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# Which of the following lines in the xy-plane does not

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Re: Which of the following lines in the xy-plane does not contai [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?

(A) y = x
(B) y = x + 1/2
(C) y = x + 5
(D) y = x*1/2
(E) y = x/2 + 5

We see that the point (1,1) is on the line y = x (answer choice A); (1, 6) on y = x + 5 (C); (2, 1) on y = x*1/2 (D); and (2, 6) on y = x/2 + 5 (E). Thus, the only line that won’t have any point with integers as both coordinates is y = x + 1/2 (answer choice B). The reason is simple: if x is an integer, then y can’t be an integer, since the sum of an integer and 1/2 will never be an integer. Similarly, if y is an integer, then x can’t be an integer, since the difference of an integer and 1/2 (notice that x = y - 1/2) can never be an integer.

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Re: Which of the following lines in the xy-plane does not [#permalink]
Can y or x be integers?
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Re: Which of the following lines in the xy-plane does not [#permalink]
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Can y or x be integers?

Line y = x + 1/2 contains points with integers as one of the coordinates but not both. For example, the line contains points (1, 1.5) and (2.5, 3) but it does not contain any point with (integer, integer).
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Re: Which of the following lines in the xy-plane does not [#permalink]
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Re: Which of the following lines in the xy-plane does not [#permalink]
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