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05 Oct 2020, 03:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:06) correct
31%
(01:58)
wrong
based on 376
sessions
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Not Attempted Yet
Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS?
(1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).
(2) The coordinates of point S are (6.0).
(1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).
(2) The coordinates of point S are (6.0).
05 Oct 2020, 04:56
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Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS?
Explanation: Clearly Quadrilateral PQRS is a parallelogram with PQ||RS and QR||P5
(S1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).
Not enough information about remaining two vertices coordinate orside lengths.
Hence S1 is insufficient.
(S2) The coordinates of point S are (6.0).
Not enough information about remaining three vertices coordinate orside lengths.
Hence S2 is insufficient.
Combining S1 and S2
Now we have 3 vertices P(2,0) S(6,0) R(8,2) and Q(x,y)
now for parallelogram PQRS PQ=RS=2√2 and PS=QR=4
and height h=(2√2 )^2-2^2 (draw a perpendicular from R and apply Pythagoras)
i.e h=2
area Parallelogram PQRS= base*height
=PS*2
=4*2
=8
Hence C is the correct answer IMO
Explanation: Clearly Quadrilateral PQRS is a parallelogram with PQ||RS and QR||P5
(S1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).
Not enough information about remaining two vertices coordinate orside lengths.
Hence S1 is insufficient.
(S2) The coordinates of point S are (6.0).
Not enough information about remaining three vertices coordinate orside lengths.
Hence S2 is insufficient.
Combining S1 and S2
Now we have 3 vertices P(2,0) S(6,0) R(8,2) and Q(x,y)
now for parallelogram PQRS PQ=RS=2√2 and PS=QR=4
and height h=(2√2 )^2-2^2 (draw a perpendicular from R and apply Pythagoras)
i.e h=2
area Parallelogram PQRS= base*height
=PS*2
=4*2
=8
Hence C is the correct answer IMO
Target4bschool
Joined: 29 Dec 2019
Last visit: 19 Nov 2025
Posts: 61
Given Kudos: 181
Schools: IE MiM (Sep 21 Start) (A)
09 Oct 2020, 02:44
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Given a parallelogram. Area = height * length
(1) The coordinates of point P are (2,0), and the coordinates of point R are (8,2).
Point Q and S can change and hence change the height and length.
not sufficient.
(2) The coordinates of point S are (6,0).
Not sufficient.
Combine: P, R, S are fixed. Q will also get fixed given PQRS is a parallelogram
So, Sufficient.
IMO, C
----------------------------------------------------------------------------------------
Not necessarily but if you wish to solve:
Take PS as a length. PS = 4
Height =2 [coordinates of R- (8,2)]
So, area = 8
(1) The coordinates of point P are (2,0), and the coordinates of point R are (8,2).
Point Q and S can change and hence change the height and length.
not sufficient.
(2) The coordinates of point S are (6,0).
Not sufficient.
Combine: P, R, S are fixed. Q will also get fixed given PQRS is a parallelogram
So, Sufficient.
IMO, C
----------------------------------------------------------------------------------------
Not necessarily but if you wish to solve:
Take PS as a length. PS = 4
Height =2 [coordinates of R- (8,2)]
So, area = 8
