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If p is a positive odd integer, what is the remainder when p [#permalink]
 17 Mar 2008, 07:51
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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
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Senior Manager
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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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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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Senior Manager
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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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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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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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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 +1So, the second statement is unsufficient! Edit: Ok i miss what is said here p positive odd integerSo it's D.
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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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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??
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