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perimeter

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by grandh01 » Sat Aug 04, 2012 5:41 pm
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.
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Source: — Data Sufficiency |
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by eagleeye » Sat Aug 04, 2012 7:50 pm
grandh01 wrote: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.
Perimeter of square = 4S.
Perimeter of triangle= 3T

We need to find if 4S > 3T => S/T > 3/4. So we rephrase the question as Is S/T > 3/4?

With that in mind, lets look at the options:

(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 . Clearly S/T > 3/4. sufficient.

(2) The sum of the lengths of a side
of S and a side of T is 18.
S+ T = 18. We cant find S/T from this equation. Insufficient.

A is right :)
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by Anurag@Gurome » Sat Aug 04, 2012 9:05 pm
grandh01 wrote: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.
Let each side of square = s and each side of triangle = t
Then perimeter of square = 4s and perimeter of triangle = 3t
Question: Is 4s > 3t?

(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 or s = 4t/5
Perimeter of square = 4s = 4 * (4t/5) = 16t/5, which is definitely greater than 3t (perimeter of triangle); SUFFICIENT.

(2) The sum of the lengths of a side of S and a side of T is 18 implies s + t = 18
But there can be many such combinations when s + t = 18; NOT sufficient.

The correct answer is A.
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Re: perimeter

by Brent@GMATPrepNow » Mon Jul 05, 2021 5:08 am
grandh01 wrote: ↑
Sat Aug 04, 2012 5:41 pm
 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.
Target question: Is the perimeter of square S greater than the perimeter of equilateral triangle T?

Statement 1: The ratio of the length of a side of S to the length of a side of T is 4:5.
Let x = the length of EACH side of the square
Let y = the length of EACH side of the equilateral triangle

So, we can write: x/y = 4/5
Cross multiply to get: 5x = 4y
Divide both sides by 5 to get x =4y/5
We can also write: x = 0.8y

The perimeter of the equilateral triangle = y + y + y = 3y
The perimeter of the square = x + x + x + x = 4x

Since we now know x = 0.8y, we can replace x with 0.8y to get:
The perimeter of the square = 0.8y + 0.8y + 0.8y + 0.8y = 3.2y

Since the perimeter of the equilateral triangle = 3y, and the perimeter of the square = 3.2y, the answer to the target question is YES, the perimeter of square S is greater than the perimeter of equilateral triangle T
Statement 1 is SUFFICIENT

Statement 2: The sum of the lengths of a side of S and a side of T is 18.
There are several scenarios that satisfy statement 2. Here are two:
Case a: Each side of the square has length 17, and each side of the equilateral triangle has length 1. So the perimeter of the square = 17 + 17 + 17 + 17 = 68, and the perimeter of the triangle = 1 + 1 + 1 = 3. In this case, the answer to the target question is YES, the perimeter of square S is greater than the perimeter of equilateral triangle T
Case b: Each side of the square has length 1, and each side of the equilateral triangle has length 18. So the perimeter of the square = 1 + 1 + 1 + 1 = 4, and the perimeter of the triangle = 17 + 17 + 17 = 51. In this case, the answer to the target question is NOT, the perimeter of square S is not greater than the perimeter of equilateral triangle T
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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