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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.

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. _________________

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.

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!

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

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, ...

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.

Bunuel,

Thanks for explaining the relationship b/w even/odd & integer!

So, the right way to approach statement [1] is --> m/2 is not an even integer or m/2 is not even... The above analysis - then also opens up the possibility that m/2 could also be a fraction

Hence, given that m/2 could be odd or could be a fraction --> m can take even or odd values, therefore INSUFFICIENT.

So, GMAT wants to test us by giving us the FACT that m is an integer but m/2 can be even or odd [still an integer] or it could be a fraction!

(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.

(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.

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. _________________

Kindly support by giving Kudos, if my post helped you!

(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.

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. _________________

Data Sufficiency - Question 72 from the Official Guideline GMAT 2015 [#permalink]

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08 May 2016, 09:13

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This might be posted somewhere else but I cannot find it.

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

My original answer was (D), EACH Alone are sufficient, however, the correct answer is (B), only (2) is sufficient. The explanation of why (1) is not sufficient is kind of confusing, at least for me.

"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 definitely whether m is odd or even"

This is my reasoning... if m is 3... 3/2 is not an integer... so 3/2 could not be even considered [u]because we are working with integer only? Then 3 does NOT satisfy the condition. So m equals every odd number multiple by 2 which is always an even number... therefore you can answer the question saying that m is NOT 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.

(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.

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

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,

gmatclubot

Re: If m is an integer, is m odd?
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13 Nov 2013, 17:07

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