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(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.

(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.

(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. _________________

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!

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]

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25 Apr 2013, 20:46

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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

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.

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

(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,

(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

Merging similar topics. Please refer to the solutions above.

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 [1], 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!

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 [1], 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!

I agree with Natalia! The wording of statement 1 is confusing. One could think that m is an integer but not even ==> m is an odd integer. Is it correct wording? By the way there are some guys who do not care about correct wording. How come should i guess that x^2y is not x to the power of 2y but x(^2)y??? Moderators please pay attention to this=)) _________________

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 [1], 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!

First of all this is OG question, so it's as good as it gets.

Next, only integers can be odd or even. So, there is no difference in saying x is even and x is an even integer. _________________

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 [1], 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!

I agree with Natalia! The wording of statement 1 is confusing. One could think that m is an integer but not even ==> m is an odd integer. Is it correct wording? By the way there are some guys who do not care about correct wording. How come should i guess that x^2y is not x to the power of 2y but x(^2)y??? Moderators please pay attention to this=))

x^2y means x^2*y ONLY. If it were x to the power of 2y, then it would be written as x^(2y). _________________

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