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.
Is N odd?
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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.
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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Target question: Is the integer n odd?kamalakarthi wrote:Is the integer n odd?
1. n² - 2n is not a multiple of 4.
2. n is a multiple of 3.
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
Cheers,
Brent
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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.
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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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.
GMAT assassins aren't born, they're made,
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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.
GMAT assassins aren't born, they're made,
Rich
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"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.
As I mentioned in the first reply, 0 is a multiple of 4.
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One important property that isn't intuitive to most students is that 0 is a multiple of EVERY integer.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.
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.