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Re: If p is a positive odd integer, what is the remainder when p [#permalink]
23 Feb 2012, 07:57

21

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If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5 --> \(p=8q+5=(8q+4)+1=4(2q+1)+1\) --> so the remainder upon division of p by 4 is 1 (since first term is divisible by 4 and second term yields remainder of 1 upon division by 4). Sufficient.

(2) p is the sum of the squares of two positive integers --> since p is an odd integer then one of the integers must be even and another odd: \(p=(2n)^2+(2m+1)^2=4n^2+4m^2+4m+1=4(n^2+m^2+m)+1\) --> the same way as above: the remainder upon division of p by 4 is 1 (since first term is divisible by 4 and second term yields remainder of 1 upon division by 4). Sufficient.

If p is a positive odd integer, what is the remainder when p [#permalink]
26 Jul 2012, 07:05

I am not sure if this is discussed, tried to find it but couldn't find easily.

If p is a positive odd integer, what is the remainder when p is divided by 4 ? (1) When p is divided by 8, the remainder is 5. (2) p is the sum of the squares of two positive integers.

I need help, here i thought the answer was A but the official answer given is D. Here's how i did it

(1) P = 8Q + 5, so for all values of Q starting from 1, 4 divided by P results in remainder 1. So sufficient (2) P = X^2+ Y^2, ex X=Y=1, P= 2, remainder 2. ex X=1,Y=2, P=5, remainder 1. Hence Not Sufficient.

Re: If p is a positive odd integer, what is the remainder when p [#permalink]
26 Jul 2012, 07:09

1

This post received KUDOS

Expert's post

summer101 wrote:

I am not sure if this is discussed, tried to find it but couldn't find easily.

If p is a positive odd integer, what is the remainder when p is divided by 4 ? (1) When p is divided by 8, the remainder is 5. (2) p is the sum of the squares of two positive integers.

I need help, here i thought the answer was A but the official answer given is D. Here's how i did it

(1) P = 8Q + 5, so for all values of Q starting from 1, 4 divided by P results in remainder 1. So sufficient (2) P = X^2+ Y^2, ex X=Y=1, P= 2, remainder 2. ex X=1,Y=2, P=5, remainder 1. Hence Not Sufficient.

Confused?

Merging similar topics.

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Re: If p is a positive odd integer, what is the remainder when p [#permalink]
25 Jan 2013, 20:43

number plugging is the fastest approach for remainder problems.. because there emerges a definite pattern.. that can make the stem sufficient. _________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Re: If p is a positive odd integer, what is the remainder when p [#permalink]
31 Jan 2013, 04:03

OK.. Let me quote here something..

Let's consider x=1 and y=2... square of two number is 5 (a positive odd integer) and leaves remainder 5 when divided by 8 Again..consider x=1 and y = 6, square of two numbers is 37 (a positive odd integer) and leaves remainder 5 when divided by 8 hence, both the statements are either sufficient to ans this problem..

Re: If p is a positive odd integer, what is the remainder when p [#permalink]
04 Sep 2013, 10:12

D

1) Is sufficient 5,13 all give 1 as remainder. 2) sum of squares of any two positive integers, but one of them has to be odd and other an even number because p is an odd integer. So consider any pair 3,2 (3^2+2^2) (9+4)/4 1 as remainder. Or 5,2 =>29/4 =>1 as remainder. _________________

--It's one thing to get defeated, but another to accept it.

The question asks what will be the remainder when P is divided by 4.

Statement 1 says: p=8n+5…..which is when P is divided by 8 we get remainder 5. Now from here on you can do two things. 1. think logically 8n is divided by 4 so we won't have any remainder if we divide 8n by 4 but if we divide 5 by 4 we always get remainder 1. The value of N doesn't really matter because 8N will always be divisible by 4 and 5 will always give remainder 1. 2. plug in number and see what happens. If we put n=1,2,3,4 or so on….we get 13,21,29 respectively. Now in each case we get remainder 1.

So statement 1 is sufficient. Answer should be either A or D. So cross out B C and E.

Statement 2 says: p is sum of square of two integers just plug in numbers and see you will always get remainder 1. So statement 2 is sufficient and Answer is D.

Re: If p is a positive odd integer, what is the remainder when p [#permalink]
28 Sep 2014, 06:29

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If p is a positive odd integer, what is the remainder when p [#permalink]
20 Jul 2015, 09:23

Can you please explain why the other number has to be even as p is odd? When we take two odd numbers ie {(1,3),(3,5),(5,7)} etc.. the sum of squares are (10,34,74) and all those give a remainder of 2. Please do explain.

Re: If p is a positive odd integer, what is the remainder when p [#permalink]
21 Jul 2015, 00:46

1

This post received KUDOS

chandrae wrote:

Can you please explain why the other number has to be even as p is odd? When we take two odd numbers ie {(1,3),(3,5),(5,7)} etc.. the sum of squares are (10,34,74) and all those give a remainder of 2. Please do explain.

Hi Chandrae,

According to the question, p needs to be a positive odd integer.

If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5. (2) p is the sum of the squares of two positive integers.

In statement 2, p can only be odd if one of the squares is odd and the other is even. ( Even + Even = Even, Odd + Odd = Even and Even + Odd = Odd).

Therefore, the cases you mentioned (in which the sum of squares is even) can not be considered as eligible values of p as per the question.

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