Good Question +1
This question reminds me that GMAT is not only about math, Its MATH + LOGIC skills.
Let's try to analyze this question.
In the rectangular coordinate system above, if OP < PQ, i
s the area of region OPQ greater than 48?
(1)
The coordinates of point P are (6,8)Attachment:
gcpic.JPG [ 19.48 KiB | Viewed 1031 times ]
If you drop a perpendicular from point P to the base OQ and meet at a point S and this line will divide the △ POQ into 2 triangles.
△1 would be a right-angled triangle with base OS and height PS.
By using the coordinates of point P (6,8 ), we can say that side OS = 6 and PS = 8.
Hence,
Area of △1 = 1/2 * base * height =
1/2 * 6 * 8 = 24.
Now let us consider △2. It will also be a right-angled triangle with base SQ and height PS.
Since it is given in the question that the hypotenuse PQ > OP,
\(OS^2 + PS^2 = OP^2 \) in △1
\(SQ^2 + PS^2 = PQ^2 \) in △ 2
Comparing both equations, since
PQ > OP, we can conclude that the base
SQ > OS.
Since the height of 2 triangles, PS is the same.
The base of △ 2 is greater than △ 1.
Area of △2 = 1/2 * base SQ * height PS
Area of △1 = 1/2 * base OS * height PS = 24.
Therefore, we conclude that the area of △2 is greater than △ 1 i.e 24.
So
the combined area of 2 triangles should be greater than 24+24 i.e 48This will answer the question stem. Hence,
Statement 1 alone is sufficient.(2) The coordinates of point Q are (13,0)
From the coordinates of Q, we can say that the base OQ=13 but we don't have any idea about the coordinates of P.
Coordinates of P will determine the height of the triangle. Since the height is unknown, we will not be able to figure out if the area of △ OPQ is greater than 48 or not.
Statement 2 alone is not sufficient.
Option A is the correct answer.Thanks,
Clifin J Francis,
GMAT QUANT SME