DAT Math Question

[DAT-TAKER]

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Let x and y be the coordinates of a point on the perimeter of a circle centered at the origin. What is the value of x + y?

1) x/y = 1
2) x2 + y2 = 4

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

 

[DAT Destroyer]

Let x and y be the coordinates of a point on the perimeter of a circle centered at the origin. What is the value of x + y?

1) x/y = 1
2) x2 + y2 = 4

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

From statement 1 we get x = y. Which means that the point could be in either quadrant 1 or quadrant 3. This is not enough to find x + y.
from statement 2 we get that the radius of the circle is 2. Statement 1 and 2 together will help us find x and y... Since x=y we get x = sqrt(2) and y = sqrt(2)
x + y = 2sqrt(2).( If the point is in quadrant 1) and x + y = -2sqrt(2) ( if the point is in Quadrant 3). Therefore the answer is E since we don't have enough information to figure out in which quadrant lies the point.