Last visit was: 22 Dec 2024, 21:36 It is currently 22 Dec 2024, 21:36

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 30475
Own Kudos [?]: 36824 [2]
Given Kudos: 26100
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 30475
Own Kudos [?]: 36824 [1]
Given Kudos: 26100
Send PM
Retired Moderator
Joined: 09 Jun 2020
Posts: 205
Own Kudos [?]: 235 [3]
Given Kudos: 34
GPA: 3.21
Send PM
avatar
Intern
Intern
Joined: 03 Oct 2020
Posts: 2
Own Kudos [?]: 5 [1]
Given Kudos: 0
Send PM
Re: ABCD is a square, AD = 6, EB = 6 − 2b, the triangle [#permalink]
1
Since ABCD is a square, it is clear that AB=6.
Therefore, if EB= 6-2b then AE= 2b.
AE is the base of the shaded triangle.
If the probability of a randomly selected point lying in the shaded triangle is 1/3. This will equal the (Area of the shaded triangle/ area of the square).
The area of the square ABDE is 6^2= 36.
Determined by 1/3= Area of triangle/ 36. This will give the area of the triangle to be 12.

The area of the triangle = (2b*2b)/2, which is 2b^2=12.
b^2=6 and therefore the value of b= √6 > 2.
Giving us the the answer A

Thanks and best of luck of everyone :)
Manager
Manager
Joined: 11 Jun 2023
Posts: 77
Own Kudos [?]: 78 [1]
Given Kudos: 14
Send PM
ABCD is a square, AD = 6, EB = 6 2b, the triangle [#permalink]
1
We are given that side of the square is 6, and that the shaded region is composed of an isos. triangle.

Area of the square is therefore 36. If there is a 1/3 chance of randomly going to the shaded region, it implies that the area of the isos. triangle must be 1/3 of the squares area, which is 12.

If the area of the isos triangle is 12, then that implies that the two legs of the triangle are:
\(x^2/2=24\)
\(x=2\sqrt{6}\)

Since the side of the angle must add up to 6, we know that:
\(2\sqrt{6}+6-2b=6\)
\(2\sqrt{6}=2b\)
\(\sqrt{6}=b\)
Since 2 is equal to root 4, that implies that b is greater than 2, so QA is larger than QB.

A.
Prep Club for GRE Bot
ABCD is a square, AD = 6, EB = 6 2b, the triangle [#permalink]
Moderators:
GRE Instructor
88 posts
GRE Forum Moderator
37 posts
Moderator
1115 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne