GRE考满分·题库

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题目内容
What is the least positive integer n for which $$\frac{n}{2}$$, $$\frac{n}{3}$$, $$\frac{n}{4}$$, $$\frac{n}{5}$$, $$\frac{n}{6}$$, $$\frac{n}{8}$$ and $$\frac{n}{9}$$ are integers?
The positive numbers a, b, c, d, e, and f are different from each other.

Quantity A

The range of the numbers a, b, c, d, e, and f

Quantity B

The range of the numbers $$a^{2}$$, $$b^{2}$$, $$c^{2}$$, $$d^{2}$$, $$e^{2}$$ and $$f^{2}$$


The monthly commission for a sales representative is computed using the table above. If a sales representative had sales of $13,000 in June, what was her commission for that month?
Kim, Megan, Nina, and Paula are planning to go to a movie theater, where three different movies--A, B and C--are being shown simultaneously in different auditoriums. Each of them will see only one of the movies but not necessarily the same movie as any of the other three people. One possible outcome is that Kim and Megan will see C while Nina and Paula will see A. How many possible outcomes are there?
When the positive integer n is divided by 7, the remainder is 2.

Quantity A

The remainder when 2n+1 is divided by 7

Quantity B

5
For each set of three distinct nonzero digits, consider the sum of all positive three-digit integers that can be formed by the digits. For example, for the three digits 1, 2, and 3, the sum of all positive three-digit integers that can be formed by the digits is 123 + 132 + 213 + 231 + 312 + 321 = 1,332. How many different integers are equal to such a sum?
The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean x is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences, $$(x_{i}- x)^{2}$$ for 1 ≤ i ≤ n.

List S: 3, 4, 7, 9, 10, 15

For which of the following lists is the standard deviation of the numbers in the list equal to 4 times the standard deivation of the numbers in list S?

Indicate all such lists.
The four-digit integer $$8,82X$$ is a multiple of 9, where $$X$$ is the units digit.

Quantity A

$$X$$

Quantity B

2
Nancy invested $5,000 for x years at an annual interest rate of 6 percent, compounded annually.

David invested $6,000 for y years at an annual interest rate of 6 percent, compounded semiannually.

Quantity A

The total amount of interest that Nancy`s investment earned

Quantity B

The total amount of interest that David`s investment earned
$$0 < a < b < c$$

Quantity A

The standard deviation of the seven numbers $$-c, -b, -a, 0, a, b, c$$

Quantity B

The standard deviation of the seven numbers $$-c^{2}, -b^{2}, -a^{2}, 0, a^{2}, b^{2}, c^{2}$$


Square ABCD has sides of length 1. Arc AC is an arc of the circle of radius 1 centered at B. Arc BD is an arc of the circle of radius 1 centered at A. These arcs divide the square into four regions, $$S_1, S_2, S_3$$, and $$S_4$$.

Quantity A

The area of region $$S_1$$ minus the area of region $$S_3$$

Quantity B

$$\frac{π}{2}$$ -1


The circle shown has center O, and arc EPF is a semicircle. Quadrilateral EAOD, ABCD, and OBFC are squares, and the length of each side of ABCD is 1. What is the perimeter of region EPFCD?


For each of 20 brands of protein bars, the number of grams of protein per bar was rounded to the nearest gram and recorded. The histogram shows the frequency distribution of the recorded numbers of grams of protein per bar for the 20 brands, where each interval shown includes its left endpoint and excludes its right endpoint. Based on the histogram, which of the following could be the average (arithmetic mean) and the median, respectively, of the recorded numbers of grams of protein per bar for the 20 brands?
0 < a < b < c < d < e

List X: a, b, c, d, e

List Y: -2a, -2b, -2c, -2d, -2e

Quantity A

The standard deviation of the numbers in list X

Quantity B

The standard deviation of the numbers in list Y
$$B_n=\frac{n}{n+1}$$ for all integers $$n$$ > 1.

$$C_n=B_n + B_{n-1}$$ for all integers $$n$$ > 2.

The integer $$k$$ is greater than 2.

Quantity A

$$C_k$$

Quantity B

$$\frac{2k^2-1}{k+k}$$
Working continuously for a total of 120 hours, a machine first assembled x units of product A and then assembled y units of product B. where x and y are positive integers. It took the machine 3 hours to assemble each unit of product A and 5 hours to assemble each unit of product B. Which of the following could be the total number of units of product A and product B that the machine assembled in the 120 hours?

Indicate all such numbers.

Quantity A

The number of integers between 10,000 and 25,000 that are multiples of 14

Quantity B

The number of integers between 10,000 and 26,000 that are multiples of 15
In a probability experiment, R and S are independent events such that 0 < P(R) < $$\frac{1}{2}$$ and 0 < P(S) < 1.

Quantity A

The probability that S will occur given that R has occurred

Quantity B

P(R)


If the perimeter of the isosceles right triangle is (1+$$\sqrt{2}$$), what is the area of the triangular region?
The least and greatest values in data set $$X$$ are $$j$$ and $$k$$. respectively, and the least and greatest values in data set $$Y$$ are $$p$$ and $$r$$, respectively, where $$j < k < p < r$$. The least value in data set $$Z$$ is the average (arithmetic mean) of $$j$$ and $$k$$, and the greatest value in data set $$Z$$ is the average of $$p$$ and $$r$$.

Quantity A

The average of the range of the values in data set $$X$$ and the range of the values in data set $$Y$$

Quantity B

The range of the values in data set $$Z$$

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