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Is N odd?

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by kamalakarthi » 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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by fcabanski » Mon Oct 06, 2014 10:05 am
A multiple of 4 is the result of multiplying 4 by an integer. 0 is an integer.

4*0 = 0. 0 is a multiple of 4.

0 is a multiple of every number. 0 is not a factor of any number.
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by Brent@GMATPrepNow » Mon Oct 06, 2014 10:58 am
kamalakarthi wrote:Is the integer n odd?

1. n² - 2n is not a multiple of 4.
2. n is a multiple of 3.
Target question: Is the integer n odd?

Given: n is an INTEGER

Statement 1: n² - 2n is not a multiple of 4.
Factor to get: n(n - 2) is NOT a multiple of 4

Underlying concepts:
Integer n is 2 greater than n-2
If n is ODD, then n-2 is also ODD, so n(n - 2) = (ODD)(ODD) = ODD. In this case, n(n-2) cannot be divisible by 4
If n is EVEN, then n-2 is also EVEN, so n(n - 2) = (EVEN)(EVEN) = EVEN. More importantly, n and n-2 are CONSECUTIVE even integers, and the product of two CONSECUTIVE even integers is always a multiple of 4

Statement 1 tells us that n(n - 2) is NOT a multiple of 4
So, it cannot be the case that n is EVEN
In other words, it MUST be the case that n is ODD
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is a multiple of 3
There are several values of n that satisfy this condition. Here are two:
Case a: n = 3, in which case n n is ODD
Case b: n = 6, in which case n n is EVEN
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
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by kamalakarthi » 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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by [email protected] » 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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by fcabanski » 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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by Matt@VeritasPrep » 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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