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Is the integer P odd?

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Is the integer P odd?  [#permalink]

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Is the integer P odd?

(1) The sum of P, P + 4, and P+ 11 is even.
(2) The sum of P – 3, P, and P+ 11 is odd.

Originally posted by jrzayev001 on 16 Oct 2013, 22:08.
Last edited by Bunuel on 17 Oct 2013, 01:31, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Is the integer P odd? - DS  [#permalink]

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New post 16 Oct 2013, 22:13
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jrzayev001 wrote:
Is the integer P odd?
(1) The sum of P,P + 4, and P+ 11 is even.
(2) The sum of P – 3,P, and P+ 11 is odd.



(1)p+p+4+p+11 = 3p+15 = even --> 3p = even-odd = odd. Thus, as 3p = odd, p has to be odd.Sufficient.

(2)p-3+p+p+11 = 3p+8 = odd --> 3p = odd-even = odd , just as above, p is odd. Sufficient.

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Re: Is the integer P odd? - DS  [#permalink]

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New post 16 Oct 2013, 22:15
What about P to be zero?
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Re: Is the integer P odd? - DS  [#permalink]

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New post 16 Oct 2013, 22:16
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jrzayev001 wrote:
What about P to be zero?



p cannot be zero, because then the given fact statements will not hold good. Think about it.
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Re: Is the integer P odd? - DS  [#permalink]

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New post 16 Oct 2013, 22:24
Yes, i did not think about that :)
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Re: Is the integer P odd?  [#permalink]

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New post 27 Oct 2013, 14:43
Is the integer P odd?

(1) The sum of P, P + 4, and P+ 11 is even.
(2) The sum of P – 3, P, and P+ 11 is odd.


St 1: Let us add all the terms; we get,

3P + 15 = even ..... Hence, 3P is odd ( since even - 15 = Odd)
Therefore P is odd
Sufficient.

St 2: Let us add all the terms; we get,

3P + 8 = odd .... Hence, 3P is odd (since, odd- 8 = odd)
Therefore P is odd
Sufficient.

Answer D
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Re: Is the integer P odd?  [#permalink]

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New post 16 Sep 2018, 02:53
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St 1: P + P+4+P+11 = 3p +15 =3(P+5) = Even
Odd * Even ( Odd + Odd) = Even

St 2: P-3+P+P+11 = 3P + 8 = Odd
Odd (Odd * Odd) + Even = Odd

Hence, D
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Re: Is the integer P odd?  [#permalink]

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New post 16 Sep 2018, 05:31
jrzayev001 wrote:
Is the integer P odd?

(1) The sum of P, P + 4, and P+ 11 is even.
(2) The sum of P – 3, P, and P+ 11 is odd.



1 means 3p + 15 is even, so 3p is odd,
so yes p is odd

2 means 3p + 8 is odd, so 3p is odd - 8 = odd
So p is odd.

D it is
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Re: Is the integer P odd? &nbs [#permalink] 16 Sep 2018, 05:31
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