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If j and k are integers, and 2j + k = 15, which of the following must

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If j and k are integers, and 2j + k = 15, which of the following must  [#permalink]

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New post 18 Oct 2019, 03:00
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A
B
C
D
E

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Question Stats:

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Re: If j and k are integers, and 2j + k = 15, which of the following must  [#permalink]

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New post 18 Oct 2019, 06:05
Top Contributor
Bunuel wrote:
If j and k are integers, and 2j + k = 15, which of the following must be true?

A. j + k is odd.
B. j + k is even.
C. j is odd.
D. k is odd.
E. k > j


15 is ODD
2j is EVEN for all integer values of j

So, 2j + k = 15 becomes: (some EVEN number) + k = ODD
So, it must be the case that k is ODD

Answer: D

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Brent
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Re: If j and k are integers, and 2j + k = 15, which of the following must  [#permalink]

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New post 18 Oct 2019, 07:38
Bunuel wrote:
If j and k are integers, and 2j + k = 15, which of the following must be true?

A. j + k is odd.
B. j + k is even.
C. j is odd.
D. k is odd.
E. k > j


Asked: If j and k are integers, and 2j + k = 15, which of the following must be true?
2j = even
15 = odd
k = odd - even = odd

IMO D
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Re: If j and k are integers, and 2j + k = 15, which of the following must  [#permalink]

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New post 20 Oct 2019, 10:03
Bunuel wrote:
If j and k are integers, and 2j + k = 15, which of the following must be true?

A. j + k is odd.
B. j + k is even.
C. j is odd.
D. k is odd.
E. k > j


We see that 2j must be even. Since even + odd = odd, then k must be odd.

Answer: D
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Re: If j and k are integers, and 2j + k = 15, which of the following must  [#permalink]

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New post 22 Oct 2019, 22:19

Solution


Given:
    • j and k are integers
    • 2j + k = 15

To find:
    • Which of the given choices must be true

Approach and Working Out:
    • Given, 2j + k = 15
      o We know 2j is always even, for any value of j
      o Thus, even + k = odd

Therefore, k must be odd

Hence, the correct answer is Option D.

Answer: D
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Re: If j and k are integers, and 2j + k = 15, which of the following must   [#permalink] 22 Oct 2019, 22:19
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