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If p is a positive odd integer, what is the remainder when p

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If p is a positive odd integer, what is the remainder when p [#permalink] New post 23 Feb 2012, 07:09
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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.
(2) p is the sum of the squares of two positive integers.
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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 23 Feb 2012, 07:57
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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.

Answer: D.
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If p is a positive odd integer, what is the remainder when p [#permalink] New post 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.

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


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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 26 Jul 2012, 07:11
Hi Summer101

For St 2: U have to make P an odd Integer. If u select X = Y = 1, Then P become 2 i.e. even. Thats why D is the correct answer.
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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 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.
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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 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..
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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 03 Sep 2013, 09:02
BANON wrote:
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 think if you would work straight with digits you would get same result, reminder 1.
Just try 9 and 16, or 4 and 9
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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 03 Sep 2013, 15:32
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Nice one, second part is tricky and needs more focus.
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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 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.
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If P is a positiv [#permalink] New post 19 Sep 2013, 08:47
If P is a positive odd integer, what is the remainder when P is divided by 4 ?

S1) When P is divided by 8, the remainder is 5.

S2) P is the sum of the squares of two positive integers.




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Re: Gmatprep quant question [#permalink] New post 20 Sep 2013, 19:24
m4ch1n3 wrote:
I believe answer is wrong:


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.
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Re: If P is a positiv [#permalink] New post 22 Sep 2013, 05:33
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m4ch1n3 wrote:
If P is a positive odd integer, what is the remainder when P is divided by 4 ?

S1) When P is divided by 8, the remainder is 5.

S2) P is the sum of the squares of two positive integers.




Please pay attention to the following rules.....

1) Always type the question and post. Do not attach mere a screen shot of the question.

2) Always Post the question along with OA. (OA should be in spoiler)

3) Always post the Question in RELEVANT Forum. (e.g. This Quant (DS) question was posted in Verbal Forum)

Thanks.


Merging similar topics. Please refer to the solutions above.
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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 odd integer, what is the remainder when p [#permalink] New post 28 Sep 2014, 06:29
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If p is a positive odd integer, what is the remainder when p [#permalink] New post 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.
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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 21 Jul 2015, 00:46
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.

Hope it clears your doubt.

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