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Re: If m is an integer, is m odd?  [#permalink]

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Not wanting to find excuses, but I do think that statement 1 is wrongly phrased. Epsecially since the gmat is quite strict in verbal, when it comes to meaning!

So, for me, "m is not an even integer" means that it is an integer that is not even. Otherwise, it should have been: m is not even. Then it can be whatever - integer or not - as long as it is not even. Then, the question stem would make sense:

The stem says "If m is an integer, is m odd?", which means: in the case than m is an integer, is it odd? So, it leaves some space on m being an integer or not.

Reading , you actually read "m is an integer that is not odd", because "not an even" describes the word integer. So, the adjective "even" describes the word "integer". "Not even" is also used as an adjective, and it still describes the word "integer". This does not leave any space for confusion: m should be an integer.

If a verbal genius is around perhaps he/she could refute this argument! Haha! Intern  Joined: 16 May 2015
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Re: If m is an integer, is m odd?  [#permalink]

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okay..got it..we don't have to consider fraction when we talk about Even and ODD. How about negative integer? Can we exclude it too for Odd and Even Qs? Thanks
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Re: If m is an integer, is m odd?  [#permalink]

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katzzzz wrote:
okay..got it..we don't have to consider fraction when we talk about Even and ODD. How about negative integer? Can we exclude it too for Odd and Even Qs? Thanks

1. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. Even integers are: ..., -6, -4, -2, 0, 2, 4, 6, 8, ...

2. An odd number is an integer that is not evenly divisible by 2: ..., -5, -3, -1, 1, 3, 5, ...

Theory on Number Properties: math-number-theory-88376.html
Tips on Number Properties: number-properties-tips-and-hints-174996.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

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Re: If m is an integer, is m odd?  [#permalink]

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Quote:
If m is an integer, is m odd?

(1) m/2 is not an even integer.
(2) m – 3 is an even integer.

This thread sure had some interesting discussion related to St. 1 Here's an alternate, visual, way of processing St. 1:

We'll try to get a visual sense of what St. 1 is conveying.

We know that 'Integers' is a subset within the set of ALL Real Numbers. And, this set of 'Integers' is further divided into two subsets - Even and Odd.

So, if I represent the subset 'Even Integers' with Red color, then the blue zone represents 'Integers that are not Even, that is, Odd Integers'. And the white zone represents 'Non-Integers.' Now, if you are told that a real number X is not an Even Integer, that only means that X doesn't lie in the Red Zone.

Can X lie in the blue zone? Sure it can.

Can X lie in the white zone? It can.

So, if you are told that some real number is not an even integer, you are only sure about what this integer is NOT. This number can be an odd integer, or it can be a non-integer (in other words, a fraction).

So, when St. 1 tells you that m/2 is not an even integer, two possibilities arise:

Case 1. m/2 is an odd integer
=> m = 2*odd = Even integer

Case 2. m/2 is a non-integer.
That is, m is not completely divisible by 2.
That is, m leaves a non-zero remainder when divided by 2.

Now, the only possible non-zero remainder that results when a number is divided by 2, is 1 (because 0 ≤ Remainder < Divisor)

This means, m = 2q + 1

That is, m = Odd integer.

Thus, from St. 1, we see that m can either be an even integer or an odd integer. So, St. 1 is not sufficient to arrive at a unique answer.

Hope this visual representation helped further cement your understanding of why St. 1 is insufficient. Best Regards

Japinder
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Re: If m is an integer, is m odd?  [#permalink]

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Bunuel wrote:
If m is an integer, is m odd?

(1) m/2 is not an even integer --> $$\frac{m}{2}\neq{even}$$ could occur when $$m$$ is odd as well as when $$m$$ is even (10 and 5 for example) --> $$\frac{m}{2}=\frac{10}{2}=5\neq{even}$$ and $$\frac{m}{2}=\frac{5}{2}=2.5\neq{even}$$. Not sufficient.

(2) m-3 is an even integer --> $$m-odd=even$$ --> $$m=even+odd=odd$$. Sufficient.

statement 1 - m/2 is not an even integer, i am a bit confused, what i interpreted is that the outcome of m/2 has to be an integer.

So if you consider the outcome to be an integer, than m will always be even.
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Re: If m is an integer, is m odd?  [#permalink]

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harishbiyani8888 wrote:
Bunuel wrote:
If m is an integer, is m odd?

(1) m/2 is not an even integer --> $$\frac{m}{2}\neq{even}$$ could occur when $$m$$ is odd as well as when $$m$$ is even (10 and 5 for example) --> $$\frac{m}{2}=\frac{10}{2}=5\neq{even}$$ and $$\frac{m}{2}=\frac{5}{2}=2.5\neq{even}$$. Not sufficient.

(2) m-3 is an even integer --> $$m-odd=even$$ --> $$m=even+odd=odd$$. Sufficient.

statement 1 - m/2 is not an even integer, i am a bit confused, what i interpreted is that the outcome of m/2 has to be an integer.

So if you consider the outcome to be an integer, than m will always be even.

Your interpretation is not correct.

For m/2 not to be an even integer m can be even (10) as well as odd (5). (1) just says that m/2 is not an even integer, from which you can no way assume that m/2 is an odd integer, it can not be an integer at all.
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Re: If m is an integer, is m odd?  [#permalink]

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dzodzo85 wrote:
If m is an integer, is m odd?

(1) m/2 is not an even integer.
(2) m – 3 is an even integer.

We are given that m is an integer and we must determine whether it is odd.

Statement One Alone:

m/2 is not an even integer.

The information in statement one is not enough to determine whether m is odd since m can be odd or even. For example, if m = 3 (an odd number), m/2 = 3/2 = 1.5 is not an even integer. On the other hand, if m = 2 (an even number), m/2 = 2/2 = 1 is not an even integer also.

Thus, statement one is not sufficient to determine whether m is odd. We can eliminate answer choices A and D.

Statement Two Alone:

m – 3 is an even integer.

Since m – 3 is an even integer, we can say m – 3 = even. That is, m = even + 3. Since 3 is odd and we know that even + odd = odd, we know that m must be an odd integer.

Statement two is sufficient to answer the question.

The answer is B.
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Re: If m is an integer, is m odd?  [#permalink]

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- In 1st case

m/2 is not an even integer , so if m is divisible by 2 then m has to be even.

How can we test by substituting m=5 ?

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Re: If m is an integer, is m odd?  [#permalink]

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prags1989 wrote:
- In 1st case

m/2 is not an even integer , so if m is divisible by 2 then m has to be even.

How can we test by substituting m=5 ?

m/2 is not an even integer does not mean that m/2 is necessarily an odd integer, it can be non-integer too.
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Re: If m is an integer, is m odd?  [#permalink]

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Bunuel wrote:
If m is an integer, is m odd?

(1) m/2 is not an even integer --> $$\frac{m}{2}\neq{even}$$ could occur when $$m$$ is odd as well as when $$m$$ is even (10 and 5 for example) --> $$\frac{m}{2}=\frac{10}{2}=5\neq{even}$$ and $$\frac{m}{2}=\frac{5}{2}=2.5\neq{even}$$. Not sufficient.

(2) m-3 is an even integer --> $$m-odd=even$$ --> $$m=even+odd=odd$$. Sufficient.

Why isn't '0' not taken into consideration here? 0 is an integer too.
Statement 1 says m/2 is NOT an even integer. Could it mean that m/2 is zero or positive?
The answer is B, I agree. But for clarification, I'd like to know whether '0' is a possible scenario in statement 1.

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Re: If m is an integer, is m odd?  [#permalink]

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ganesh999 wrote:
Bunuel wrote:
If m is an integer, is m odd?

(1) m/2 is not an even integer --> $$\frac{m}{2}\neq{even}$$ could occur when $$m$$ is odd as well as when $$m$$ is even (10 and 5 for example) --> $$\frac{m}{2}=\frac{10}{2}=5\neq{even}$$ and $$\frac{m}{2}=\frac{5}{2}=2.5\neq{even}$$. Not sufficient.

(2) m-3 is an even integer --> $$m-odd=even$$ --> $$m=even+odd=odd$$. Sufficient.

Why isn't '0' not taken into consideration here? 0 is an integer too.
Statement 1 says m/2 is NOT an even integer. Could it mean that m/2 is zero or positive?
The answer is B, I agree. But for clarification, I'd like to know whether '0' is a possible scenario in statement 1.

Yes, m is an integer. More, it's even integer. So, m cannot be 0 in (1) because in this case m/2 = 0/2 = 0 = even, which contradicts the given fact that m/2 is not an even integer.
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Re: If m is an integer, is m odd?  [#permalink]

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