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.
Which of the following lines in the xy-plane does not
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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.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.
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7274
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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.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.
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews