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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, 08:09
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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, 08:57
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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, 08:05
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, 08:09
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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:


Merging similar topics.

Please hide OA under the spoiler.
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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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!


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Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 26 Jul 2012, 08:11
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, 21:43
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, 05:03
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] 31 Jan 2013, 05:03
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