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Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 722
Let side of square be s. Let side of triangle be t.  [#permalink]

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Difficulty:   15% (low)

Question Stats: 87% (00:57) correct 13% (01:02) wrong based on 55 sessions

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Let side of square be s. Let side of triangle be t.

Rephrasing the question.
Q Is ratio of s/t known?
1) Insufficient. s + t = 22. two var, one equation.
2) Sufficient.
4s / 3t = 5/6

Hence B.

kamalkicks wrote:
IS AREA OF SQUARE S GREATER THAN THE AREA OF EQUILATERAL TRIANGLE T ?

A) THE SUM THE LENGTH OF A SIDE S AND A SIDE OF T IS 22 ?

B) THE RATIO OF THE PERIMETER OF SQUARE S TO THE PERIMETER OF TRIANGLE T IS 5 TO 6 ?
Retired Moderator B
Joined: 16 Nov 2010
Posts: 1402
Location: United States (IN)
Concentration: Strategy, Technology
Re: IS AREA OF SQUARE S GREATER ....  [#permalink]

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My take on this :

Let side of square - S

Let side of triangle - T

Square = S^2

Eq Triangle = sqrt(3)/4 * T^2

From (1)

S + T = 22

(22 - T)^2 > sqrt(3)/4 * T^2

484 - 44T + T^2 - sqrt(3)/4 * T^2 > 0

T^2 - sqrt(3)/4 * T^2 is always +ve

But for values of T > 11 (484 - 44T) is -ve

Since the exact value of T is not known, so not sufficient

From (1) we have:

4S/3T = 5/6

=> S = 5T/8

So (2) is sufficient
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Director  Joined: 01 Feb 2011
Posts: 653
Re: IS AREA OF SQUARE S GREATER ....  [#permalink]

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1 is not Sufficient ( diff values of T leads to different answer)

2 s/T =5/8 ,clearly is sufficient to compare the areas.

Hence answer is B.
Manager  Joined: 28 Jul 2011
Posts: 89
Re: IS AREA OF SQUARE S GREATER ....  [#permalink]

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how can we prove this?
Math Expert V
Joined: 02 Sep 2009
Posts: 53716
Re: Let side of square be s. Let side of triangle be t.  [#permalink]

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gmat1220 wrote:
Let side of square be s. Let side of triangle be t.

Rephrasing the question.
Q Is ratio of s/t known?
1) Insufficient. s + t = 22. two var, one equation.
2) Sufficient.
4s / 3t = 5/6

Hence B.

kamalkicks wrote:
IS AREA OF SQUARE S GREATER THAN THE AREA OF EQUILATERAL TRIANGLE T ?

A) THE SUM THE LENGTH OF A SIDE S AND A SIDE OF T IS 22 ?

B) THE RATIO OF THE PERIMETER OF SQUARE S TO THE PERIMETER OF TRIANGLE T IS 5 TO 6 ?

Discussed here: https://gmatclub.com/forum/is-the-lengt ... 10989.html
_________________ Re: Let side of square be s. Let side of triangle be t.   [#permalink] 03 Jan 2019, 03:44
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# Let side of square be s. Let side of triangle be t.

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