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 350,000 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:

Re: Is the length of a side of equilateral triangle E less than [#permalink]
07 Dec 2012, 12:41

1

This post received KUDOS

Expert's post

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Re: Is the length of a side of equilateral triangle E less than [#permalink]
04 Mar 2014, 17:35

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

Re: Is the length of a side of equilateral triangle E less than [#permalink]
04 Mar 2014, 20:25

bparrish89 wrote:

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

The second statement states the ratio as 2√3 : 3√2 &, the calculated ratio is x√3/2 : y√2. Now if these two ratios are same, we just need to simplify the equation, which gives the ratio of x:y to 4:3.

Re: Is the length of a side of equilateral triangle E less than [#permalink]
05 Mar 2014, 00:09

Expert's post

bparrish89 wrote:

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

Re: Is the length of a side of equilateral triangle E less than [#permalink]
05 Mar 2014, 08:07

bparrish89 wrote:

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

If equilateral triangle has height 2square root 3.. that means its all sides will be 4.. and if diagonal of square is 3 square root2 that means square has all sides 3.

we got No ! equilateral triangle length is greater than square's length _________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Re: Is the length of a side of equilateral triangle E less than [#permalink]
05 Mar 2014, 15:05

Bunuel wrote:

bparrish89 wrote:

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

Re: Is the length of a side of equilateral triangle E less than [#permalink]
05 Mar 2014, 17:22

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Re: Is the length of a side of equilateral triangle E less than [#permalink]
05 Mar 2014, 23:58

Expert's post

X017in wrote:

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

In 2 above, can you tell me how you got y√2?

y is the length of a side of square F. Now, the diagonal of a square is the hypotenuse of a right isosceles triangle made by the sides:

Attachment:

square.jpg [ 10.18 KiB | Viewed 1904 times ]

Therefore by Pythagorean theorem \(y^2+y^2=diagonal^2\) --> \(2y^2=diagonal^2\) --> \(diagonal=y\sqrt{2}\).

Re: Is the length of a side of equilateral triangle E less than [#permalink]
17 Mar 2015, 19:12

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 length of a side of equilateral triangle E less than [#permalink]
17 Mar 2015, 19:42

millopezle wrote:

Could you please explain how did you get the calculated height of the equilateral triangle in statement 2? Thanks

hi millopezle Is the length of a side of equilateral triangle E less than the length of a side of square F?

(1) The perimeter of E and the perimeter of F are equal. (2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2

since you are asking specific question about statement 2.. it is giving us the ratio of height of triangle E to the diagonal of square F as 2√3 : 3√2... since its a ratio ,we can multiply both by x, although we dont require that because final answer is also a ratio... from height of triangle , we can get its side by formula.. h=side1*√3/2... from diagonal of square we can get side by formula... diagonal=√2*side2 what you require is side1/side2= 2h/√3*dia/√2=2/√6*h/dia=2/√6*2√3/3√2=2/3... so we have the ratio as 2/3.. so we can say side of square >side of tri... sufficient

Re: Is the length of a side of equilateral triangle E less than [#permalink]
20 May 2015, 14:02

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

I have a Question, why do we assume that sides of these figures (triangle and square) are integers? If its a non-integer then the entire answer changes to E.

Re: Is the length of a side of equilateral triangle E less than [#permalink]
20 May 2015, 18:26

Expert's post

Hi earnit,

You bring up a fair point - we don't have to assume that the side lengths are integers, but it makes dealing with the 'logic' behind this question easier. As it stands, using non-integers will NOT change the answer to the question, but certain DS questions will require that you consider non-integer values, so it's a good idea to keep them in mind.

Re: Is the length of a side of equilateral triangle E less than [#permalink]
20 May 2015, 23:36

EMPOWERgmatRichC wrote:

Hi earnit,

You bring up a fair point - we don't have to assume that the side lengths are integers, but it makes dealing with the 'logic' behind this question easier. As it stands, using non-integers will NOT change the answer to the question, but certain DS questions will require that you consider non-integer values, so it's a good idea to keep them in mind.

GMAT assassins aren't born, they're made, Rich

Thank you. I accidentally also missed the fact that changing the values to non-integer will not affect the ratio and the answer.

gmatclubot

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
20 May 2015, 23:36