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18 May 2024, 11:16
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
100% (01:09) correct
0% (00:00) wrong based on 4 sessions
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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
The area of rectangle A
Quantity B
The area of rectangle B
Quantity A
The area of rectangle A
Quantity B
The area of rectangle B
19 May 2024, 12:25
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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.
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.
07 Jul 2024, 11:32
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Official Explanation
In this question you are asked to compare the area of rectangle A and the area of rectangle B. Since the information given relates the dimensions of both rectangle A and rectangle B to the corresponding dimensions of rectangle C, you can try to use the relationships to make the desired comparison.
If ℓ represents the length of rectangle C and w represents its width, then the length and width of rectangles A and B can be translated into algebraic expressions as follows.
In terms of ℓ and w, the area of rectangle A is (1.1ℓ)(0.9w), or 0.99ℓw.
In terms of ℓ and w, the area of rectangle B is (1.2ℓ)(0.8w), or 0.96ℓw.
Since 0.99ℓw is greater than 0.96ℓw, Quantity A is greater than Quantity B, and the correct answer is Choice A.
In this question you are asked to compare the area of rectangle A and the area of rectangle B. Since the information given relates the dimensions of both rectangle A and rectangle B to the corresponding dimensions of rectangle C, you can try to use the relationships to make the desired comparison.
If ℓ represents the length of rectangle C and w represents its width, then the length and width of rectangles A and B can be translated into algebraic expressions as follows.
- The length of rectangle A is 10 percent greater than the length of rectangle C, or 1.1ℓ.
- The width of rectangle A is 10 percent less than the width of rectangle C, or 0.9w.
- The length of rectangle B is 20 percent greater than the length of rectangle C, or 1.2ℓ.
- The width of rectangle B is 20 percent less than the width of rectangle C, or 0.8w.
In terms of ℓ and w, the area of rectangle A is (1.1ℓ)(0.9w), or 0.99ℓw.
In terms of ℓ and w, the area of rectangle B is (1.2ℓ)(0.8w), or 0.96ℓw.
Since 0.99ℓw is greater than 0.96ℓw, Quantity A is greater than Quantity B, and the correct answer is Choice A.
