +1
C: 3x^2
D: 3x^2 /2
E: 3x^2 /2 +1


E will always be odd
Re: Even and Odd   [#permalink] 26 Nov 2007, 18:28
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