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

 It is currently 17 Jul 2018, 12:37

### 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 length of a side of equilateral triangle E less than

Author Message
TAGS:

### Hide Tags

Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 172
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

07 Dec 2012, 13:27
6
1
00:00

Difficulty:

25% (medium)

Question Stats:

81% (01:16) correct 19% (01:27) wrong based on 152 sessions

### HideShow timer Statistics

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.

If anyone find this post helpful plz give+1 kudos
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

07 Dec 2012, 13:41
1
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.

_________________
Intern
Joined: 05 Dec 2013
Posts: 15
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

04 Mar 2014, 18:35
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.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?
Intern
Joined: 07 Feb 2011
Posts: 14
GMAT 1: 580 Q47 V24
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

04 Mar 2014, 21:25
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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

05 Mar 2014, 01:09
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.

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

Sure.

$$\frac{(\frac{x\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}$$;

$$\frac{x\sqrt{3}}{2(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}$$;

Divide both sides by $$\frac{\sqrt{3}}{\sqrt{2}}$$: $$\frac{x}{2y}=\frac{2}{3}$$;

Multiply by 2: $$\frac{x}{y}=\frac{4}{3}$$.

Hope it's clear.
_________________
Senior Manager
Joined: 06 Aug 2011
Posts: 360
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

05 Mar 2014, 09:07
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.

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 !

Intern
Joined: 05 Dec 2013
Posts: 15
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

05 Mar 2014, 16:05
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.

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

Sure.

$$\frac{(\frac{x\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}$$;

$$\frac{x\sqrt{3}}{2(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}$$;

Divide both sides by $$\frac{\sqrt{3}}{\sqrt{2}}$$: $$\frac{x}{2y}=\frac{2}{3}$$;

Multiply by 2: $$\frac{x}{y}=\frac{4}{3}$$.

Hope it's clear.

That's exactly what I was looking for. Thanks!
Intern
Affiliations: CA, SAP FICO
Joined: 22 Nov 2012
Posts: 35
Location: India
Concentration: Finance, Sustainability
GMAT 1: 620 Q42 V33
GMAT 2: 720 Q47 V41
GPA: 3.2
WE: Corporate Finance (Energy and Utilities)
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

05 Mar 2014, 18:22
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.

In 2 above, can you tell me how you got y√2?
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

06 Mar 2014, 00:58
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.

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 5466 times ]

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

Hope it's clear.
_________________
Intern
Joined: 06 May 2013
Posts: 2
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

17 Mar 2015, 20:28
Could you please explain how did you get the calculated height of the equilateral triangle in statement 2?
Thanks
Math Expert
Joined: 02 Aug 2009
Posts: 6219
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

17 Mar 2015, 20:42
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

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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Current Student
Joined: 06 Mar 2014
Posts: 257
Location: India
GMAT Date: 04-30-2015
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

20 May 2015, 15:02
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.

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.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11979
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

20 May 2015, 19:26
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
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Current Student
Joined: 06 Mar 2014
Posts: 257
Location: India
GMAT Date: 04-30-2015
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

21 May 2015, 00:36
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.
Non-Human User
Joined: 09 Sep 2013
Posts: 7277
Re: Is the length of a side of equilateral triangle E less than [#permalink]

### Show Tags

21 Oct 2017, 14:04
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] 21 Oct 2017, 14:04
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.