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Re: If m is an integer, is m odd? [#permalink]
27 Mar 2012, 02:24

Expert's post

2

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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.

Re: If m is an integer, is m odd? [#permalink]
31 Mar 2012, 05:18

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.

Answer: B.

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

Re: If m is an integer, is m odd? [#permalink]
31 Mar 2012, 05:23

2

This post received KUDOS

Expert's post

Rigorous 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.

Answer: B.

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

Not so. (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. _________________

If M is an integer, is m odd? [#permalink]
02 Feb 2013, 10:31

(1) m/2 is not an even integer

(2) m-3 is an even integer

I was a bit confused about what statement 1 even meant to be honest. The correct answer is B (only state 2 being sufficient). Can someone help me understand what statement 1 is saying... as well as why it is insufficient? Thanks!

Re: If M is an integer, is m odd? [#permalink]
02 Feb 2013, 11:12

Expert's post

1

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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. _________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

Re: Number Properties related question [#permalink]
25 Apr 2013, 19:46

2

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ahatoval wrote:

Hey guys,

Can anybody explain me why the following is B?

If m is an integer, is m odd?

(1) m/2 is NOT an even integer (2) m - 3 is an even integer.

My thought process was:

(1) Since m/2 is NOT an even integer, then => it IS an odd integer. subsequently ODD * 2 = EVEN. Sufficient

Many thanks,

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

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.

Re: If M is an integer, is m odd? [#permalink]
07 May 2013, 08:18

exploringm wrote:

(1) m/2 is not an even integer

(2) m-3 is an even integer

I was a bit confused about what statement 1 even meant to be honest. The correct answer is B (only state 2 being sufficient). Can someone help me understand what statement 1 is saying... as well as why it is insufficient? Thanks!

in my opinion,m/2 is not an even integer means that m/2 could be an odd integer,but also can not be an integer at all, e.g. a decimal

Re: If m is an integer, is m odd? [#permalink]
13 Nov 2013, 16:07

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.

Answer: B.

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,

Re: If m is an integer, is m odd? [#permalink]
14 Nov 2013, 00:42

Expert's post

selfishmofo 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.

Answer: B.

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. _________________

If m is an integer, is m odd? 1. (m/2) is not an even integer 2. m - 3 is an even integer

The answer is B. This is how the explanation is: 1. Since m could be either the odd integer 3 or the even integer 10 and still satisfy this condition, there is no information to show definitively whether m is odd or even; NOT sufficient 2. If m-3 is an even integer, then m-3 = 2k for some integer k m = 2k +3 = 2(k+1) + 1, which is odd; Sufficient.

My question, I understand why 2 is sufficient. When I look at 1, it states that (m/2) is not an even integer. I said if (m/2) is not even then it is odd then:

(m/2) could be (1, 3, 5, 7, 9, 11, etc) then: m would be (2, 6, 10, 14, 18, 22, etc). This would mean that m has to be even which is sufficient to answer the question. Can somebody explain why the way I approached it was wrong? Thank You

If m is an integer, is m odd? 1. (m/2) is not an even integer 2. m - 3 is an even integer

The answer is B. This is how the explanation is: 1. Since m could be either the odd integer 3 or the even integer 10 and still satisfy this condition, there is no information to show definitively whether m is odd or even; NOT sufficient 2. If m-3 is an even integer, then m-3 = 2k for some integer k m = 2k +3 = 2(k+1) + 1, which is odd; Sufficient.

My question, I understand why 2 is sufficient. When I look at 1, it states that (m/2) is not an even integer. I said if (m/2) is not even then it is odd then:

(m/2) could be (1, 3, 5, 7, 9, 11, etc) then: m would be (2, 6, 10, 14, 18, 22, etc). This would mean that m has to be even which is sufficient to answer the question. Can somebody explain why the way I approached it was wrong? Thank You

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