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25 Dec 2020, 01:56
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C
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Difficulty:
25%
(medium)
Question Stats:
73% (01:31) correct
27%
(01:23)
wrong
based on 56
sessions
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Not Attempted Yet
In the rectangular co-ordinate system above, is the area of region MNP greater than 30?
(1) The coordinates of point N are (6,6)
(2) MN = NP
(1) The coordinates of point N are (6,6)
(2) MN = NP
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image.jpeg [ 18.21 KiB | Viewed 1372 times ]
26 Dec 2020, 00:00
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Refer Attached Image (O is a perpendicular drawn from N to MP)
The thing to note and (not assume) in the question is that MNP is NOT given as a right angle triangle.
To find area of MNP if we know the height of the triangle and length of MP then we can find the area. (or if we know the coordinates of N and P (As M is (0,0))
STAT1: The coordinates of point N are (6,6)
=> OM = ON = 6
We can find value of MN from this and get that angle NMP is 45 degree but this doesn't give all we need to find area of the triangle.
So, NOT SUFFICIENT
STAT2: MN = NP
=> MNP is isosceles triangle. But we do not know any length from this statement.
So, NOT SUFFICIENT
Taking both of them together we have
OM = ON = 6 and MNP is Isosceles with MN = NP
Now, we know that Perpendicular drawn from a vertex to a non-equal side of the isosceles triangle touches becomes the perpendicular bisector of that side.
=> NO is perpendicular bisector of MP
=> MO = OP = 6
So, MP = 12
ON = 6
So, SUFFICIENT to find the area of MNP
So, answer will be C
Hope it helps!
The thing to note and (not assume) in the question is that MNP is NOT given as a right angle triangle.
To find area of MNP if we know the height of the triangle and length of MP then we can find the area. (or if we know the coordinates of N and P (As M is (0,0))
STAT1: The coordinates of point N are (6,6)
=> OM = ON = 6
We can find value of MN from this and get that angle NMP is 45 degree but this doesn't give all we need to find area of the triangle.
So, NOT SUFFICIENT
STAT2: MN = NP
=> MNP is isosceles triangle. But we do not know any length from this statement.
So, NOT SUFFICIENT
Taking both of them together we have
OM = ON = 6 and MNP is Isosceles with MN = NP
Now, we know that Perpendicular drawn from a vertex to a non-equal side of the isosceles triangle touches becomes the perpendicular bisector of that side.
=> NO is perpendicular bisector of MP
=> MO = OP = 6
So, MP = 12
ON = 6
So, SUFFICIENT to find the area of MNP
So, answer will be C
Hope it helps!
Attachments
File comment: Image
Screenshot 2020-12-26 122046.jpg [ 34.45 KiB | Viewed 1232 times ]
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