Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than π ／100square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains?
(1) Jack's rug covers an area of 9π square feet.
(2) The centers of the stains are less than 4 feet apart.
A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.
p是兀哈....不好打
(1) Given that the circular rug has area 9p ft^2, the radius of the rug, R ft, satisfies the equation pR^2=9p, and so R^2=9,or R=3. If the centers of the circular stains are 4 ft apart, then the midpoint of the centers will be a distance of at most (1/10+2+1/10)ft=2.2 ft from any point on the stains. Thus, if the circular rug (which has radius 3 ft) were placed so that its center lies on that midpoint, them the rug would cover both stains. However, if the centers of the circular stains are 7 ft apart, then the circular rug (which has diameter 6 ft) cannot be placed to cover both stains; NOT sufficient.
(2)Given that the centers of the circular stains are less than 4 ft apart, it is not possible to determine whether the circular rug can be placed to cover both stains since nothing is given about the size of the circular rug; NOT sufficient.
Taking (1) and (2) together, the centers of the circular stains are less than 4 ft apart and it follows from the discussion in (1) that the circular rug can be placed to cover both stains.
作者: StacyTwon 时间: 2017-11-13 11:13
我也做到这一题了，看不太懂OG解析的（1/10+2+1/10）是什么意思。
If the centers of the circular stains are 4 ft apart, then the midpoint of the centers will be a distance of at most (1/10+2+1/10)ft=2.2 ft from any point on the stains.
我的理解是这句话说两个circular stains的圆心距为4英尺，则两个圆心距的中点到任何stain上一点的距离最远（1/10+2+1/10）。
但是我画图后看，距离最远不是应该是（2+1/10）吗？
求解答~~谢谢！作者: StacyTwon 时间: 2017-11-13 11:28
刚刚去beatgmat论坛看了，这个解析比较清楚，和我思考的也一样。（但我上面的问题还是没解决啊）
The situation is depicted in the image below. Since the area of each stain is less than π/100 sq feet, we have A < π/100 sq feet; A = Area of each stain πr^2 < π/100; r = Radius of each stain => r < 1/10 or d < 1/5; d = diametere of each stain Statement 1: Rug covers an area of 9π sq feet Area of rug = 9π sq feet = πR^2; R = Radius of the rug => R = 3 feet or D = 6 feet; D = diametere of the rug Since we do not know how far the stains are from each other, we cannot determine whether the rug can cover both the stains. If the stains are too close to each other, the rug can cover both the stains since (twice the diameter of the stains = 2*1/5 = 2/5) < (The diameter of the rug = 6). Insufficient. Statement 2: The centers of the stains are less than 4 feet apart. Let's take the extreme case. Let's assume that the centers of the stains 4 feet apart and their area = π/100 sq feet each. Thus, the maximum distance between the two stains = 4 + the diameters of the stains = 4 + 1/5 = 4.20 feet We do not know the diameter of the rug. Insufficient. Statement 1 & 2: Since 4.20 feet (Maximum distance between the stains to be covered) < 6 feet (Diameter of the rug), the rug can cover both the stains. Sufficient. The correct answer: C
——【转自BEATGMAT】作者: p1coSuss1 时间: 2017-11-28 10:46
我觉得按og的后一句话Thus, if the circular rug (which has radius 3 ft) were placed so that its center lies on that midpoint, them the rug would cover both stains. 来看是用地毯的中点放在midpoint然后用半径和midpoint到stains的最长距离做比较，应该就是（2+1/10），应该是og的错误吧。。吧。。吧。。
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