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If a is an even integer and a/18 is an odd integer, which of the

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Senior Manager
Joined: 21 Oct 2013
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If a is an even integer and a/18 is an odd integer, which of the [#permalink]

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02 Dec 2014, 10:13
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If a is an even integer and a/18 is an odd integer, which of the following is NOT an even integer?

A (a^2)/54
B (a^2)/12
C (a^2)/9
D (a^2)/6
E (a^2)/2
[Reveal] Spoiler: OA
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Joined: 13 Jun 2013
Posts: 278
If a is an even integer and a/18 is an odd integer, which of the [#permalink]

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02 Dec 2014, 10:57
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goodyear2013 wrote:
If a is an even integer and a/18 is an odd integer, which of the following is NOT an even integer?

A (a^2)/54
B (a^2)/12
C (a^2)/9
D (a^2)/6
E (a^2)/2

since a is an even integer and a/18 is an odd integer. thus maximum power of 2 in a is one. why ?? because if the power of 2 in the expression has been 2 or greater, then the a/18 must have been an even integer. (18=2*3^2. as 18 contain only one 2 in the expression)

now, any expression in which we have 4 at the denominator will be odd. out of the given options only 12 is a multiple of 4. hence answer should be B
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Re: If a is an even integer and a/18 is an odd integer, which of the [#permalink]

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02 Dec 2014, 20:19
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goodyear2013 wrote:
If a is an even integer and a/18 is an odd integer, which of the following is NOT an even integer?

A (a^2)/54
B (a^2)/12
C (a^2)/9
D (a^2)/6
E (a^2)/2

"a is an even integer"
implies a has at least one 2 as a factor.

"a/18 is an odd integer"
18 = 2*9
When you divide a by 18, all its 2s get canceled. Since 18 has only one 2, it means a had only one 2 too.

So a^2 has 2^2 = 4 as a factor but not 8.
Since 12 has two 2s as well, both the 2s of a^2 will get canceled and hence you will not get an even integer.
All other options cancel only a single 2 of a^2.

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Re: If a is an even integer and a/18 is an odd integer, which of the [#permalink]

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02 Dec 2014, 23:28
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Let a = 54 (Even); $$\frac{a}{18} = \frac{54}{18} = 3$$ (Odd)

Checking the OA

A: $$\frac{54 * 54}{54} = 54$$(Even)

B: $$\frac{54 * 54}{12} = 9*27$$ (Odd)
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Manager
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Re: If a is an even integer and a/18 is an odd integer, which of the [#permalink]

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04 May 2015, 13:08
Great concept this. Thx folks.
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Re: If a is an even integer and a/18 is an odd integer, which of the [#permalink]

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24 Oct 2016, 03:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a is an even integer and a/18 is an odd integer, which of the [#permalink]

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19 Aug 2017, 06:32
Substituting a=18 we can quickly check option B is odd
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Re: If a is an even integer and a/18 is an odd integer, which of the   [#permalink] 19 Aug 2017, 06:32
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