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, ABCD is a rectangle. Points P, Q, R, S, and T
[#permalink]
19 Mar 2019, 05:47
19 Mar 2019, 05:47
Expert Reply
00:00
Question Stats:
86% (01:49) correct
13% (01:18) wrong based on 29 sessions
Hide Show timer Statistics
Attachment:
#GREpracticequestion In the figure, ABCD is a rectangle.jpg [ 60.36 KiB | Viewed 4128 times ]
In the figure, ABCD is a rectangle. Points P, Q, R, S, and T cut side AB of the rectangle such that AP = 3, PQ = QR = RS = ST = 1. E is a point on AD such that AE = 3. Which one of the following line segments is parallel to the diagonal BD of the rectangle?
(A) EP
(B) EQ
(C) ER
(D) ES
(E) ET
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: In the figure, ABCD is a rectangle. Points P, Q, R, S, and T
[#permalink]
07 Jun 2020, 02:25
07 Jun 2020, 02:25
1
This question is based on the concept of Similar triangles.
If Two triangles are similar then their corresponding angles are equal.(And if we are able to prove that the angles are equal then we can prove that the sides are parallel)
We need to find a triangle which is similar to triangle ADB, which will be triangle AEX (We need to find which vertex is X -> P/Q/R/S/T)
We are going to use the property of similar triangle to find the similar triangle
If two triangles are similar then their sides will be in the same ratio.
\(\frac{AE}{AD}\) = \(\frac{AX}{AB}\)
=> AX = \(\frac{AB*AE}{AD}\) = \(\frac{15*3}{9}\) = 5
=> AX = 5 => X is nothing but R
So, AER ~ ADB
=> Angle ARE = Angle ABD
=> ER || DB
So, answer will be C
Hope it helps!
If Two triangles are similar then their corresponding angles are equal.(And if we are able to prove that the angles are equal then we can prove that the sides are parallel)
We need to find a triangle which is similar to triangle ADB, which will be triangle AEX (We need to find which vertex is X -> P/Q/R/S/T)
We are going to use the property of similar triangle to find the similar triangle
If two triangles are similar then their sides will be in the same ratio.
\(\frac{AE}{AD}\) = \(\frac{AX}{AB}\)
=> AX = \(\frac{AB*AE}{AD}\) = \(\frac{15*3}{9}\) = 5
=> AX = 5 => X is nothing but R
So, AER ~ ADB
=> Angle ARE = Angle ABD
=> ER || DB
So, answer will be C
Hope it helps!
gmatclubot
Re: In the figure, ABCD is a rectangle. Points P, Q, R, S, and T [#permalink]
07 Jun 2020, 02:25
Moderators:
