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

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Manager
Joined: 28 Feb 2003
Posts: 100
Followers: 1

Kudos [?]: 3 [0], given: 0

What is the remainder when p^2 + p is divided by 2? 1) p [#permalink]  19 May 2003, 02:54
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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
Joined: 28 Feb 2003
Posts: 100
Followers: 1

Kudos [?]: 3 [0], given: 0

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
SVP
Joined: 03 Feb 2003
Posts: 1613
Followers: 6

Kudos [?]: 46 [0], given: 0

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.
Intern
Joined: 04 Nov 2004
Posts: 15
Location: Hamilton Ontario
Followers: 0

Kudos [?]: 0 [0], given: 0

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.
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