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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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07 Feb 2014, 12:52

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(A) y = x: Solving for x & y intercepts, we get (0, 0) Integer (B) y = x + 1/2: Solving for x & y intercepts, we get (-1/2, 1/2) Non-Integer (Correct) (C) y = x + 5: Solving for x & y intercepts, we get (-5, 5) Integer (D) y = x*1/2: Solving for x & y intercepts, we get (0, 0) Integer (E) y = x/2 + 5: Solving for x & y intercepts, we get (-10, 5) Integer

Re: Which of the following lines in the xy-plane does not contai [#permalink]

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07 Jul 2015, 06:37

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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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17 Sep 2016, 08:43

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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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15 Jun 2017, 16:22

Just Plot the line for each option . We will get a clear ans as B . How to plot ? to get y , put x=0 and to get x , put y=o and then join the points to get the line .
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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.

Answer: B
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