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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]

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17 Mar 2008, 06:51
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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, remainder is 5
(2) p is the sum of the squares of 2 positive integers
Senior Manager
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17 Mar 2008, 07:40
D. Just pick some examples. In the first case it's always 3, and in the second case it's always 1.
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17 Mar 2008, 07:50
Thanks, after a while i can prove it systematically, i missed out the (2) at the 1st time, (1) is easy...

Another one...

Each employee of Z is an employee of either Division X or Division Y, not both. If each has some part-time employees, is the ratio of the number of full-time to part-time employees greater for X than for Z?
(1) Ratio of full-time to the number of part-time is less for Y than for Z
(2) More than half of the full-time employees of Z are employees of X, and more than half of the part-time are Y.

Common sense .. can guess out, but is there any way of proving? what i mean 'short' is maybe less than 1min, but sure on the result.... welcome input
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17 Mar 2008, 08:58
AlbertNTN wrote:
Thanks, after a while i can prove it systematically, i missed out the (2) at the 1st time, (1) is easy...

Another one...

Each employee of Z is an employee of either Division X or Division Y, not both. If each has some part-time employees, is the ratio of the number of full-time to part-time employees greater for X than for Z?
(1) Ratio of full-time to the number of part-time is less for Y than for Z
(2) More than half of the full-time employees of Z are employees of X, and more than half of the part-time are Y.

Common sense .. can guess out, but is there any way of proving? what i mean 'short' is maybe less than 1min, but sure on the result.... welcome input

D

I would personally prefer to atleast write it down in some form of equation or inequality before taking a shot at it. From statement 1 you can say:
(Fx+Fy)/(Px+Py) > Fy/Py so it makes sense to say (Fx+Fy)/(Px+Py) < Fx/Px
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22 May 2008, 05:00
AlbertNTN 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, remainder is 5
(2) p is the sum of the squares of 2 positive integers

1- List of numbers that when divided by 8 have a remainder of 5:
5, 13, 21, 29, 37,...
divide all these numbers by 4. Here remainder is 1.

2. p is odd, so we need one odd and one even for the sum to be odd.

1^2 + 2^2 = 5 =>remainder = 1
2^2 + 11^2 = 125 ==> remainder = 1

D.
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22 May 2008, 05:02
sreehari wrote:
D. Just pick some examples. In the first case it's always 3, and in the second case it's always 1.

I believe this is GMATPrep question and in GMAT both A and B, if answer is D, should produce same result - so if you come across the case where you get two different results in A and B something is wrong
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23 May 2008, 01:30
sreehari wrote:
D. Just pick some examples. In the first case it's always 3, and in the second case it's always 1.

Hello, i found A here.
I don't get what you affirm here because for stmt 2, if p=52 we have remainder(p/4)=0 since 4*12=52 and p=52=16+36=4^2+6^2
But if p=25=16+9=4^2+3^2, remainder(p/4)=1 since 25=4*6+1
So, the second statement is unsufficient!

Edit:
Ok i miss what is said here p positive odd integer
So it's D.
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23 May 2008, 04:41
mbawaters wrote:
AlbertNTN 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, remainder is 5
(2) p is the sum of the squares of 2 positive integers

1- List of numbers that when divided by 8 have a remainder of 5:
5, 13, 21, 29, 37,...
divide all these numbers by 4. Here remainder is 1.

2. p is odd, so we need one odd and one even for the sum to be odd.
1^2 + 2^2 = 5 =>remainder = 1
2^2 + 11^2 = 125 ==> remainder = 1

D.

Heres the clue =>

p is odd, so we need one odd and one even for the sum to be odd =>
sum of sqaures is of the form => (2x)^2 + (2x+1)^2 => 4(2x^2+x)+1
Thus, the remainder is always one.
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23 May 2008, 08:50
AlbertNTN 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, remainder is 5
(2) p is the sum of the squares of 2 positive integers

I think it´s A:

(1) when p is divided by 8, remainder is 5 - OK, suff
(2) p is the sum of the squares of 2 positive integers - Lest´s try
1^2 + 1^2 = 2 - remainder 2
2^2 + 2^2 = 8 - remainder 0
3^2 + 3^2 = 18 - remainder 2
4^2 + 4^2 = 32 - remainder 0
5^2 + 5^2 = 50 - remainder 2

HOW CAN IT BE SUFFICIENT??
Re: DS prob   [#permalink] 23 May 2008, 08:50
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