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Kritisood
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Hi nick1816
(1) Point Q lies on the x-axis 6 units from point P.
(2) Point R is 5 units away from the x-axis
Since P & Q lie on the x-axis, 6 units away from each other, base of triangle = 6
Since R is 5 units away from the x-axis i.e. base of the triangle, height = 5; R may be above or below x-axis and may have any x-coordinate.
Since base and height are known, area of triangle is known

IMO C
Please see my solution

nick1816
Statement 1- It gives the length of PQ and location of the Q on X-axis. We have no idea about point R.
Insufficient

Statement 2- It just tells that point R lies on either y=5 or y=-5. We have no idea about point P and Q.
Insufficient

Combining both statements.

Suppose the coordinates of Q are (c,0). Point P will lie on the circle whose radius is 6 and center is Q. Point R lies of y=5 or y=-5.

PQR (in Grey) is a possible triangle, which satisfies both statements

Area of PQR = 1/2 * (b+5) * QS

PQR' (in blue) is another possible triangle, which satisfies both statements

Area of PQR' = 1/2 * (b+5) * QT

We can clearly see that QS> QT. Hence there is no definite answer for the area of the triangle which satisfies both statements.

IMO it's E (Bunuel Isn't the OA wrong)




Kritisood
On the x-y coordinate grid, if points P, Q, and R make a triangle (not shown), what is the area of the triangle?
(1) Point Q lies on the x-axis 6 units from point P.
(2) Point R is 5 units away from the x-axis
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Kinshook

I guess you made an assumption that P also lies on the X-axis. IMO statement 1 doesn't imply that or it's written poorly.
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nick1816
Kinshook

I guess you made an assumption that P also lies on the X-axis. IMO statement 1 doesn't imply that or it's written poorly.

Yes. The intended meaning of (1) Point Q lies on the x-axis 6 units from point P, is that BOTH P and Q lie on the x-axis and the distance between them is 6 units. Poor wording. Tagginf the question Poor quality and locking.

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