GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the figure shown, PQRS is a square, T is the midpoint of
[#permalink]
21 Nov 2019, 11:35
21 Nov 2019, 11:35
1
Expert Reply
2
Bookmarks
00:00
A
B
C
D
E
Question Stats:
71% (01:38) correct
28% (02:17) wrong based on 42 sessions
Show timer Statistics
Attachment:
#greprepclub In the figure shown.jpg [ 27.25 KiB | Viewed 6269 times ]
In the figure shown, PQRS is a square, T is the midpoint of side PS, and U is the midpoint of side QR. The area of the shaded region is what fraction of the area of square PQRS ?
A. 16
B. 18
C. 15
D. 14
E. 13
Kudos for the right answer and solution.
Re: In the figure shown, PQRS is a square, T is the midpoint of
[#permalink]
20 Apr 2020, 15:55
20 Apr 2020, 15:55
3
Expert Reply
PTUR is a parallelogram so the area is x/2*x = x^2/2
the shaded portion is half of this
so it is x^2/4
Area of square x^2
(x^2/4)/x^2
=1/4
the shaded portion is half of this
so it is x^2/4
Area of square x^2
(x^2/4)/x^2
=1/4
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the figure shown, PQRS is a square, T is the midpoint of
[#permalink]
28 Jul 2020, 06:26
28 Jul 2020, 06:26
2
1
Carcass wrote:
Attachment:
#greprepclub In the figure shown.jpg
In the figure shown, PQRS is a square, T is the midpoint of side PS, and U is the midpoint of side QR. The area of the shaded region is what fraction of the area of square PQRS ?
A. 16
B. 18
C. 15
D. 14
E. 13
Kudos for the right answer and solution.
Let's say that each side of the square has length 2
Which means its area = (2)(2) = 4
Since T and U are midpoints, we get the following measurements:
Since URPT is a parallelogram, its area = (base)(height) = (1)(2) = 2
Since the blue line divides parallelogram URPT into 2 EQUAL pieces, the area of the shaded region = 1/2 of 2, which is 1
The area of the shaded region is what fraction of the area of square PQRS?
Fraction = 1/4
Answer: D
Cheers,
Brent
