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# If j is an integer, is k an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
If j is an integer, is k an integer?  [#permalink]

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08 Jan 2018, 07:38
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Difficulty:

55% (hard)

Question Stats:

61% (01:06) correct 39% (01:30) wrong based on 46 sessions

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If j is an integer, is k an integer?

(1) j = 2k
(2) The average (arithmetic mean) of j and k is not an integer.

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If j is an integer, is k an integer?  [#permalink]

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08 Jan 2018, 09:24
Bunuel wrote:
If j is an integer, is k an integer?

(1) j = 2k
(2) The average (arithmetic mean) of j and k is not an integer.

Statement 1: implies $$k=\frac{j}{2}$$

if $$j$$ is even, $$k$$ is an integer but if $$j$$ is Odd then $$k$$ is not an integer. Insufficient

Statement 2: implies $$j+k=2*$$non integer. we don't know the values of $$j$$ & $$k$$. Insufficient

Combining 1 & 2: $$2k+k=2*$$non integer

$$=>k=\frac{2}{3}*$$non integer. if non integer$$=\frac{3}{2}$$, then $$k$$ is an integer but if non integer $$= \frac{1}{2}$$, then $$k$$ is not an integer. Insufficient

Option E
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Joined: 30 May 2017
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GMAT 1: 730 Q49 V41
Re: If j is an integer, is k an integer?  [#permalink]

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08 Jan 2018, 10:54
If j is an integer, is k an integer?

(1) j = 2k
(2) The average (arithmetic mean) of j and k is not an integer.

Hi,
1.) k=1/2 -----No
k=1------yes

bce

2.) (j+k)/2 isn't an integer

k=1, j=4

Yes K is an integer

k=1/2 j=1

No K isn't an integer.

CE

from 1 and 2 ----- (2k+k)/2 isn't an integer

3k/2 isn't an integer.

this can be valid for k= 1 and k=1/2 Hence E is the answer.
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Re: If j is an integer, is k an integer?  [#permalink]

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08 Jan 2018, 11:29
1
Hi Bunuel,
Should all mathematics question be done with pen and paper or orally. I personally mashup data orally when information become too much to remember. What should be a good approach ?
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Re: If j is an integer, is k an integer?  [#permalink]

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08 Jan 2018, 22:40
pilltaker wrote:
Hi Bunuel,
Should all mathematics question be done with pen and paper or orally. I personally mashup data orally when information become too much to remember. What should be a good approach ?

Bunuel is the best to answer this, but I will also give my perspective. Initially when you are learning, solving with pen and paper is much better. Depending on which stage of preparation you are in (and how much you have practised already), you would find some questions easy/very easy that you can solve orally, some questions would be medium level for you which you can solve quickly and more efficiently with pen and paper. For such kind of questions, its better to solve with pen and paper until you get comfortable enough to solve them mentally.

Tough questions wont be easy to solve mentally, and trying to do that might lead to confusion, quick exhaustion, and a lot of mistakes. Of course, as your Quant aptitude keeps increasing with consistent practice, you might be able to do some tough questions also mentally. But even if you cannot, its not a big deal and please dont feel bad for that
Re: If j is an integer, is k an integer?   [#permalink] 08 Jan 2018, 22:40
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