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If x and y are positive integers, is y odd?

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If x and y are positive integers, is y odd?  [#permalink]

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New post 07 Mar 2019, 06:49
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If x and y are positive integers, is y odd?

(1) (y+2)!/x! is an odd integer.
(2) (y+2)!/x! is greater than 2.

For this question I'm curious how can we assume that (y+2) should be odd? I'm not sure if there are rule that established relationship when odd number is divided by odd OR even divided by even?

Thanks everyone :)
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If x and y are positive integers, is y odd?  [#permalink]

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New post 07 Mar 2019, 06:57
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pichitrat wrote:
If x and y are positive integers, is y odd?

(1) (y+2)!/x! is an odd integer.
(2) (y+2)!/x! is greater than 2.

For this question I'm curious how can we assume that (y+2) should be odd? I'm not sure if there are rule that established relationship when odd number is divided by odd OR even divided by even?

Thanks everyone :)


for example \(\frac{9!}{8!}\) = 9 which is odd

let 9 = (y+2)
and 8 = x
now you can find the relation between x and y in general : x = y + 1
in this case, y must be odd.

but another option is that y+2 = x,
in this case \(\frac{(y+2)!}{x!}\) = 1 which is odd
in this case, y can be even or odd ( no restriction)

since we can't decide which one is correct, so statement 1 is insufficient.
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Re: If x and y are positive integers, is y odd?  [#permalink]

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New post 07 Mar 2019, 07:05
pichitrat wrote:
If x and y are positive integers, is y odd?

(1) (y+2)!/x! is an odd integer.
(2) (y+2)!/x! is greater than 2.

For this question I'm curious how can we assume that (y+2) should be odd? I'm not sure if there are rule that established relationship when odd number is divided by odd OR even divided by even?

Thanks everyone :)


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Re: If x and y are positive integers, is y odd?   [#permalink] 07 Mar 2019, 07:05
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