【美国留学】GMAT数学逻辑每日一练

　　【数学】

　　The rate of a certain chemical reaction is directlyproportional to the square of the concentration of chemical A present andinversely proportional to the concentration of chemical B present. If the concentration of chemical B isincreased by 100 percent, which of the following is closest to the percentchange in the concentration of chemical A required to keep the reaction rateunchanged?

　　(A) 100% decrease

　　(B) 50% decrease

　　(C) 40% decrease

　　(D) 40% increase

　　(E) 50% increase

　　【逻辑】

　　Two centuries ago, Tufe Peninsula became separated from the mainland, isolating on the newly formed Tufe Island a population of sunflowers.

　　This population's descendants grow to be, on average, 40 centimeters shorter than sunflowers found on the mainland. Tufe Island is significantly drier than Tufe Peninsula was. So the current average height of sunflowers is undoubtedly at least partially attributable to changes in Tufe’s environmental conditions.

　　Which of the following is an assumption on which the argument depends?

　　A. There are no types of vegetation on Tufe Island that are known to benefit from dry conditions.

　　B. There were about as many sunflowers on Tufe Peninsula two centuries ago as there are on Tufe Island today.

　　C. The mainland‘s environment has not changed in ways that have resulted in sunflowers on the mainland growing to be 40 centimeters taller than they did two centuries ago.

　　D. The soil on Tufe Island, unlike that on the mainland, lacks important nutrients that help sunflowers survive and grow tall in a dry environment.

　　E. The 40-centimeter height difference between the sunflowers on Tufe Island and those on the mainland is the only difference between the two populations.

　　答案

　　数学

　　题目翻译：某种化学物的反应与化学物 A 含量的平房，与 B 的含量成反比。如果化学物 B 的含量增加了 100%，若要保持此种化学物的反应速率不变的话，化学物 A需要怎么样的变动?

　　思路点拨： B 增加了多少倍，为了保持恒等，那么 A 要相应减少同样的倍数。 题目全解：B 增加 100% ，即 B 变成了两倍，则反应速率变成 1/2。若保持速率不变，则 A 需使反应速率需要变为两倍，根据题目，A 的平方与速率成正比，那么 A 平方就等于 2， A 就等于根号 2=1.41，选 D。

　　Caution!：理解正比，反比，以及此种化学物的反应速率是与 A的浓度的平方的关系。

　　逻辑

　　Reasoning

　　What must be true in orderfor the given information to justify the conclusion that changes in Tufe'senvironmental conditions have affected the heights of sunflowers? The argumentimplies that the drying of Tufe's climate has made

　　thesunflowers shorter than sunflowers on Tufe used to be. In comparing the heightsof Tufe Island's sunflowers to those of mainland sunflowers, the argumentassumes that on the mainland today, the sunflowers are the same height assunflowers on Tufe Peninsula were two centuries ago, or at least no taller.

　　A. Even if the dry climate of TufeIsland has stunted the sunflowers, it may have benefited other vegetation.

　　B. The argument does not discussthe number of sunflowers, only their average heights.

　　C. Correct. If changes in the mainland'senvironment had made mainland sunflowers taller than they used to be, then themainland sunflowers’ greater height would not justify the conclusion thatsunflowers on Tufe Island are shorter than they used to be.

　　D. Even if the dry of Tufe Islandhas stunted the sunflowers, the soil may be no different from that on themainland.

　　E. The dry cfimate of Tufe Islandcould both stunt the sunflowers and change them in other ways not affectingmainland sunflowers.

　　The correct answer is C.

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