January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score. January 21, 2019 January 21, 2019 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
Author 
Message 
TAGS:

Hide Tags

Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 123
Location: Bangladesh
Concentration: Accounting
GMAT Date: 04062013
GPA: 3.65

Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
07 Dec 2012, 12:27
Question Stats:
83% (01:20) correct 17% (01:31) wrong based on 173 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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 52296

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



Intern
Joined: 05 Dec 2013
Posts: 14

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
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?



Intern
Joined: 07 Feb 2011
Posts: 13

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
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.



Math Expert
Joined: 02 Sep 2009
Posts: 52296

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
05 Mar 2014, 00:09
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.
Answer: D. 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 06 Aug 2011
Posts: 336

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
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 !



Intern
Joined: 05 Dec 2013
Posts: 14

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
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? 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!



Current Student
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, 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.
Answer: D. In 2 above, can you tell me how you got y√2?



Math Expert
Joined: 02 Sep 2009
Posts: 52296

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
05 Mar 2014, 23:58
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.
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 6237 times ]
Therefore by Pythagorean theorem \(y^2+y^2=diagonal^2\) > \(2y^2=diagonal^2\) > \(diagonal=y\sqrt{2}\). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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, 19:28
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: 7209

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
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 millopezleIs 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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Manager
Joined: 06 Mar 2014
Posts: 239
Location: India
GMAT Date: 04302015

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
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 noninteger then the entire answer changes to E.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13361
Location: United States (CA)

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
20 May 2015, 18:26
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 nonintegers will NOT change the answer to the question, but certain DS questions will require that you consider noninteger 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
CoFounder & 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!*****



Manager
Joined: 06 Mar 2014
Posts: 239
Location: India
GMAT Date: 04302015

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
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 nonintegers will NOT change the answer to the question, but certain DS questions will require that you consider noninteger 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 noninteger will not affect the ratio and the answer.



Intern
Joined: 13 Oct 2018
Posts: 9

Re: Is the length of a side of equilateral triangle E less than
[#permalink]
Show Tags
29 Oct 2018, 10:28
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 find myself a bit offtrack here :/ The question says "is the length of a side of the equilateral triangle less than the length of a side of the square?" If we assume the length of a side of the equilateral triangle = x and the length of a side of the square = y; aren't we looking for if x<y as explicitly stated in the question? Why did we look for if x>y? Please explain. Regards,




Re: Is the length of a side of equilateral triangle E less than &nbs
[#permalink]
29 Oct 2018, 10:28






