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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]

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20 Dec 2010, 21:56
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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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21 Dec 2010, 01:29
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psirus wrote:
If m is an integer, is m odd?
(1) m/2 is not an even integer
(2) m-3 is an even integer

I chose D.

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.

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21 Dec 2010, 08:37
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)

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21 Dec 2010, 08:41
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psirus wrote:
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.
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21 Dec 2010, 09:29
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?

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21 Dec 2010, 09:39
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PASSINGGMAT wrote:
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.
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Getting confused, probably a long day... [#permalink]

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30 Nov 2011, 19:09

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.

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Re: Getting confused, probably a long day... [#permalink]

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02 Dec 2011, 08:08
Newbie here, but attempting to answer:

Statement 1: You tested an even number and got a result that was not an even number. You concluded that m is NOT odd, and that statement is sufficient. This could be true, but you should try out other numbers to ensure that m is NEVER odd.

What if m is 3? If m is 3, then m/2 gives 3/2, or 1.5. 1.5 is not an even number either. But m is now odd and the statement is still true.

This shows that m can be odd OR even. Insufficient.

Statement 2: Your approach is correct here. A simple rule for this statement is as follows:

odd +/- odd = even
even +/- even = even
odd +/- even = odd

This statement falls in the first category. We are subtracting an odd number and getting an even number. The only time this can happen is when the first number is also odd. So m is always odd. Sufficient.

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Re: Getting confused, probably a long day... [#permalink]

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05 Dec 2011, 06:04
Answer is C. But answer in statement A is No and Answer in statement 2 is Yes. funny one

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Re: Getting confused, probably a long day... [#permalink]

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05 Dec 2011, 11:32
pratk wrote:

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.

1. m = 10 so m/2=5 is not odd, you are right
But You are missing one thing that m = 5, so m/2 = 2.5, which is not even but m is odd.
Thus statement 1 is not sufficient.

Ans. B
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Re: Getting confused, probably a long day... [#permalink]

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03 Feb 2012, 09:23
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pratk wrote:
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.

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.

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

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.
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Re: If m is an integer, is m odd? [#permalink]

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24 May 2013, 04:21
Bumping for review and further discussion.
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Re: If m is an integer, is m odd? [#permalink]

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17 Feb 2016, 06:21
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Re: If m is an integer, is m odd? [#permalink]

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22 Jan 2017, 02:09
Bunuel wrote:
pratk wrote:
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.

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.

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

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.

Though its old topic and already discussed in detail but still I just want to clarify concept

m/2 is not an even integer. --> m2≠evenm2≠even could occur when mm is odd as well as when mm is even (10 and 5 for example) --> m2=102=5≠evenm2=102=5≠even and m2=52=2.5≠even m 2= 5/2=2.5≠even. So this statement is not sufficient

As per my understanding only integers can be Even or Odd not fractions. If thats true than how 2.5≠even.? Please explain.. Thank you

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Re: If m is an integer, is m odd? [#permalink]

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22 Jan 2017, 03:57
53698 wrote:
Bunuel wrote:
pratk wrote:
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.

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.

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

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.

Though its old topic and already discussed in detail but still I just want to clarify concept

m/2 is not an even integer. --> m2≠evenm2≠even could occur when mm is odd as well as when mm is even (10 and 5 for example) --> m2=102=5≠evenm2=102=5≠even and m2=52=2.5≠even m 2= 5/2=2.5≠even. So this statement is not sufficient

As per my understanding only integers can be Even or Odd not fractions. If thats true than how 2.5≠even.? Please explain.. Thank you

2.5 is not an integer and thus cannot and is not an even integer.
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If m is an integer, is m odd? [#permalink]

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04 Jun 2017, 23:05
Hey, what if you consider M= 1, the second stem will result to -3, since gmat considers 1 as an odd, we have one going against stem 2, won't it cancel the option ? Bunuel, could you please suggest

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Re: If m is an integer, is m odd? [#permalink]

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04 Jun 2017, 23:21
kanaav wrote:
Hey, what if you consider M= 1, the second stem will result to -3, since gmat considers 1 as an odd, we have one going against stem 2, won't it cancel the option ? Bunuel, could you please suggest

It's not clear what you mean but if m = 1 in (2), then we'd have m - 3 = 1 - 3 = -2 = even.
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Re: If m is an integer, is m odd? [#permalink]

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06 Jun 2017, 16:49
psirus wrote:
If m is an integer, is m odd?

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

We need to determine whether integer m is odd.

Statement One Alone:

m/2 is not an even integer

This is not enough information, since m can be odd or even. For example, if m = 5, then m/2 = 5/2, which is not an even integer. Likewise, if m = 6, then m/2 = 3, which is not an even integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

m - 3 is an even integer

If m - 3 is an even integer, then m must be odd, since odd - odd = even. Statement two alone is sufficient to answer the question.

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Re: If m is an integer, is m odd?   [#permalink] 06 Jun 2017, 16:49
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