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Is product 2*x*5*y an even integer? a. 2 + x + 5 + y is an

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Is product 2*x*5*y an even integer? a. 2 + x + 5 + y is an [#permalink] New post 23 May 2008, 02:18
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Is product 2*x*5*y an even integer?

a. 2 + x + 5 + y is an even integer
b. x - y is an odd integer
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Re: M16-18 [#permalink] New post 23 May 2008, 02:42
I guess it is C.

1. 2*x*5*y is always even integer if x and y are integers. But for non integers, for example,x=1/3, y=1/3, the expression will not be an integer.

2. the first condition: 2 + x + 5 + y is an even integer if only x+y is an odd integer. Again, x=4/3 and y=2/3 make the result of the expression non integer value.

3. the second condition: x=4/3 and y=1/3 make the result of the expression non integer value.

4. two conditions. It is obviously that x+y and x-y can be integers only if non integers are x=a+0.5, y=b+0.5. (a and b are integers)

So, 1-st condition: x+y=a+b+1 is odd or a+b is even; 2-nd condition: a-b is odd. For any a,b It is impossible to satisfy both conditions if x or y are non integers. Therefore, C.
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Re: M16-18 [#permalink] New post 23 May 2008, 05:33
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walker wrote:
I guess it is C.

1. 2*x*5*y is always even integer if x and y are integers. But for non integers, for example,x=1/3, y=1/3, the expression will not be an integer.

2. the first condition: 2 + x + 5 + y is an even integer if only x+y is an odd integer. Again, x=4/3 and y=2/3 make the result of the expression non integer value.

3. the second condition: x=4/3 and y=1/3 make the result of the expression non integer value.

4. two conditions. It is obviously that x+y and x-y can be integers only if non integers are x=a+0.5, y=b+0.5. (a and b are integers)

So, 1-st condition: x+y=a+b+1 is odd or a+b is even; 2-nd condition: a-b is odd. For any a,b It is impossible to satisfy both conditions if x or y are non integers. Therefore, C.


Good expl. I agree.
Re: M16-18   [#permalink] 23 May 2008, 05:33
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