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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Is the perimeter of triangle T greater than the perimeter of square S ? (1) T is an isoceles right triangle. (2) The length of the longest side of T is equal to the length of a diagonal of S.

(1) T is an isoceles right triangle --> no info about the square. Not sufficient.

(2) The length of the longest side of T is equal to the length of a diagonal of S --> let the side of the square be \(s\) --> the longest side of the triangle will be \(\sqrt{2}s\) and \(P_{square}=4s\). Now the max perimeter of the triangle T will be if this triangle is equilateral, then \(P_{triangle}=3\sqrt{2}s>4s=P_{square}\), but if triangle T is half of the square S (isosceles right triangle), then \(P_{triangle}=\sqrt{2}s+s+s=s(\sqrt{2}+2)<4s=P_{square}\). Two different answers. Not sufficient.

(1)+(2) Statement (1) says that we have the second case from statement (2), hence \(P_{triangle}=\sqrt{2}s+s+s=s(\sqrt{2}+2)<4s=P_{square}\). Sufficient.

Re: Triangles and Squares - comparing perimeter [#permalink]

Show Tags

02 Jul 2010, 21:07

I get B

i). Not sufficient

ii). a - longest side of triangle x - side of square Given, a = sqrt(2)*x, so perimeter of square, 4x = 2*sqrt(2)*a Perimeter of triangle (of sides a,b,c) = a+b+c is < 2a (sum of the two sides (b+c) < a)

Re: Triangles and Squares - comparing perimeter [#permalink]

Show Tags

24 May 2011, 07:38

2

This post was BOOKMARKED

Is the perimeter of triangle T greater than the perimeter of square S ? (1) T is an isosceles right triangle. (2) The length of the longest side of T is equal to the length of a diagonal of S.

Solution: Bunnuel is right the ans is C. (1) No information about S is given, so insufficient (2) Let the one side of s = x, so Diagonal of s = x√2 Perimeter of S = 4x Thus, the longest side of T = x√2 No other information is given about other sides of T, So insufficient.

Considering C the sides of T = x, x, x√2 [Sides of triangle with 90 degree, 45 degree and 45 degree is s, s, s√2] Perimeter of T = x + x + x√2 which is Less than 4x. Ans. C
_________________

Re: perimeter of triangle T greater than the perimeter of square [#permalink]

Show Tags

09 Feb 2012, 20:09

subhajeet wrote:

Is the perimeter of triangle T greater than the perimeter of square S ?

(1) T is an isoceles right triangle.

(2) The length of the longest side of T is equal to the length of a diagonal of S.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Can anyone please provide a solution for this.

Let a, b, and c denote the three sides of triangle T, with c as the largest side, and let s denote a side of square S. The question then becomes: is \((a+b+c)>4s\)?

(1) Does not give any information about the square S. Thus, Not Sufficient.

(2) \(c = s\sqrt{2}\). From the triangle property, we know that sum of lengths of any two sides of a triangle is always greater than the length of third side. Thus, for triangle T, we have: \(a+b>c\) \(a+b+c>2c\) \(a+b+c> 2\sqrt{2}s\) This still is insufficient data, as we cannot prove weather \(4s>(a+b+c)>2\sqrt{2}s\) OR \((a+b+c)>4s\) (true in case of equilateral triangles)

(1)+(2) a = b, and \(c = a\sqrt{2} = s\sqrt{2}\) Thus, we get a = s. \(a+b+c = a(2+\sqrt{2}) < 4s\). Thus, we can have our answer to the question: is (a+b+c)>4s? No!

So correct answer is (C): (1) and (2) are sufficient together, but not alone..

Re: Is the perimeter of triangle T greater than the perimeter of [#permalink]

Show Tags

30 Jul 2014, 14:01

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 triangle T greater than the perimeter of [#permalink]

Show Tags

08 Nov 2015, 08:50

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.
_________________

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the perimeter of triangle T greater than the perimeter of square S?

(1) T is an isoceles right triangle. (2) The length of the longest side of T is equal to the length of a diagonal of S.

There are 3 variables (3 sides) in a triangle and 1 (one side) in a square. We need 4 equations when only 2 equations are given by the conditions, so there is high chance (E) will be our answer. Looking at the conditions together, perimeter of T < perimeter of S, so the answer is 'no' and this is sufficient. The answer becomes (C).

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...