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MGMAT- is x divisible by 4?

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by scoobydooby » Thu Dec 04, 2008 5:21 am
austin wrote:y is an odd number. square of an odd number divided by 8 leaves remainder 1.

p = x^2 + y^2
when p is divided by 8, the remainder is 5
When y^2 is divided by 8, the remainder is 1 (from above)
=> when x^2 is divided by 8, the remanider is 4
=> x^2 is divisible by 4 => x is divisible by 4

The remainder when p is divided by 8 = the remainder when X^2 is divided by 8 + the remainder when y^2 is divided by 8...

Hope its clear now...
have a doubt austin:
if x^2 divisible by 4. say x^2=4 or x=2, then x will not be divisible by 4. am i missing something?
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by mental » Tue Dec 09, 2008 6:10 am
An after thought

WHY Y^2 when divided by 8 will leave remainder 1?

given y is odd

let y = (2k + 1).....where k is an integer 0,1,2,3,4,....and so on

y^2 = (2k + 1)^2 = (4k^2 + 4k + 1) = {4k(k+1) + 1}

now k(k+1) are two consecutive integers and the product will always be divisible by 2
Hence 4k(k+1) will always be divisible by 8
so the remainder will be 1

whenever the square of an odd number is divided by 8 it will leave remainder as 1

Also:
whenever the square of an odd number is divided by 8 or 4 or 2 it will leave remainder as 1
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by mental » Tue Dec 09, 2008 6:11 am
An after thought

WHY Y^2 when divided by 8 will leave remainder 1?

given y is odd

let y = (2k + 1).....where k is an integer 0,1,2,3,4,....and so on

y^2 = (2k + 1)^2 = (4k^2 + 4k + 1) = {4k(k+1) + 1}

now k(k+1) are two consecutive integers and the product will always be divisible by 2
Hence 4k(k+1) will always be divisible by 8
so the remainder will be 1

whenever the square of an odd number is divided by 8 it will leave remainder as 1

Also:
whenever the square of an odd number is divided by 8 or 4 or 2 it will leave remainder as 1
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by srisl11 » Tue Dec 09, 2008 7:22 am
mental wrote:

whenever the square of an odd number is divided by 8 it will leave remainder as 1

Also:
whenever the square of an odd number is divided by 8 or 4 or 2 it will leave remainder as 1
Very useful tip , Thank you :)
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by Mo2men » Wed Jul 05, 2017 4:34 am
srisl11 wrote:If p, x, and y are positive integers, y is odd, and p = x^2 + y^2, is x divisible by 4?

(1) When p is divided by 8, the remainder is 5.

(2) x � y = 3

Please help
OA A
Dear GMATGuru,

Can you show an easy way for dealing with statement 1???
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by GMATGuruNY » Wed Jul 05, 2017 4:42 am
Mo2men wrote:Dear GMATGuru,

Can you show an easy way for dealing with statement 1???
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