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What is the remainder when p^2 + p is divided by 2? 1) p

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Manager
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What is the remainder when p^2 + p is divided by 2? 1) p [#permalink] New post 19 May 2003, 02:54
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B
C
D
E

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What is the remainder when p^2 + p is divided by 2?

1) p > 2
2) p is an integer
Manager
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 [#permalink] New post 19 May 2003, 20:56
no, the answer is B

from statement 1......
p can be 2.5, 5.7, etc....in which case the remainder will be different....

from statement 2.....
p can be 0, 1, -1, 2, 3, -3, 10,11.......in all the cases the remainder will be zero....therefore 2 alone is sufficient........answer is B
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 [#permalink] New post 19 May 2003, 21:52
sure it is B.

Take a look at p(p+1) -- a product of two CONSEQUTIVE numbers. One of them HAS to be EVEN. This fact is sufficient to insist that the remainder when divided by 2 is 0.
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 [#permalink] New post 30 Nov 2004, 19:37
I look at it like this

p^2 + p

if p is an integer then its either even or even.

IF odd then
odd x odd = odd (p * p)
odd + odd = even (p^2 + p) -which can be divided by 2

IF even then
even x even = even (p * p)
even + even = even (p^2 + p)

Hence B is sufficient.
In (I) if could be 2.5 and there are lot of possibilites. :wink:
  [#permalink] 30 Nov 2004, 19:37
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