Last visit was: 27 Dec 2024, 14:32 It is currently 27 Dec 2024, 14:32
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

The triangle shown above is Obtuse, where AC is the longest side and A

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30520
Own Kudos [?]: 36889 [2]
Given Kudos: 26113
Send PM
The triangle shown above is Obtuse, where AC is the longest side and A [#permalink] New post   30 Apr 2023, 23:10
Expert Reply
2
Bookmarks
00:00

Question Stats:

42% (01:37) correct 57% (01:42) wrong based on 21 sessions

Hide Show timer Statistics

Attachment:
GRE The triangle shown above is Obtuse,.jpg
GRE The triangle shown above is Obtuse,.jpg [ 11.94 KiB | Viewed 2085 times ]


The triangle shown above is Obtuse, where AC is the longest side and AB is the shortest side .What are all possible lengths of AB if k is a positive integer?

Indicate all that apply


3
4
5


Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos

\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
ShowHide Answer
Official Answer
B
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30520
Own Kudos [?]: 36889 [0]
Given Kudos: 26113
Send PM
Re: The triangle shown above is Obtuse, where AC is the longest side and A [#permalink] New post   28 May 2023, 00:44
Expert Reply
OE


Given that, ABC is an obtuse angled triangle, where AC is the longest side and AB is the
shortest side.
In a triangle,
(Difference of other two sides) < Any side of the triangle < (Sum of other two sides)
So,
3k – k < 10 < 3k + k
2k < 10 < 4k
Therefore, 2k < 10 and 10 < 4k
that is, k < 5 and 2.5 < k
Therefore, k lies between 2.5 and 5.
It is given that k is an integer,
Therefore, K can be 3 or 4.
If k = 3,

AC = 3k = 9
But it is given that AC is longest side
Hence, k cannot be 3.
If k = 4,
AB = 4 and AC = 3k = 12
This satisfies the statements given in the question.
The only value of k possible is 4.
Ans. (B)
avatar
SHITANGSHU
Intern
Intern
Joined: 06 Jul 2023
Posts: 3
Own Kudos [?]: 8 [2]
Given Kudos: 1
Send PM
Re: The triangle shown above is Obtuse, where AC is the longest side and A [#permalink] New post   13 Jul 2023, 01:57
2
Pick the the number 4 what only satisfies the conditions about the triangle's sides- AC as the longest side and any two sides sum and difference are more and less respectively than the other side.
avatar
Nandita175
Intern
Intern
Joined: 17 Aug 2022
Posts: 4
Own Kudos [?]: 6 [1]
Given Kudos: 1
Send PM
Re: The triangle shown above is Obtuse, where AC is the longest side and A [#permalink] New post   16 Jul 2023, 02:20
1
Difference between 2 sides < third side < Sum of 2 sides of a triangle
Side 1 = k
Side 2 = 3k
Side 3 = 10

(3k-k) < 10 < (3k+k)
2k < 10 < 4k
5 < 10 < 2.5

Since the required value is an integer, the only possible solution is 4.
Prep Club for GRE Bot
gmatclubot
Re: The triangle shown above is Obtuse, where AC is the longest side and A [#permalink]
16 Jul 2023, 02:20
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1116 posts
VibhuAnurag
GRE Instructor
234 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact