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Is the length of a side of equilateral triangle E less than

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Is the length of a side of equilateral triangle E less than [#permalink] New post 07 Dec 2012, 12:27
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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.

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Re: Is the length of a side of equilateral triangle E less than [#permalink] New post 07 Dec 2012, 12:41
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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.
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Re: Is the length of a side of equilateral triangle E less than [#permalink] New post 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?
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Re: Is the length of a side of equilateral triangle E less than [#permalink] New post 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.
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Re: Is the length of a side of equilateral triangle E less than [#permalink] New post 05 Mar 2014, 00:09
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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.
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Re: Is the length of a side of equilateral triangle E less than [#permalink] New post 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
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Re: Is the length of a side of equilateral triangle E less than [#permalink] New post 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!
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Re: Is the length of a side of equilateral triangle E less than [#permalink] New post 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?
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Re: Is the length of a side of equilateral triangle E less than [#permalink] New post 05 Mar 2014, 23:58
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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
square.jpg [ 10.18 KiB | Viewed 361 times ]

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

Hope it's clear.
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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.


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