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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]  22 Sep 2008, 05:02
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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 integer.

Can anyone explain how to answer this quickly?
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Re: DS from GMATPrep - good one [#permalink]  22 Sep 2008, 05:31
I think A is suff.

No. if divided by 8 (4 *2) gives reminder 5.. so if we divide reminder 5 by 4 we will get1 ...so A is suff.

B is not suff.. last digit of any square no. will be 1,4,5,6,9

1+4 = 5 % 4 = 1

1+5 = 6 % 4 = 2

so we will not get sure answer. B is not sufficient

Thanks
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Re: DS from GMATPrep - good one [#permalink]  22 Sep 2008, 08:49
I find both statements independently as sufficient.
A - 'coz when a number is divisible by 8,it's also divisible by 4.remainder 5 divided by 4 will always leave 1 as remainder.
so from choice A ,1 will be remainder.

B- is sufficient 'coz any even number will be of the form 2x.so if p = sq(2a) + sq(2b)= 4[sq(a) + sq(b)].dividing such a number
by 4 will always give remainder 0.

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Re: DS from GMATPrep - good one [#permalink]  22 Sep 2008, 09:31
[quote="Nerdboy"]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 integer.

from one

when p is devided by 2(4) the remainder is 5 thus when p is devided by 4 remainder is 1

suff

from 2

just try any 2 values

4+1/4 , remainder is 1.

9+4/4 reminder is 1.

16+49/4 remainder 1

81+64 / 4 remainder 1
................suff

Last edited by yezz on 22 Sep 2008, 12:21, edited 1 time in total.
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Re: DS from GMATPrep - good one [#permalink]  22 Sep 2008, 09:35
I find both statements independently as sufficient.
A - 'coz when a number is divisible by 8,it's also divisible by 4.remainder 5 divided by 4 will always leave 1 as remainder.
so from choice A ,1 will be remainder.

B- is sufficient 'coz any even number will be of the form 2x.so if p = sq(2a) + sq(2b)= 4[sq(a) + sq(b)].dividing such a number
by 4 will always give remainder 0.

How do you get even number? To me, stmt2 simply says that p = a^2 + b^2.
For a=1 and b=2, p = 5 and remainder = 1 when divided by 4.
For a=1 and b=3, p = 10 and remainder = 2 when divided by 4.

Hence, B is insufficient.
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Re: DS from GMATPrep - good one [#permalink]  22 Sep 2008, 09:46
P is an odd integer...

you cant have 49+25..

i think D is correct
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Re: DS from GMATPrep - good one [#permalink]  22 Sep 2008, 09:53
fresinha12 wrote:
P is an odd integer...

you cant have 49+25..

i think D is correct

Why is p an odd integer?

If p = a^2 + b^2 then both a and b can be odd, even or one odd and the other even and accordingly, p can be odd or even.
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Re: DS from GMATPrep - good one [#permalink]  22 Sep 2008, 10:09
The problem states that p is an odd positive integer.

Therefore by statement 2

p = (2k+1)^2+(2n)^2= 4k^2+4k+1+4n^2

Therefore remainder one.

Therefore sufficient.
Re: DS from GMATPrep - good one   [#permalink] 22 Sep 2008, 10:09
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