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If x and y are positive integers, is x an even integer ? 1 -

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If x and y are positive integers, is x an even integer ? 1 - [#permalink] New post 10 Sep 2005, 12:28
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A
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C
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E

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If x and y are positive integers, is x an even integer ?

1 - x(y+5) is even
2 - 6y^2 + 41y + 25 is even

I answered C but apparently it's wrong

My logic :
1 alone is not sufficent
2 alone is not sufficent
now if we take take them together, from 2 we know that 41y is odd thus y is odd. Since y is odd, x must be even.

The right answer is E but don't understand why !! help
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Re: DS - is X even ? [#permalink] New post 10 Sep 2005, 13:28
Hello Zoom!! Let me try to explain why it is E. =)

In 1, the equation will be even if X is even, if y+5 is even, or if both are even. The general rule is even x even = even and odd x even = even. Since y can equal any number, 1 alone is not sufficient.

In 2, you know nothing about x so it alone is not sufficient.

When we add the two equations together, you can try to plug in numbers for y in (2). You'll notice that only when y=an odd number will equation (2) equate to an even result. If we plug in an odd number for y into (1), y=5 will always be even. Going back to our general rules, x can be both even or odd to make (1) true.

I hope that helps!!

zoom wrote:
If x and y are positive integers, is x an even integer ?

1 - x(y+5) is even
2 - 6y^2 + 41y + 25 is even

I answered C but apparently it's wrong

My logic :
1 alone is not sufficent
2 alone is not sufficent
now if we take take them together, from 2 we know that 41y is odd thus y is odd. Since y is odd, x must be even.

The right answer is E but don't understand why !! help
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Re: DS - is X even ? [#permalink] New post 10 Sep 2005, 14:54
zoom wrote:
Since y is odd, x must be even.


Actually if y is odd, x can be even or odd. Because y+5 will be even if y is odd, then we have x being multiplied by an even number, which automatically will yield an even product regardless of the value of x.

So statements 1 and 2 together are insufficient.
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 [#permalink] New post 10 Sep 2005, 15:11
thanks for explanation ... I understand better why it's E
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Re: DS - is X even ? [#permalink] New post 13 Sep 2005, 05:16
zoom wrote:
If x and y are positive integers, is x an even integer ?

1 - x(y+5) is even
2 - 6y^2 + 41y + 25 is even

I answered C but apparently it's wrong

My logic :
1 alone is not sufficent
2 alone is not sufficent
now if we take take them together, from 2 we know that 41y is odd thus y is odd. Since y is odd, x must be even.

The right answer is E but don't understand why !! help


All we need to do is plug in numbers to see if x can be an even or an odd number. We also know that Even x Even = Even, Even x Odd (or vice versa) = Even, and the only time a multiplication results in an odd is when an odd is multiplied by another odd #.

1) is insufficient as x could be either
2) is also insufficient since we know nothing about x by itself
1 + 2 putting the 2 statements together since y can be even or odd to yield an even for statement 2 this is also insufficient

Answer is E
Re: DS - is X even ?   [#permalink] 13 Sep 2005, 05:16
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