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

Question

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

magbot · Answer

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

EgmatQuantExpert · Answer

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

LevanKhukhunashvili · Answer

The question doesn't ask about possible choice, but "MUST" choice

KSBGC · Answer

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.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards