Last visit was: 25 Apr 2026, 08:02 It is currently 25 Apr 2026, 08:02
Home
Messages
Tests
Schools
Events
Close
GMAT 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 GMAT 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
Back to Forum
Create Topic
705-805 (Hard)|   Geometry|      
User avatar
mau5
User avatar
Verbal Forum Moderator
Joined: 10 Oct 2012
Last visit: 31 Dec 2024
Posts: 478
Own Kudos:
3,387
 [8]
Given Kudos: 141
Posts: 478
Kudos: 3,387
 [8]
For a given triangle with sides x,3x and 24, what is the 01 Aug 2013, 03:37
5
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

46% (01:50) correct 54% (01:51) wrong based on 135 sessions

History

Date
Time
Result
Not Attempted Yet
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
Zarrolou
User avatar
Joined: 02 Sep 2012
Last visit: 11 Dec 2013
Posts: 842
Own Kudos:
5,188
 [8]
Given Kudos: 219
Status:Far, far away!
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Posts: 842
Kudos: 5,188
 [8]
For a given triangle with sides x,3x and 24, what is the 01 Aug 2013, 04:47
6
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Rule for triangles: the sum of two sides must be grater than the third side.

For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. \((x-3)(x-10) = 0\)
So x can be 3, and the sides would be \(3,9,24\) <== this is not a triangle as \(3+9<24\).
Or x can be 10, and the sides would be \(10,30,24\) <== this is a legit triangle.
Sufficient

II.The perimeter is a perfect square.
Applying the rule we get
\(3x+x>24\) or \(x>6\)
\(24+3x>x\) or \(12+2x>0\) (this is irrelevant as it's always true-x must be positive)
\(24+x>3x\) or \(12>x\). So \(12>x>6\) and the perimeter will range from
if \(x=12\), \(P=72\) - if \(x=6\) \(P=48\).
Between 48 and 72 there are the following perfect squares: \(49,64\). Thus x could have two values, and the perimeter would change.
Not sufficient
General Discussion
User avatar
MzJavert
User avatar
Joined: 22 Apr 2013
Last visit: 03 Mar 2014
Posts: 68
Own Kudos:
59
Given Kudos: 95
Posts: 68
Kudos: 59
For a given triangle with sides x,3x and 24, what is the 01 Aug 2013, 04:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mau5
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

OA after some discussion.
Show more


From I X = 3 or X = 10, Plugging into stem- 3 + 9 + 24 = 36 or 10 + 30 + 24 = 64...not sufficient

From II...not enough info

I + II both potential answers are perfect squares, not sufficient..
avatar
bboev
avatar
Joined: 21 Oct 2003
Last visit: 03 Aug 2013
Posts: 1
Location: usa
Posts: 1
Kudos: 0
For a given triangle with sides x,3x and 24, what is the 03 Aug 2013, 08:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mau5
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.
Show more

I is sufficient- it is clear
II x+3x+24=A*2
4x+24=A*2
4(X+6)=A*2
2*2 (X+6)= A*2
solution are x = 3, 10, 19, 30, 43...
for x=3 sides would be 3, 9, 24, but 3+9<24 can not be sides of triangle
x=10 sides would be 10, 30, 24 and 10+24>30 , x can be 10
x=19 sides would be 19, 57, 24 but 19+24<57 , x can not be 19
x=30, sides would be 30,90, 24 but 30+24<90 , x can not be 30
So from II statement x is only 10
The answer is D.
User avatar
mau5
User avatar
Verbal Forum Moderator
Joined: 10 Oct 2012
Last visit: 31 Dec 2024
Posts: 478
Own Kudos:
3,387
Given Kudos: 141
Posts: 478
Kudos: 3,387
For a given triangle with sides x,3x and 24, what is the 03 Aug 2013, 08:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bboev
mau5
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.

I is sufficient- it is clear
II x+3x+24=A*2
4x+24=A*2
4(X+6)=A*2
2*2 (X+6)= A*2
solution are x = 3, 10, 19, 30, 43...
for x=3 sides would be 3, 9, 24, but 3+9<24 can not be sides of triangle
x=10 sides would be 10, 30, 24 and 10+24>30 , x can be 10
x=19 sides would be 19, 57, 24 but 19+24<57 , x can not be 19
x=30, sides would be 30,90, 24 but 30+24<90 , x can not be 30
So from II statement x is only 10
The answer is D.
Show more

You are assuming that x can only be an integer. you get a perfect square for \(x = \frac{25}{4}\) and forms a valid triangle.
avatar
AMITAGARWAL2
avatar
Joined: 06 Jul 2013
Last visit: 08 May 2014
Posts: 71
Own Kudos:
109
Given Kudos: 42
Schools: McCombs PT '16 Jones '16
GMAT 1: 620 Q48 V28
GMAT 2: 700 Q50 V33
Products:
My Reviews
Schools: McCombs PT '16 Jones '16
GMAT 2: 700 Q50 V33
Posts: 71
Kudos: 109
For a given triangle with sides x,3x and 24, what is the 03 Aug 2013, 08:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D
User avatar
mau5
User avatar
Verbal Forum Moderator
Joined: 10 Oct 2012
Last visit: 31 Dec 2024
Posts: 478
Own Kudos:
3,387
Given Kudos: 141
Posts: 478
Kudos: 3,387
For a given triangle with sides x,3x and 24, what is the 03 Aug 2013, 08:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AMITAGARWAL2
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D
Show more

Nope.Please refer to the post above.

Thanks.
avatar
Asifpirlo
avatar
Joined: 10 Jul 2013
Last visit: 26 Jan 2014
Posts: 220
Own Kudos:
1,195
Given Kudos: 102
Posts: 220
Kudos: 1,195
For a given triangle with sides x,3x and 24, what is the 05 Aug 2013, 14:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mau5
AMITAGARWAL2
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D

Nope.Please refer to the post above.

Thanks.
Show more

it's an obvious (A).
because x=3 or x=10 .
for a triangle with such sides (x,3x and 24) it's not possible that x=3. because x+3x>24 have to be true always). so x=10 and we know the perimeter = 4x+24=64
st(2) is not needed at all.
Answer is (A)
avatar
theSachin
avatar
Joined: 14 Jun 2018
Last visit: 05 Mar 2025
Posts: 10
Own Kudos:
4
 [1]
Given Kudos: 2
Location: India
Schools: Columbia '27 Stern '27 Johnson '27 Booth '27 Ross '27 Fuqua '27
GMAT Focus 1: 615 Q84 V76 DI81
GMAT Focus 2: 645 Q90 V78 DI78
GPA: 7.51
Schools: Columbia '27 Stern '27 Johnson '27 Booth '27 Ross '27 Fuqua '27
GMAT Focus 2: 645 Q90 V78 DI78
Posts: 10
Kudos: 4
 [1]
For a given triangle with sides x,3x and 24, what is the 05 Jul 2018, 00:44
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
mau5
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.
Show more
#From first statement we have one value satisfying triangle's properties..ie x=10
*Strike out BCE. Ans must be A or D
*Now perimeter is 4x+24
#According to statement 2 it must b a perfect square...and because of traingles properties x must b greater than equals to 7 and less than 12(PROPERTY OF TRIANGLE I M TALKING ABOUT IS THAT SUM OF ANY TWO SIDES IS ALWAYS GREATER THAN THE THIRD ONE)
*4x+24= 64 is only condition in which x lies b/w 7 and 12(7 inclusive)
**SO ANS IS (D)
I ASSUMED THAT IS AN INTEGER


Sent from my Redmi Note 4 using GMAT Club Forum mobile app
User avatar
CounterSniper
User avatar
Joined: 20 Feb 2015
Last visit: 14 Apr 2023
Posts: 611
Own Kudos:
859
Given Kudos: 74
Concentration: Strategy, General Management
Posts: 611
Kudos: 859
For a given triangle with sides x,3x and 24, what is the 05 Jul 2018, 01:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mau5
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.
Show more


sides x, 3x and 24
so
x+3x > 24
4x > 24
x > 6

1.x=3,x=10
since x is > 6 , x=10 sufficient

2. x+3x+24 = a^2
4x+24=perfect square
perfect squares > 24 are
36 for which 4x=12 , x =3
but x should be > 6
49 for which 4x=25 , x=6.25
64 for which 4x=30 , x=7.50
...
insufficient

A it is !!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,984
Own Kudos:
1,117
Posts: 38,984
Kudos: 1,117
For a given triangle with sides x,3x and 24, what is the 14 Sep 2023, 10:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109827 posts
kingbucky
498 posts
Gmat860sanskar
212 posts