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Doubt - If m is an integer, is m odd?

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Doubt - If m is an integer, is m odd?

by jaspreetsra » Tue Oct 07, 2014 9:43 pm

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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.
Source: The official guide for GMAT 13 edition
(1) m = 2, 6, 10, and so on - fulfills the condition. So, m is even i.e. definite answer - no. Sufficient
(2) m = 5, 7, and so on, so m is odd i.e. definite answer -yes. Sufficient.
My answer is D.
Should it be B? WHy?
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by fcabanski » Tue Oct 07, 2014 10:59 pm

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1. If m is odd, m/2 is a fraction (not an integer, so not an even integer.) If m is even, m/2 could be an even integer (when m is a multiple of 4) or odd (not an even integer, when m is even but not a multiple of 4).

If that's not enough, then think about specific examples. You need one m that is odd and one m that is even, with the result m/2 not an even integer.

m=3. m is odd. 3/2 = 1.5 is not an even integer.
m=6. m is even. 6/2 =3 is not an even integer.

2, odd - odd = even. even - odd = odd. Those are facts. 3 is odd. m-3 = even, so m must be odd. This answers the question.

B.
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by Brent@GMATPrepNow » Wed Oct 08, 2014 4:56 am

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jaspreetsra wrote:If m is an integer, is m odd?
(1) m/2 is not an even integer.
(2) m-3 is an even integer.
Source: The official guide for GMAT 13 edition
(1) m = 2, 6, 10, and so on - fulfills the condition. So, m is even i.e. definite answer - no. Sufficient
(2) m = 5, 7, and so on, so m is odd i.e. definite answer -yes. Sufficient.
My answer is D.
Should it be B? WHy?
You are assuming that m/2 must be an integer.
m = 1, 3, 5 etc ALSO fulfills the condition that m/2 is not an even integer
Do, m can be EITHER even OR odd.

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by Brent@GMATPrepNow » Wed Oct 08, 2014 5:03 am

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jaspreetsra wrote:If m is an integer, is m odd?
(1) m/2 is not an even integer.
(2) m-3 is an even integer.
Target question: Is m odd?

Statement 1: m/2 is not an even integer.
There are several values of m that satisfy this condition. Here are two:
case a) m = 3 (3/2 is not an even integer), which means m is ODD
case b) m = 6 (6/2 is not an even integer), which means m is EVEN
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: m - 3 = an EVEN integer
Rewrite as m = EVEN + 3
3 is ODD, so we get: m = EVEN + ODD
Simplify: m = ODD [since EVEN + ODD = ODD]
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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by Matt@VeritasPrep » Sun Oct 12, 2014 10:00 pm

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An important deduction here, as Brent implied, is that "x is NOT an even integer" means one of two things: (1) x is an odd integer; (2) x isn't an integer at all!

Watch out for this sort of slippery wording: you'll find it in quant, IR, and critical reasoning, so it's vital to understand.
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by Scott@TargetTestPrep » Sun Nov 04, 2018 5:07 pm

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jaspreetsra wrote:If m is an integer, is m odd?
(1) m/2 is not an even integer.
(2) m-3 is an even integer.
Source: The official guide for GMAT 13 edition
(1) m = 2, 6, 10, and so on - fulfills the condition. So, m is even i.e. definite answer - no. Sufficient
(2) m = 5, 7, and so on, so m is odd i.e. definite answer -yes. Sufficient.
We are given that m is an integer, and we must determine whether it is odd.

Statement One Alone:

m/2 is not an even integer.

The information in statement one is not enough to determine whether m is odd since m can be odd or even. For example, if m = 3 (an odd number), m/2 = 3/2 = 1.5 is not an even integer. On the other hand, if m = 2 (an even number), m/2 = 2/2 = 1 is also not an even integer.

Thus, statement one is not sufficient to determine whether m is odd.

Statement Two Alone:

m - 3 is an even integer.

Since m - 3 is an even integer, we can say m - 3 = even. That is, m = even + 3. Since 3 is odd and we know that even + odd = odd, we know that m must be an odd integer.

Statement two is sufficient to answer the question.

Answer: B

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