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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] New post 20 Jun 2014, 16:50
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75% (01:42) correct 25% (00:39) wrong based on 51 sessions
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, 17:40, edited 1 time in total.
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Re: If p is a positive integer, is p even? [#permalink] New post 20 Jun 2014, 17:08
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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] New post 20 Jun 2014, 17:28
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] New post 20 Jun 2014, 20:49
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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



Answer would be "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] New post 21 Jun 2014, 03:15
Expert's post
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.

Answer: B.

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Re: If p is a positive integer, is p even? [#permalink] New post 21 Jun 2014, 03:24
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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


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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If p is a positive integer, is p even? [#permalink] New post 19 Aug 2014, 04:05
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.
Re: If p is a positive integer, is p even?   [#permalink] 19 Aug 2014, 04:05
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