If m is an integer, is m odd?

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.

Answer: B.

Ok thanks guys. I assumed that 1) meant m/2 is an integer that is not even. I guess when they say it's not an even integer, I should always interpret it as anything but an even integer (therefore, it can be odd integer or odd non-integer)

Only integers can be even or odd, so "m/2 is not an even integer" means that m/2 is odd (integer) or not an integer at all.

I have just a quick question. How can you use 10 for an example in your explaination of m/2. m must always be a negative number. So actually 1 is not sufficient because you would never get a integer. Right?

We are not told that m must be a negative number, so 10 is fine for an example.

Again: "m/2 is not an even integer" means that either m/2 is odd (integer) or not an integer at all.

\(\frac{m}{2}=\frac{10}{2}=5=odd\) --> \(m=even\);
\(\frac{m}{2}=\frac{5}{2}=2.5=not \ an \ integer\) --> \(m=odd\).

Hope it's clear.

Can someone please help me understand this. Is my approach correct?

If m is an integer, is m odd?

1. m/2 is not an even number
2. m-3 is an even number

My understanding is that each choice should not lead to a "Maybe" answer. But can it be sufficient if it leads to a "NO" or does it always have to be a "YES".

1. If we take m=10, the result is 5 which is not even. Therefore statement is sufficient in answering No m is not odd.

2. 5-3=2 which is even. Therefore statement 2 is sufficient because it also has a unique Yes answer that m is odd.

Thus the answer is D.

1. Says m/2 is not even then m cannot be even .Hence it can be only be odd number (since it is given m is an integer). YES> Sufficient

2. m-3 is even number. We will get even number only if "m" is "odd"...because only odd-/+odd or even-/+even will give you even .Since we have 3 (odd) the only option to get even is m being ODD.
YES > SUFFICIENT

Hence D is the answer

No, your approach is not quite right here. When you looked at Statement 1, you only picked one value for m, m=10. You will always get *some* answer to the question when you pick a value for m. Unfortunately that doesn't tell you much. If Statement 1 is sufficient, that means the answer must *always* be the same, for *every* value of m. So you can never only test one value in a DS question. Here, using Statement 1 alone, m could certainly be 10 and thus be even, but m could also be 11 and be odd. So we can get both a yes and a no answer using Statement 1, and it is not sufficient.

Statement 2 is sufficient, however, since if m - 3 is equal to an even number, then m is equal to an even number plus 3, so must be odd.

Finally, I'd add that in real GMAT questions, the two statements can never be inconsistent. If, in a yes/no DS question, each Statement is sufficient alone, they will both need to always give the same answer: either both will always give a yes answer or both will always give a no answer. If you think one statement always gives a yes answer and the other always gives a no answer, that's a certain sign that you've done something wrong.

@ IanStewart

Statement 1 is what actually confused me. According to what you said, if we use m=10 (an even number), we get 5 which is not even satisfying statement 1 and proving m is not odd. When we use m=11, 11/2 gives us 5 1/2 which is not even but it is not odd either. So can we actually use 11 or any odd number to test?

Statement 1 says that "m/2 is not an even number". If m = 11, then 11/2 is not an even number - it's not an integer at all, so it's not even or odd. So with Statement 1, m could certainly be 11, or could certainly be 10, and the statement is not sufficient.

Answer is C. But answer in statement A is No and Answer in statement 2 is Yes. funny one

Your understanding of DS is correct. It's a YES/NO DS question. In a Yes/No Data Sufficiency question, each statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no".

Though you're missing a point for statement (1), which says: 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 \(\frac{m}{2}=\frac{5}{2}=2.5\neq{even}\). So this statement is not sufficient.



First of all answer to the question is B, not C. Next, your case can never happen on the GMAT: as on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

So we can not have answer NO from statement (1) and answer YES from statement (2) (as you got in your solution), because in this case statements would contradict each other.

Hope it's clear.

Isn't \(\frac{m}{2}\) said to be an integer (though not even)? So that \(\frac{5}{2}\) is not the case.

Posted from GMAT ToolKit

Hi there,

m/2 is not an even integer

This means that if you divide the variable m (which represents some number) that the result will not be an even (a number divisible by 2) integer (a whole number: -1,-2,0,1,2...). So M cannot be the number 4 because 4/2 =2 which is an even integer. m could be 5 because 5/2 = 2.5 which is not an integer nor is it even. M could be 6 because 6/2 =3 which is an integer but is not even.

So the main point of this statement is that there are two possibilities for m: m is either an even number with only ONE 2 as a factor (2, 6, 14...) or m is odd. Therefore the statement is insufficient because m could be an even number or an odd number.

I hope this helps. Let me know if you need any more advise on this.

HG.

Hi ahatoval, this is a common mistake the GMAT likes to exploit, so it's good to have a complete understanding of it. The key is keeping track of what must be an integer, and what doesn't have to be.

Statement 2 is correct because m has to be an integer, so any odd integer -3 (or -5 or -7) would be even. Sufficient.

You seem to be more concerned with statement 1. This statement tells us that m is an integer, but that m/2 is not an even integer. This is not the same thing as being an odd integer. Let's look at values of m/2 for different m's

m=1 --) m/2 = 0.5
m=2 --) m/2 = 1
m=3 --) m/2 = 1.5
m=4 --) m/2 = 2
...
pattern repeats

Therefore, if m/2 is not an even integer, then m=4 is excluded from the list of possibilities. This leaves m=1, m=2 and m=3. M/2 can therefore be an odd integer or a non-integer. Since we have examples of both, we cannot conclude with certainty whether m is an odd integer, it can be either 1 or 2 or 3 (or 5 or 6 or 7...)

The assumption you make that leads you down the rabbit hole on this question is that m/2 must be an integer. This is not stated in the question and easily demonstrated to be false with a few small examples. On Data Sufficiency, it's often a good idea to try a few numbers and see if you can discern a pattern.

Hope this helps!
-Ron

Banuel,

Statement 2 Threw me off When I read it. M-3= Even. This is a true statement to the GMAT correct, so does this mean that I now start testing for M. Would it be better to test odd #'s first, then move to even numbers? Such as M=3,5,7,9,

\(m-odd=even\) means that m is odd: \(m=even+odd=odd\). So, you have an YES answer to the question and don't need to test any numbers at all.