GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 11:50

### 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

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

# Is the perimeter of equilateral triangle T equal to the circumference

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 442
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Is the perimeter of equilateral triangle T equal to the circumference  [#permalink]

### Show Tags

02 Apr 2012, 03:10
1
2
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:47) correct 37% (01:33) wrong based on 83 sessions

### HideShow timer Statistics

Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Intern
Joined: 02 Mar 2017
Posts: 3
Re: Is the perimeter of equilateral triangle T equal to the circumference  [#permalink]

### Show Tags

15 Jan 2018, 06:46
5
i tried doing the following:

since one side of the triangle is the diameter, the triangle becomes a right triangle inscribed in the circle. Hence is not equilateral and the statement becomes void. M i using the right logic?
##### General Discussion
Intern
Joined: 02 Apr 2012
Posts: 1
Re: Is the perimeter of equilateral triangle T equal to the circumference  [#permalink]

### Show Tags

02 Apr 2012, 20:48
This is a tricky one

Let's say t = a side of the equilateral triangle T
P = perimeter
C = circumference

Statement I

Sum of the lengths of a side of T and the radius of C is 9.
-> t + r = 9 => r = 9 - t
-> perimeter = 3t
-> circumference = 2(pi) (9-t)
-> 3t = 2(pi)(9-t)
-> 3t = 18pi - 2(pi)t
-> 3t + 2(pi)t = 18pi
Without doing the actual calculation, you should be able to infer that they can equal to each other, which means that perimeter and the circumference can equal to each other. Unfortunately this information is rather useless because it doesn't narrow down your answer. This statement essentially says that (could be) P < C or P = C or P > C

Statement II

The length of a side of T is equal to the diameter of C.

This statement sets up a distinct relationship
-> 3t & t*pi
Since pi is greater than 3, the circumference of the circle C cannot equal to perimeter of the triangle T. 3t cannot be greater than t*pi (because t > 0). Therefore Sufficient

Statement 2 on its own conclusively proves that they cannot equal to each other, but statement 1 doesn't. Therefore, the answer has to be (B)

This is how I see it, but I could be wrong. I think it's way more complicated than it needs to be which always makes me nervous about my answer. Let me know if I'm wrong somewhere.
Math Expert
Joined: 02 Sep 2009
Posts: 58453
Re: Is the perimeter of equilateral triangle T equal to the circumference  [#permalink]

### Show Tags

03 Apr 2012, 05:33
1
Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9 --> we can split 9, between the lengths of a side and the radius, so that the perimeter to be equal to the circumference as well as not to be equal. Not sufficient.

(2) The length of a side of T is equal to the diameter of C --> we have fixed relationship between the side and the radius, hence we can say whether the perimeter equals to the circumference. Sufficient.

To elaborate more: question asks whether $$3a=2\pi{r}$$, where $$a$$ is the length of a side of triangle T and $$r$$ is the radius of C. Given: $$a=2r$$ --> $$perimeter=3a=6r$$ and $$circumference =2\pi{r}\approx{6.28r}$$, so $$P<C$$.

_________________
Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 160
Schools: Johnson '15
Re: Is the perimeter of equilateral triangle T equal to the circumference  [#permalink]

### Show Tags

03 Apr 2012, 05:49
enigma123 wrote:
Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.

How come the answer is B?

i hope to try n explain....plz correct me if i am wrong...

P=3t where t is the side of the triangle

1. t+r = 9
clearly not sufficient

2. t=r
so 3r = 2pir...definately no...Hence B along is sufficient to tell that the perimeter is not equal to Circumference
_________________
Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs
Math Expert
Joined: 02 Sep 2009
Posts: 58453
Re: Is the perimeter of equilateral triangle T equal to the circumference  [#permalink]

### Show Tags

03 Apr 2012, 06:03
harshavmrg wrote:
enigma123 wrote:
Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.

How come the answer is B?

i hope to try n explain....plz correct me if i am wrong...

P=3t where t is the side of the triangle

1. t+r = 9
clearly not sufficient

2. t=r
so 3r = 2pir...definately no...Hence B along is sufficient to tell that the perimeter is not equal to Circumference

(2) The length of a side of T is equal to the diameter of C. So, $$t=2r$$. Else is correct.
_________________
Retired Moderator
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: Is the perimeter of equilateral triangle T equal to the circumference  [#permalink]

### Show Tags

19 Jan 2018, 07:26
Prachikh wrote:
i tried doing the following:

since one side of the triangle is the diameter, the triangle becomes a right triangle inscribed in the circle. Hence is not equilateral and the statement becomes void. M i using the right logic?

Hi

I dont think its correct to say that the statement becomes void. There is an equilateral triangle separately whose side is say 'x'. So its perimeter becomes '3x'.
Now there is another circle separately which happens to have the same diameter as the length of side of our equilateral triangle, i,e, 'x'.

So here we have to compare perimeter of an equilateral triangle with side x, and circumference of a circle with diameter x. It doesn't mean that our earlier triangle has to be inscribed in this circle.
Non-Human User
Joined: 09 Sep 2013
Posts: 13259
Re: Is the perimeter of equilateral triangle T equal to the circumference  [#permalink]

### Show Tags

13 Oct 2019, 00:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Is the perimeter of equilateral triangle T equal to the circumference   [#permalink] 13 Oct 2019, 00:58
Display posts from previous: Sort by