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GRE - Quantitative Reasoning - Number Theory

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

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

Given j - k is even

=> either both j and k are odd or both are even

Option A - Incorrect because k will be odd if j is odd and k will be even if j is even

Option B. Incorrect because if j,k are odd, the product is odd, if they are even product is even

Option C. Incorrect j + 2k = j - k + 3k = even + 3k dependent on value of k

Option D. jk + j = j ( k + 1), if j is odd, k will be odd -> k + 1 will be even, hence j (k+1) will be even

If j is even j (k+1) will always be even

Correct

 

Correct option D.