Question: Is n Even?

Comment on Is n Even?

I'm confused on statement 1. If multiply 3*4 and divide by 6 I get 2...Which is an even number and "N" is an even number. If I multiply 3*2 and divide by 6 I get 1.. which is an odd number and N is an even number. Doesn't that contradict one another, making the statement insufficient?
gmat-admin's picture

Statement 1 tells us that 3n/6 is ODD.
This means that n cannot equal 4 (as you suggest), since 3(4)/6 = 2, and 2 is EVEN

could you also answer this question by substituting n with variables of odd and even for each statement to find that both statements are sufficient? that's the route I took and I got the same answer
gmat-admin's picture

The problem with the "testing numbers" approach is that, when the statement is sufficient, you cannot be 100% certain the statement is sufficient if you just test values.

For example, let's say we're working with statement 1, and we plug in n = 4, and it satisfies the condition that 3n/6 is an odd integer. Since 4 is even, can we then conclude that statement 1 is sufficient? No. We can't make that conclusion, because there may exist a different value of n (and ODD value) that also satisfies the condition in satisfies the condition.

More on that here:

I still did not understand statement 1) eg:

n=1► 3*1/6 = 3/6 = 0.5 not applicable
n=2► 3*2/6 = 6/6 = 1 sufficient since 1 is odd
n=3► 3*3/6 = 9/6 = 1.5 not applicable
n=4► 3*4/6 = 12/6 = 2 but 2 is not an odd integer hence two statements contradict each other i.e when n=2 we get 1 which is odd and n=4 where we get 2 which is an even integer which goes against the statement 1. Doesnt that mean statement 1 is insufficient?

Am I missing something?

gmat-admin's picture

If 3n/6 is an ODD integer (statement 1), then some possible values of n are: 2, 6, 10, 14, 18, 22, etc

In all of the above possible cases, n is always even.

ASIDE: n cannot equal 4 since 3(4)/6 = 2, and 2 is not an odd integer.

statement 1 where 3n/6 is an odd integer. Does this mean the only integer n can have is 2? Eg: 3*2/6= 1 is an odd integer. For remaining integers
3*1/6 gives us decimal, not possible
3*3/6 gives us decimal, not possible
3*4/6 = 12/6 = 2 it gives us an even integer which cannot be possible

Am I assuming it right?

Thanks and regards,
Shirish Nayak
gmat-admin's picture

You are correct in that n cannot equal 4, since 3(4)/6 = 2, and 2 is not an odd integer.

However, there are infinitely other possible values of n (see my post above)

When determining if the statements in the above video were sufficient, I used the following approach:

1. 3n / 6 = odd integer
6 * odd integer = 3n
Since 6 is even, 3n must be even.
3 is odd, so n must be even

2. 6 / 3n = odd integer
3n * odd = 6
So, 3n must be even. Since 3 is odd, n must be even

Is this valid and can it be applied in all cases?
gmat-admin's picture

That approach certainly works for this question.

YOUR QUESTION: Can it be applied in all cases?
I'm hesitant to say it will work for the infinitely-many possible integer properties questions, but it's worth trying.

please explain
gmat-admin's picture
how to handle such questions, sir, I was able to count till 4
gmat-admin's picture

In the first statement, can one rationalize this way:

3 times x/6 is odd. x/6 to be an integer, x has to be even, since 6 only divides into even numbers.

And actually, in the first statement the number being odd doesn´t add any useful insight right?

2nd statement:

For 2/x to be an integer, x has to be smaller or equal to two. As soon as the denominator is greater than the numerator, it ncan´t be an integer right?

gmat-admin's picture

You're correct on both questions.

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