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If a positive integer n, divided by 5 has a remainder 2

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If a positive integer n, divided by 5 has a remainder 2 [#permalink] New post 20 Mar 2013, 15:14
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If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2

A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III

Last edited by Bunuel on 21 Mar 2013, 02:27, edited 1 time in total.
Renamed the topic and edited the question.
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Re: if a positive integer n,divided by 5 has a remainder 2 [#permalink] New post 20 Mar 2013, 15:40
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If a positive integer n,divided by 5 has a remainder 2,which of the following must be true
I. n is odd
II. n+1 cannot be a prime number
III. (n+2)divided by 7 has remainder 2

Some valid values for n: 7, 12, 17, 22, 27, 32... or, in other words: n=(i * 5) + 2 for i=1,2,3...

I. FALSE: we see that n can we odd or even.
II. FALSE: (n+1) could be a prime number. Example: n=12 --> (n+1)=13 is prime. Other example: for n=22, (n+1)=23 is prime.
III. FALSE: for n=12, (n+2)=14, divided by 7 has remainder zero.

None answer is true.

Answer: A
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Re: if a positive integer n,divided by 5 has a remainder 2 [#permalink] New post 20 Mar 2013, 20:53
I. 22 and 27 both have a reminder of 2. So False (Options remaining - A,D,E)
II. 22 + 1 = 23 is a prime number. So False (Options remaining - A)

Ans (A)
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Re: if a positive integer n,divided by 5 has a remainder 2 [#permalink] New post 20 Mar 2013, 20:54
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chiccufrazer1 wrote:
If a positive integer n,divided by 5 has a remainder 2,which of the following must be true I. n is odd
II. n+1 cannot be a prime number
III. (n+2)divided by 7 has remainder 2

A.none
B.I only
C.I and II only
D.II and III only
E.I,II and III


n can be written as :

n = 5k+2. Thus, taking k=0, we have n=2.

I.n=2,even.False
II.2+1=3, is a prime. False.
III.n+2 = 4,4 divided by 7 leaves a remainder of 4. False.

A.
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Re: if a positive integer n,divided by 5 has a remainder 2 [#permalink] New post 21 Mar 2013, 00:36
chiccufrazer1, you forgot to provide the OA in your post. Just make sure you do provide it for your future problems. :)

Alright, let's solve this :

We know that n, a positive integer, yields a remainder of 2 when divided by 5. So according to the algebraic form of the division operation, we'll have :

n = 5*q + 2 with q being a positive integer as well.

This expression allows us to give out some valid possibilities for n by playing with the value of q, such as :

q = 0 => n = 2
q = 1 => n = 7
q= 2 => n =12

Now, from these first values we can already cross off statement I.(n is odd) , since n can be 7 (which is odd) or n can be 12 (which is even).

Statement II. (n+1 cannot be a prime number) can also be crossed off. Consider n = 12, which is not a prime number and yields a remainder of 2 when divided by 5. If we add 1 to it, we get 13, which IS a prime number, so that contradicts statement II.

Finally, statement III. (n+2 yields a remainder of 2 when divided by 7) can also be crossed off. Again consider n = 12. Add 2 to it and we get a 14 which is a multiple of 7.

In short, all statements have been contradicted and the correct answer choice to the question is A : none of the statements above are true.

Hope that helped. :-D
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Re: If a positive integer n, divided by 5 has a remainder 2 [#permalink] New post 21 Mar 2013, 03:16
Expert's post
If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2


A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III[/quote]

A positive integer n, divided by 5 has a remainder 2 --> n=5q+2, so n could be 2, 7, 12, 17, 22, 27, ...

I. n is odd. Not necessarily true, since n could be 2, so even.

II. n+1 cannot be a prime number. Not necessarily true, since n could be 2, so n+1=3=prime.

III. (n+2) divided by 7 has remainder 2. Not necessarily true, since n could be 7, so n+2=9.

Answer: A.

Hope it's clear.
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Re: If a positive integer n, divided by 5 has a remainder 2   [#permalink] 21 Mar 2013, 03:16
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