GMAT数学逻辑推理题解析

2022-06-02 21:06:20

  

  利润=收入-支出

  该关系也是逻辑题目经常涉及的一类考题,请看题!

  例.In 1984 Exco, which sells it's products only through mail-order catalogs, began distributing its catalog to people who had never purchased Exco's products, while it continued to distribute the catalog to previous customers. Total dollar sales increased in 1984, but Exco's profits that year were smaller than in 1983.

  Which of the following, if true, contributes most to an explanation of Exco's smaller profits in 1984as compared to 1983?

  (A)There was a two percent increase in 1984in the sales tax that consumers had to pay on all purchase from the catalog.

  (B)A greater number of catalogs were sent to previous customers than to people who never purchased products from Exco.

  (C)In 1984 Exco's product-manufacturing costs increased by a smaller amount than the products' selling prices Increased.

  (D)Customers who never previously purchased products from Exco purchased, on the average, fewer products in 1984 than did previous customers.

  (E)The increase between 1983 and 1984 in the cost of mailing the catalogs was greater than the increase in sales from l983 to 1984.

  解析:最后一句话说总的销量增加了,但是例如减少了,说明成本上升了,答案选E。

  四、控制变量型题目表现为:A=B*C;A=B/C;A=B+C.

  1.A=B*C型

  例. Sparva, unlike Treland's other provinces, requires automobile insurers to pay for any medical treatments sought by someone who has been involved in an accident; in the other provinces, insurers pay for nonemergency treatment only if they preapprove the treatment. Clearly, Sparva's less restrictive policy must be the explanation for the fact that altogether insurers there pay for far more treatments after accidents than insurers in other provinces, even though Sparva does not have the largest population.

  Which of the following, if true, most strengthen the argument?

  A.Car insurance costs more in Sparva than in any other province.

  B.The cost of medical care in Sparva is higher than the national average.

  C.Difference insurance companies have different standards for determining what constitutes emergency treatment.

  D.Fewer insurance companies operate in Sparva than in any other province.

  E.There are fewer traffic accidents annually in Sparva than in any of the provinces of comparable or great population.

  解析:文中要加强是“less restrictive policy”,对该信息可以表现为两种方式。

  一种是题目一开始提到的,别的地方不赔的,Sparva赔,另外一种形式就是:别的地方赔少的, Sparva赔多。E选项就是第二种情况:total payments=the number of accident*the payment per accident。total payments多,而the number of accident少,说明the payment per accident多,从而加强了文中的less restrictive policy。

  2.A=B/C型

  例:One state adds a 7 percent sales tax to the price of most products purchased within its jurisdiction. This tax, therefore, if viewed as tax on income, has the reverse effect of the federal income tax: the lower the income, the higher the annual percentage rate at which the income is taxed.

  The conclusion above would be properly drawn if which of the following were assumed as a premise?

  A.The amount of money citizens spend on products subject to the state tax tends to be equal across income levels.

  B.The federal income tax favors citizens with high incomes, whereas the state sales tax favors citizens with low incomes.

  C.Citizens with low annual incomes can afford to pay a relatively higher percentage of their incomes in state sales tax, since their federal income tax is relatively low.

  D.The lower a state's sales tax, the more it will tend to redistribute income from the more affluent citizens to the rest of society.

  E.Citizens who fall to earn federally taxable income are also exempt from the state sales tax.

  解析:题目大意“一个州计划向买东西的人征收7%其消费额的作为税,因此,如果把这个税制看作是收入所得税的话,要对联邦的税制产生相反的效果——收入越低,收入所得税占收入的比例越高”。

  Income tax percentage=income tax/income。而题目中又给了income tax= sales tax,那么题目最后已经限定了income↓,income tax percentage↑,那么这里就要control 关系中的唯一变量income tax= sales tax,选项A满足该要求,A选项说市民按照税率花比收入水平的钱都一样,那么分子不变。

  3.A=B+C型

  例. In tests for paranoia, a serious disease, a false positive result indicates that people have paranoia when, in fact, they do not; a false negative result indicates that people do not have paranoia when, in fact, they do, To detect paranoia most accurately, physicians should use the laboratory test that has the lowest proportion of false positive results.

  Which of the following, if true, gives the most support to the recommendation above?

  A.The accepted treatment for paranoia does not have damaging side effects.

  B.The laboratory test that has the lowest proportion of false positive results causes the same minor side effects as do the other laboratory tests used to detect paranoia.

  C.In treating paranoia patients, it is essential to begin treatment as early as possible, since even a week of delay can result in loss of life.

  D.The proportion of inconclusive test results is equal for all laboratory tests used to detect paranoia.

  E. All laboratory tests to detect paranoia have the same proportion of false negative.

  解析:false result=false positive result +false negative result.

  题干说在诊断paranoia病的时候会出现两种错误结果,现在实验的方法可以把错误的positive result降到最低,文中所提及的方案最终是要把错误率降到最低,而现在false positive result降到最低,那么现在唯一需要的就是实验室情况下把false negative result 降低或者相等,那么最后总的错误结果就会降低或者实验的方法有效,答案选E。

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