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A, B, and C are three rectangles The length and width [#permalink]
24 Dec 2015, 07:25
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A, B, and C are three rectangles. The length and width of rectangle A are 10 percent greater and 10 percent less, respectively, than the length and width of rectangle C. The length and width of rectangle B are 20 percent greater and 20 percent less, respectively, than the length and width of rectangle C.
Quantity A 
Quantity B 
The area of rectangle A 
The area of rectangle B 
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given. Practice Questions Question: 4 Page: 156 Difficulty: hard
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Re: A, B, and C are three rectangles The length and width [#permalink]
24 Dec 2015, 07:32
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Let the sides of rectangle C be 100 and 100. Now from the description in the question we know that length of side A is 110 (10% more than C) and breadth of rectangle A is 90 (10% less than C). Thus Area of rectangle A is 9900. Again from the description we have length of side B is 120 (20% more than C) and breadth of rectangle B is 80 (20% less than C). Thus Area of rectangle C is 9600. Clearly A is greater.
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Re: A, B, and C are three rectangles The length and width [#permalink]
15 Mar 2018, 16:51
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correct: A A: Length_A = 1.1 * Length_C Width_A = 0.9 * Length_C B: Length_B = 1.2 * Length_C Width_A = 0.8 * Length_C C: Lenght_C Width_C
The area of rectangle A: Length_A * Width_A = 1.1 * Length_C * 0.9 * Length_C The area of rectangle B: Length_B * Width_B = 1.2 * Length_C * 0.8 * Length_C We compare 1.1 * 0.9 and 1.2* 0.8. A is bigger.
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Re: A, B, and C are three rectangles The length and width [#permalink]
15 Aug 2019, 07:04
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sandy wrote: A, B, and C are three rectangles. The length and width of rectangle A are 10 percent greater and 10 percent less, respectively, than the length and width of rectangle C. The length and width of rectangle B are 20 percent greater and 20 percent less, respectively, than the length and width of rectangle C.
Quantity A 
Quantity B 
The area of rectangle A 
The area of rectangle B 
Sandy has already provided a fast solution by assigning some nice dimensions to rectangle C. So, let's examine an algebraic approach. Let rectangle C have length L and width WThe length and width of rectangle A are 10 percent greater and 10 percent less, respectively, than the length and width of rectangle CSo, the length of rectangle A = L + (10% of L) = L + (0.1L) = 1.1LAnd, the width of rectangle A = W  (10% of W) = W  (0.1L) = 0.9WThe length and width of rectangle B are 20 percent greater and 20 percent less, respectively, than the length and width of rectangle CSo, the length of rectangle B = L + (20% of L) = L + (0.2L) = 1.2LAnd, the width of rectangle B = W  (20% of W) = W  (0.2L) = 0.8WArea or rectangle = (length)(width)We get: Quantity A: ( 1.1L)( 0.9W) Quantity B: ( 1.2L)( 0.8W) Simplify to get: Quantity A: 0.99LW Quantity B: 0.96LW Since L and W are POSITIVE, we can be certain that 0.99LW > 0.96LW Answer: A Cheers, Brent
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Re: A, B, and C are three rectangles The length and width [#permalink]
15 Aug 2019, 13:27
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Let, For C , Length 100, width 50, Area=5000 so For A, Length 110,width 45, Area=4950 and For B, Length 120, width 40, Area=4800
So A is greater.




Re: A, B, and C are three rectangles The length and width
[#permalink]
15 Aug 2019, 13:27





