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If j and k are integers and j — k is even, which of the following must

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Bunuel
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If j and k are integers and j — k is even, which of the following must [#permalink] New post   26 Jun 2018, 21:19
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E

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81% (01:22) correct 19% (01:20) wrong based on 79 sessions
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If j and k are integers and j — k is even, which of the following must be even?

A) k

B) jk

C) j + 2k

D) jk + j

E) jk — 2j
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D
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magbot
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If j and k are integers and j — k is even, which of the following must [#permalink] New post   Updated on: 27 Jun 2018, 02:54
J - K is even

Then J and K both should be both even or odd
If both J & K are even then J*k is even
If both J & K are odd then J*k is odd

Question asks only possible choice, so
answer is B

Edit:

The answer above is wrong, I misread the question

Originally posted by magbot on 26 Jun 2018, 22:33.
Last edited by magbot on 27 Jun 2018, 02:54, edited 1 time in total.
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Re: If j and k are integers and j — k is even, which of the following must [#permalink] New post   26 Jun 2018, 23:24
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Solution



Given:
    • j and k are integers
    • j — k = even

To find:
    • Among the given options, which one must be even

Approach and Working:
If j – k = even, there can be two possibilities:
    • Both j and k are individually even
    • Both j and k are individually odd

Now, checking with the options:
    • k = even OR odd
    • jk = even if both are even OR odd if both are odd
    • j + 2k = even if both are even OR odd if both are odd
    • jk + j = even always
    • jk – 2j = even if both are even OR odd if both are odd

Hence, the correct answer is option D.

Answer: D

Note: The option checking can also be done by replacing even/odd values in place of j and k
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Re: If j and k are integers and j — k is even, which of the following must [#permalink] New post   27 Jun 2018, 02:41
magesh.d wrote:
J - K is even

Then J and K both should be both even or odd
If both J & K are even then J*k is even
If both J & K are odd then J*k is odd

Question asks only possible choice, so
answer is B



The question doesn't ask about possible choice, but "MUST" choice
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Re: If j and k are integers and j — k is even, which of the following must [#permalink] New post   27 Jun 2018, 02:48
Bunuel wrote:
If j and k are integers and j — k is even, which of the following must be even?

A) k

B) jk

C) j + 2k

D) jk + j

E) jk — 2j



This question is about must be true option. It means we have to assess all the probable aspects.

We know ,

Even - Even = Even
Odd - Odd = Even

Then start implementing plugging in method.

Only option D meets out expectations.

The best answer is D.
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Re: If j and k are integers and j — k is even, which of the following must [#permalink]
27 Jun 2018, 02:48
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