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  3. Compare Quantity A and Quantity B, using additional information centered above t

Compare Quantity A and Quantity B, using additional information centered above t

游客2025-02-24  8
问题 Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
(A)Quantity A is greater.
(B)Quantity B is greater.
(C)The two quantities are equal.
(D)The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question. [br] The length of each side of rectangle R is an integer, and the area of R is 36.
选项
答案 B
解析 Because the length of each side of rectangle R is an integer and each length is a factor of the area 36, there are 5 possible rectangles: a 1 x 36 rectangle, a 2 x 18 rectangle, a 3 x 12 rectangle, a 4 × 9 rectangle, and a 6x6 rectangle.
The perimeter of the 1 × 36 rectangle is 2(1 + 36), or 74.
The perimeter of the 2 × 18 rectangle is 2(2 + 18), or 40.
The perimeter of the 3 × 12 rectangle is 2(3 + 12), or 30.
The perimeter of the 4× 9 rectangle is 2(4 + 9), or 26.
The perimeter of the 6× 6 rectangle is 2(6 + 6), or 24.
Since each of the 5 possible rectangles has a different perimeter, Quantity A, the number of possible values of the perimeter, is 5. Since Quantity B is 6, the correct answer is Choice B.
This explanation uses the following strategy.
Strategy 11: Divide into Cases
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