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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, 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

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

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

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.

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

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.

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.

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