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# If p is a positive integer, is p even?

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If p is a positive integer, is p even? [#permalink]

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20 Jun 2014, 17:50
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If p is a positive integer, is p even?

(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
[Reveal] Spoiler: OA

Last edited by langtuprovn2007 on 20 Jun 2014, 18:40, edited 1 time in total.
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Re: If p is a positive integer, is p even? [#permalink]

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20 Jun 2014, 18:08
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langtuprovn2007 wrote:
If p is a positive integer, is p even?
(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
help me with this

st.1 p=3k+1, where k is an integer. when k=0, p=1 and when k=1 p=4 and for k=2, p=7

as different values of p are possible for different values of k hence statement 1 alone is not sufficient

st.2 p=4t+1, where t is an integer. for all values of t, p will always be odd. because product of 4t will always result in even number and since 1 is odd. therefore even plus odd will always be odd.
p=even (4t) + odd (1) = odd
hence statement two alone is sufficient to answer the question.

ans. is B
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Re: If p is a positive integer, is p even? [#permalink]

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20 Jun 2014, 18:28
oh great I cannot even think about that solution ! thank you very much ! Can you help me with another problems
n is an integer between 2 and 84. What is the value of n?
(1) The square root of n is divisible by 5.
(2) n is both the square and the cube of an integer.
Tks :D
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Re: If p is a positive integer, is p even? [#permalink]

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20 Jun 2014, 21:49
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langtuprovn2007 wrote:
oh great I cannot even think about that solution ! thank you very much ! Can you help me with another problems
n is an integer between 2 and 84. What is the value of n?
(1) The square root of n is divisible by 5.
(2) n is both the square and the cube of an integer.
Tks :D

Statement 1:
n should be a perfect square as squareroot of n is divisible by 5

So perfect square between 2 and 84 are 4,9,16,25,36,49,64,81

Now only sqrt(25) is divisible by 5, hence sufficient

Statement 2:
Perfect cube between 2 and 84 are : 8,27,64..
Perfect squares are: 4,9,16,25,36,49,64,81

Hence n= 64. Sufficient.
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Re: If p is a positive integer, is p even? [#permalink]

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21 Jun 2014, 04:15
If p is a positive integer, is p even?

(1) p divided by 3 leaves a remainder of 1 --> p = 3q + 1 --> p could be 1, 4, 7, ... So, as you can see p can be odd as well as even. Not sufficient.

(2) p divided by 4 leaves a remainder of 1 --> p = 4m + 1 = even + odd = odd (p could be 1, 5, 9, ...). Sufficient.

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Re: If p is a positive integer, is p even? [#permalink]

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21 Jun 2014, 04:24
langtuprovn2007 wrote:
oh great I cannot even think about that solution ! thank you very much ! Can you help me with another problems
n is an integer between 2 and 84. What is the value of n?
(1) The square root of n is divisible by 5.
(2) n is both the square and the cube of an integer.
Tks :D

This is a poor quality question, since the values of n differ from (1) and (2), while on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem.
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Re: If p is a positive integer, is p even? [#permalink]

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19 Aug 2014, 05:05
As 3 is odd every odd multiple will be odd and every even multiple will be even, so adding 1 in it can have both even or odd results…..Insufficient.
4 is even so every multiple will be even and +1 will make it odd everytime…Sufficient. Answer is B.
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Re: If p is a positive integer, is p even? [#permalink]

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22 Aug 2016, 06:20
We need to get the even odd character of p
Statement 1 => P can be 1 or 4 ((or anything else too))=> insuff
Statement 2 => P=4p+1 => Even +odd = Odd => NO P is not even => Suff
Smash that B
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Re: If p is a positive integer, is p even?   [#permalink] 22 Aug 2016, 06:20
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