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

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by AAPL » Tue Aug 14, 2018 5:47 am

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Source: Official Guide

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

$$\text{A. }\ y=x$$
$$\text{B. }\ y=x+\frac{1}{2}$$
$$\text{C. }\ Y=x+5$$
$$\text{D. }\ y=\frac{1}{2}x$$
$$\text{E. }\ y=\frac{1}{2}x + 5$$

The OA is B.
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Source: — Problem Solving |

by Brent@GMATPrepNow » Tue Aug 14, 2018 5:54 am
AAPL wrote:Source: Official Guide

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

$$\text{A. }\ y=x$$
$$\text{B. }\ y=x+\frac{1}{2}$$
$$\text{C. }\ Y=x+5$$
$$\text{D. }\ y=\frac{1}{2}x$$
$$\text{E. }\ y=\frac{1}{2}x + 5$$

The OA is B.
Core concept: If a point (x,y) is on a given line, then the coordinates (x and y) of that point must satisfy the equation of that line.

In answer choice B, the equation (y = x + 1/2) tells us that, for ANY POINT ON THE LINE, the y-coordinate will be equal to the x-coordinate plus 1/2
So, if the x-coordinate is an integer, the y-coordinate cannot be an integer.
So, it's impossible for any point on this line to have integers as BOTH coordinates.

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Thu Apr 18, 2019 5:39 pm
AAPL wrote:Source: Official Guide

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

$$\text{A. }\ y=x$$
$$\text{B. }\ y=x+\frac{1}{2}$$
$$\text{C. }\ Y=x+5$$
$$\text{D. }\ y=\frac{1}{2}x$$
$$\text{E. }\ y=\frac{1}{2}x + 5$$

The OA is B.
Since a non-integer fraction + integer will NEVER = integer, we see that in the equation y = x + 1/2, it's impossible for both x and y to be integers.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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