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Is N odd?

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kamalakarthi Senior | Next Rank: 100 Posts Default Avatar
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Is N odd?

Post Mon Oct 06, 2014 8:42 am
Is the integer N odd ?

1. n^2-2n is not a multiple of 4.
2. N is a multiple of 3.

In this above question, I am not able to understand how statement 1 is sufficient.
Following is my analysis :-

when N is 2, I get 2^2 - 2(2) which is 0 and it is not multiple of 4 but N is even.
When N is 3, The value is get 9-6 =3 which is also not multiple of 4 but N is odd.

With the above analysis, I thought statement 1 is NOT sufficient.

I can undertstand that statement 2 will not be sufficient because n can be 3 or 6.

Can you please help me understand the statement 1.

Thank you.
-karthik.

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fcabanski Master | Next Rank: 500 Posts
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Post Mon Oct 06, 2014 11:31 am
"If I choose N as 2, then when I do N-2, the result is 0 which is not a multiple of 4. "

As I mentioned in the first reply, 0 is a multiple of 4.

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Post Sun Oct 12, 2014 10:12 pm
fcabanski wrote:
"If I choose N as 2, then when I do N-2, the result is 0 which is not a multiple of 4. "

As I mentioned in the first reply, 0 is a multiple of 4.
One important property that isn't intuitive to most students is that 0 is a multiple of EVERY integer.

Here's how we know.

(integer x) * (any other integer) = (a multiple of integer x)

Since 0 can be "any other integer", we have

x * 0 = a multiple of x

or

0 = a multiple of x

Hence 0 is a multiple of EVERY integer. You will encounter this on an official GMAT problem sometime, be it the OG, a problem from mba.com, or your actual exam, so it's a good thing to remember.

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fcabanski Master | Next Rank: 500 Posts
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Post Mon Oct 06, 2014 11:31 am
"If I choose N as 2, then when I do N-2, the result is 0 which is not a multiple of 4. "

As I mentioned in the first reply, 0 is a multiple of 4.

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Post Sun Oct 12, 2014 10:12 pm
fcabanski wrote:
"If I choose N as 2, then when I do N-2, the result is 0 which is not a multiple of 4. "

As I mentioned in the first reply, 0 is a multiple of 4.
One important property that isn't intuitive to most students is that 0 is a multiple of EVERY integer.

Here's how we know.

(integer x) * (any other integer) = (a multiple of integer x)

Since 0 can be "any other integer", we have

x * 0 = a multiple of x

or

0 = a multiple of x

Hence 0 is a multiple of EVERY integer. You will encounter this on an official GMAT problem sometime, be it the OG, a problem from mba.com, or your actual exam, so it's a good thing to remember.

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Post Mon Oct 06, 2014 11:24 am
Hi kamalakarthi,

There are some Number Property rules about the number 0 that every Test Taker should know:

1) 0 is EVEN
2) 0 is a "NULL" value; it is neither positive nor negative
3) 0 IS a multiple of EVERY integer.

So, when you multiply 0 and 2, the product = 0, which IS even.

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kamalakarthi Senior | Next Rank: 100 Posts Default Avatar
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Post Mon Oct 06, 2014 11:08 am
Brent , Thank you for your reply.

I can understand that if N is even then N-2 is also even and will be multiple of 4. I think I am missing a point when it comes to 0.

If I choose N as 2, then when I do N-2, the result is 0 which is not a multiple of 4.

I have another doubt in your explanation. "the product of two CONSECUTIVE even integers is always a multiple of 4 "

My understanding is 0 as an even integer and if I take 0 and 2, it is not multiple of 4. Am I right?

I know I am missing a point but trying to understand.

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