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If m is an integer, is m odd?

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If m is an integer, is m odd? [#permalink] New post 27 Mar 2012, 02:22
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If m is an integer, is m odd?

(1) m/2 is not an even integer.
(2) m – 3 is an even integer.
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Re: If m is an integer, is m odd? [#permalink] New post 27 Mar 2012, 02:24
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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.

Answer: B.
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Re: If m is an integer, is m odd? [#permalink] New post 27 Mar 2012, 05:54
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.

Please explain this question further


can some body please explain to me why A is INSUFFICIENT

i see it this way

given that select those items which make m/2 <> even

so take
m = 6, 10, -10, -14 etc

they give 3,5,-5,-7 etc...

so m is even , so is m odd is answered in NEGATIVE.....so this is sufficient to answer the question right?

can some please explain why it is INSUFFICIENT
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Re: If m is an integer, is m odd? [#permalink] New post 27 Mar 2012, 05:58
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harshavmrg wrote:
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.

Please explain this question further


can some body please explain to me why A is INSUFFICIENT

i see it this way

given that select those items which make m/2 <> even

so take
m = 6, 10, -10, -14 etc

they give 3,5,-5,-7 etc...

so m is even , so is m odd is answered in NEGATIVE.....so this is sufficient to answer the question right?

can some please explain why it is INSUFFICIENT


Please read the solution above:
For m/2 not to be an even integer m can be even (10) as well as odd (5).
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Re: If m is an integer, is m odd? [#permalink] New post 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.

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

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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.
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If M is an integer, is m odd? [#permalink] New post 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!
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Re: If M is an integer, is m odd? [#permalink] New post 02 Feb 2013, 11:12
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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.
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Re: Number Properties related question [#permalink] New post 25 Apr 2013, 19:46
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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

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
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Re: If M is an integer, is m odd? [#permalink] New post 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
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Re: If m is an integer, is m odd? [#permalink] New post 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,
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Re: If m is an integer, is m odd? [#permalink] New post 14 Nov 2013, 00:42
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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.
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If m is an integer, is m odd? [#permalink] New post 10 Jan 2014, 04:44
This is a question from OG 12th edition

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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Re: If m is an integer, is m odd? [#permalink] New post 10 Jan 2014, 05:39
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aelayat2 wrote:
This is a question from OG 12th edition

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


Merging similar topics. Please refer to the solutions above.

As for your doubt please check here: if-m-is-an-integer-is-m-odd-129702.html#p1067835

Hope it helps.
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Re: If m is an integer, is m odd? [#permalink] New post 24 May 2014, 20:55
1) M/2 is not an even integer

Odd / Even = Not an integer
Even / Even = Odd, Even or not an integer

Not sufficient can be odd or even

2) M - 3 is an even integer

Odd - Odd = Even
Even - Odd = Odd

Must be Odd for m - 3 to be an even integer.
Sufficient
Re: If m is an integer, is m odd?   [#permalink] 24 May 2014, 20:55
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