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

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Is P odd ? (1) The sum of P, P + 4, and P + 11 is even. (2) The sum of  [#permalink]

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New post Updated on: 31 Oct 2018, 22:05
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Originally posted by carcass on 31 Oct 2018, 10:10.
Last edited by Bunuel on 31 Oct 2018, 22:05, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Is P odd ? (1) The sum of P, P + 4, and P + 11 is even. (2) The sum of  [#permalink]

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New post 31 Oct 2018, 10:17
carcass wrote:
Is 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) The sum of P, P + 4, and P + 11 is even. ==> 3P+15 is even ==>3P is odd ==> P is odd ..... Suff
2) The sum of P – 3, P, and P + 11 is odd. ==> 3P+8 is dd ==>3P is odd ==> P is odd ..... Suff......................Thus Ans D
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Re: Is P odd ? (1) The sum of P, P + 4, and P + 11 is even. (2) The sum of  [#permalink]

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New post 31 Oct 2018, 10:21
Statement 1.
Sum of P, P + 4, and P + 11 is even.
3P + 15 is even ( 3P has to be odd)
Now two case:
1) P is integer then P has to be ODD- Sufficient
2) P in not integer P=1/3 then P is not ODD- Not sufficient
Statement 2.
Sum of P – 3, P, and P + 11 is odd.
3P +8 is ODD ( 3P has to be ODD)
Again two case as above NOT sufficient
Combine two statement no change.
SO E.
Correct me if I am wrong carcass
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Re: Is P odd ? (1) The sum of P, P + 4, and P + 11 is even. (2) The sum of  [#permalink]

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New post 31 Oct 2018, 10:22
u1983 wrote:
carcass wrote:
Is 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) The sum of P, P + 4, and P + 11 is even. ==> 3P+15 is even ==>3P is odd ==> P is odd ..... Suff
2) The sum of P – 3, P, and P + 11 is odd. ==> 3P+8 is dd ==>3P is odd ==> P is odd ..... Suff......................Thus Ans D


is it given P is an integer?? can we assume it??
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Re: Is P odd ? (1) The sum of P, P + 4, and P + 11 is even. (2) The sum of  [#permalink]

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New post 31 Oct 2018, 10:53
carcass wrote:
Is 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. Sum, 3P + 15 is even. So 3P is even - 15, odd. P is odd. Sufficient.
2. Sum, 3P + 8 is odd. 3P is odd - 8, odd. P is odd. Sufficient.

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Re: Is P odd ? (1) The sum of P, P + 4, and P + 11 is even. (2) The sum of  [#permalink]

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New post 31 Oct 2018, 11:02
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carcass wrote:
Is 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.


Ways to have an even number is if both are even or both are odd.

To get an odd the two numbers must differ meaning one is odd and the other is even.


Statement 1) 3p + 15 = even

This is odd + odd = even

So p must be odd. Sufficient.

Statement 2)

3p + 8 = odd

Odd + even = odd.

P is odd. Sufficient

Answer choice D

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Re: Is P odd ? (1) The sum of P, P + 4, and P + 11 is even. (2) The sum of   [#permalink] 31 Oct 2018, 11:02
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