A parallelogram is drawn in the xy-coordinate plane. Is the

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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sat Dec 28, 2019 10:13 am

A parallelogram is drawn in the xy-coordinate plane. Is the parallelogram's area, in square units, an integer?

1) The x and y coordinates of each of the parallelogram's four vertices are integers.
2) The parallelogram has four sides of equal length.

The OA is A

Source: Manhattan Prep

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Source: Beat The GMAT — Data Sufficiency | Sat Dec 28, 2019 10:13 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sun Dec 29, 2019 11:12 am

question: Is the parallelogram's area, in square units, an integer?
Area = base * height
So, is base and height and integer?
Statement 1: The x and y coordinates of each of the parallelogram's four vertices are integers.
If all the vertices of the parallelogram have integer coordinates, then the coordinate of height and base will be an integer as well.
Hence, statement 1 is SUFFICIENT.

Statement 2: The parallelogram has four sides of equal length.
This only tells us that the height and base are of equal length but nothing to indicate it is an integer or not.
Therefore, statement 2 is NOT SUFFICIENT.

Since only statement 1 is SUFFICIENT, the correct answer choice is option A.

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