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Is the perimeter of square S greater than the perimeter of e

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Is the perimeter of square S greater than the perimeter of e [#permalink]

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New post 12 Feb 2014, 02:09
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is the perimeter of square S greater than the perimeter of equilateral triangle T?

(1) The ratio of the length of a side of S to the length of a side of T is 4:5.
(2) The sum of the lengths of a side of S and a side of T is 18.

Data Sufficiency
Question: 88
Category: Geometry Perimeter
Page: 158
Difficulty: 650


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Re: Is the perimeter of square S greater than the perimeter of e [#permalink]

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New post 12 Feb 2014, 02:09
SOLUTION

Is the perimeter of square S greater than the perimeter of equilateral triangle T?

Let s and t be the side lengths of square S and triangle T, respectively. The question asks whether 4s > 3t or whether s/t > 3/4.

(1) The ratio of the length of a side of S to the length of a side of T is 4:5 --> s/t = 4/5. Since 4/5 > 3/4, then s/t = 4/5 > 3/4. Sufficient.

(2) The sum of the lengths of a side of S and a side of T is 18. Clearly insufficient.

Answer: A.

Similar questions to practice:
is-the-perimeter-of-triangle-t-greater-than-the-perimeter-of-96639.html
is-the-perimeter-of-the-equilateral-triangle-t-greater-than-101507.html
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Re: Is the perimeter of square S greater than the perimeter of e [#permalink]

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New post 12 Feb 2014, 03:39
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Note: The perimeter of the two figures if fixed. For a square, we can calculate this if we know any one measurement (side, diagonal). However, the shape of the triangle can vary for a fixed perimeter. But as a rule : For a given perimeter, an equilateral triangle will have the maximum area. We will use this info to solve the question.

From 1: s/t =4/5 (here s= side of the square & t= side of the triangle) => s=4x & t=5x (using ratios)
Now, we can evaluate and compare their area. (but we don't need to calculate, just know that we can)
{SUFFICIENT option A or D possible}
From 2: s+t=18. (2 unknowns and 1 equation) => cannot be solved {INSUFFICIENT}

Answer A
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Re: Is the perimeter of square S greater than the perimeter of e [#permalink]

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New post 12 Feb 2014, 06:29
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1
St1: The ratio of the length of a side of S to the length of a side of T is 4:5.

Let length of one side of the square S be 4x and that of eq. triangle T be 5x.

Perimeter (S) = 4*4x = 16x
Perimeter (T) = 3*5x = 15x

16x > 15x. Sufficient.

St2: The sum of the lengths of a side of S and a side of T is 18.

If each side of S and T is 9,

Perimeter (S) = 4*9 = 36
Perimeter (T) = 3*9 = 27

36 > 27 - yes

If one side of S is 1 and that of T is 17,

Perimeter (S) = 4*1 = 4
Perimeter (T) = 3*17 = 51

4 < 51 - no

Two different answers. Not sufficient.

Answer (A).
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Re: Is the perimeter of square S greater than the perimeter of e [#permalink]

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New post 17 Feb 2014, 02:09
SOLUTION

Is the perimeter of square S greater than the perimeter of equilateral triangle T?

Let s and t be the side lengths of square S and triangle T, respectively. The question asks whether 4s > 3t or whether s/t > 3/4.

(1) The ratio of the length of a side of S to the length of a side of T is 4:5 --> s/t = 4/5. Since 4/5 > 3/4, then s/t = 4/5 > 3/4. Sufficient.

(2) The sum of the lengths of a side of S and a side of T is 18. Clearly insufficient.

Answer: A.

Similar questions to practice:
is-the-perimeter-of-triangle-t-greater-than-the-perimeter-of-96639.html
is-the-perimeter-of-the-equilateral-triangle-t-greater-than-101507.html
_________________

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?
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Re: Is the perimeter of square S greater than the perimeter of e [#permalink]

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Re: Is the perimeter of square S greater than the perimeter of e   [#permalink] 23 Sep 2017, 03:57
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