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GMAT Practice exam 2 - Geometry

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by GMATGuruNY » Sun Jun 05, 2016 5:26 am
The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2:3 , what is the ratio of the area of region R to the are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9
Since a square has 4 equal sides, plug in multiples of 4.

Rectangle R:
Since L:W = 2:3, let L = 4*2 = 8 and W = 4*3 = 12.
Then:
Perimeter = L+W+L+W = 8+12+8+12 = 40.
Area = L*W = 8*12 = 96.

Square S:
Since S and R have the same perimeter, P = 40.
Since perimeter = 40, S=10.
Area = S² = 10² = 100.

Resulting ratio:
R/S = 96/100 = 48/50 = 24/25.

The correct answer is B.
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by Brent@GMATPrepNow » Sun Jun 05, 2016 10:26 am
The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2:3 , what is the ratio of the area of region R to the are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9
Let's PLUG IN some values that meet the given conditions.

The sides of R are in the ratio 2:3
So, let the two sides have lengths 2 and 3.
This means the area of Region R = (2)(3) = 6
This means the ENTIRE perimeter of Region R is 2 + 2 + 3 + 3 = 10


The perimeters of square region S and rectangular region R are equal.
This means the perimeter of square region S is also 10
Since all 4 sides in a square are of equal length, each side must have length 2.5
So, the area of Region S = (2.5)(2.5) = 6.25

What is the ratio of the area of region R to the are of region S ?
We get: 6 : 6.25
Check the answer choices .... no matches. So, we need to take 6 : 6.25 and find an equivalent ratio.
If we multiply both parts by 4 we get: 24 : 25
So, the correct answer is B

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by MartyMurray » Sun Jun 05, 2016 7:22 pm
The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2:3 , what is the ratio of the area of region R to the are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9
Let's call the sides of the rectangle 2x and 3x. 2x + 3x = 5x is half of the perimeter of the rectangle.

2x + 3x = 5x is also half the perimeter of the square. The length of one side of the square is 5x/2.

The area of the rectangle is 2x * 3x = 6x²

The area of the square is 5x/2 * 5x/2 = 25x²/4 = 6.25x²

Area R/Area S = 6x²/6.25x² = 6/6.25 = 24/25

The correct answer is B.
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by Matt@VeritasPrep » Tue Jun 07, 2016 11:01 pm
Suppose the rectangle has sides 2, 2, 3, and 3. That gives a perimeter of 10. The square must have sides of 10/4, or 2.5

The area ratio is (2*3)/(2.5*2.5) = 6/6.25.

To make this an integer, we multiply both top and bottom by 4 (to eliminate .25) in the denominator, giving 24/25, and we're set.
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