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

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

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03 Jan 2018, 21:15
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Difficulty:

25% (medium)

Question Stats:

83% (01:24) correct 17% (01:40) wrong based on 42 sessions

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If j is an integer, is k an integer?

(1) The average (arithmetic mean) of 1, 2k, and k – 4 is j.
(2) The average (arithmetic mean) of j and k is not an integer.

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

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03 Jan 2018, 22:03
1
Statement 1 gets reduced to k-1=j. So k=j+1. As j is an integer, k should be an integer so statement 1 is sufficient. Statement 2 can have k as integer as well as non integer for an average to be non integer. So answer is A

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

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04 Jan 2018, 01:51
Bunuel wrote:
If j is an integer, is k an integer?

(1) The average (arithmetic mean) of 1, 2k, and k – 4 is j.
(2) The average (arithmetic mean) of j and k is not an integer.

(1) Given that (1 + 2k + k-4)/3 = j. OR 3k-3 = 3j
Or 3k = 3j+3 Or k = j+1 (dividing both sides by 3).
Now since j is an integer, j+1 will also be an integer. Hence k is an integer. Sufficient.

(2) (j+k)/2 is not an integer, so j+k is not divisible by 2. But given that j is an integer.
We can have two cases: k could be an integer but such that sum j+k is odd (eg, we can have j odd and k even, say j=3, k=4).
Or k might not be an integer, in which case addition with j will be non-integer, thus anyway not divisible by 2 (say j=3, k=4.5)
So k might or might not be an integer. Not Sufficient.

Re: If j is an integer, is k an integer?   [#permalink] 04 Jan 2018, 01:51
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