Data Sufficiency

AbeNeedsAnswers wrote: ↑

Fri Jun 05, 2020 6:16 pm

OG2021DS265.png

In the xy-coordinate plane above, what are the coordinates of point N?

1. Triangle MNP is equilateral.
2. Point M has coordinates (-4, 0).

C

Target question: What are the coordinates of point N ?

Statement 1: Triangle MNP is equilateral
There are infinitely-many equilateral triangles that satisfy the given conditions. Here are two:

Since the coordinates of point N are different for the two equilateral triangles, we cannot answer the target question with certainty.
Statement 1 is NOT SUFFICIENT

Statement 2: Point M has coordinates (−4,0)
There are infinitely-many triangles that satisfy statement 2. Here are two:

Since the coordinates of point N are different for the two triangles, we cannot answer the target question with certainty.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Key property:


Since triangle MNP is equilateral, we know that the altitude from point N must bisect side MP.

The distance from point M to (0,0) is 4.
So, distance from point P to (0,0) must also be 4
So, the length of side MP = 4 + 4 = 8

Since side MP = 8, we know that all three sides of the equilateral triangle must have length 8


At this point, it's clear that we have enough information to find the coordinates of point N.
If we focus on the blue right triangle below, we can see that we COULD apply the Pythagorean theorem to find the height of the triangle, which means we COULD find the coordinates of point N (although we would never waste valuable time on test day actually calculating the coordinates)

Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent