2018年GRE数学机经抢先看

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题目

1. Two librarians, Robert and Patricia, cataloged a combined total of 180 new books, each of which was cataloged by only one of the two librarians. Although they spent the same amount of time cataloging their books, Robert spent an average of 15 minutes per book whereas Patricia spent an average of 12 minutes per book.

Quantity A：The number of books cataloged by Robert

Quantity B：60

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.

答案：A

解析：设Robert整理了x本书，Patricia整理了y本书，可得二元一次方程组，x+y=180,15x=12y.所以x=80,y=100. 所以A为80，B为60，A比B大。

2. One of the solutions of the equation x^2+bx+c= 0 is -3.

Quantity A：3b

Quantity B：c+9

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.

答案：C

解析：把x= -3带入等式，即9-3b+c=0,即3b=c+9. 所以A和B相等。

3. Which of the following is NOT the sum of a set of consecutive positive integers one of which is 1?

A. 3

B. 10

C. 15

D. 28

E. 35

答案：E

解析：从1开始的连续正整数相加，A是1+2，B是1加到4，C是1到5，D是1到7，而1到8应该是36，所以E是错误的，选E。

4. Each of the 176 people in a group drinks at least one of three beverages—coffee, tea or soda. Of the 94 people in the group who drink coffee, 50 drink only coffee. Of the 82 people in the group who drink tea, 40 drink only tea. Of the 66 people in the group who drink soda, 30 drink only soda. If 10 people in the group drink all three beverages, which of the following statements are true about the people in the group? Indicate all such statements.

A. More people drink only soda than drink only tea.

B. There are 46 people who drink only two of the beverages.

C. There are 56 people who drink more than one of the beverage.

答案：B C

解析：A选项错误，因为有30个人只喝soda,40个人只喝tea. 所以喝soda的人更少。所以A错误。

只喝一种饮料的人共有120个。一共176个人，所以有56个人喝一种以上的饮料，所以C正确。

题中又说有10个人喝三种饮料，所以只有46个人喝两种饮料，所以B正确。

5. If f(x) = 5-2x and f(3k) = f(k+1), then f(k) =?

A. 0.5

B. 1

C. 3

D. 4

E. 6

答案：D

解析：因为f(x) = 5-2x，所以f(3k) = 5-6k. f(k + 1) = 5-2(k+1) = 3-2k.

因为f(3k) = f(k + 1), 所以 5-6k = 3-2k. 所以k=0.5.

所以f(k) = f(0.5). f(0.5) = 4.所以选D.

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