GRE考满分·题库

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题目内容
How many positive integers less than or equal to 29 can be expressed as the product of two different integers greater than 1?
n=123456789101112.........499500

The digits of the integer n above are the digits of the integers from 1 to 500 written in consecutive order. How many digits does n have?
Of the paperbacks in a private library, 5 percent are biographies. If 3 percent of all the books in the library are paperbacks that are biographies, what percecnt of all the books in the library are paperbacks?
n and q are different positive integers.

Quantity A

The greatest common factor of n and q

Quantity B

The greatest common factor of 201n+2q and 100n+q
When the positive integer w is divided by 13, the remainder is 1, and when w is divided by 15, the remainder is 14. Which of the following is a possible value for w?


Each morning Betty walks from intersection P to intersection R, always walking along streets shown in the figure above and always going east or north. If she varies her walks as much as possible, taking every different path in turn before repeating the sequence of paths, on how many mornings in 48 consecutive mornings will Betty walk through intersection Q?
The integers a, b, and c are positive, and a > b > c. When a, b, and c are divided by 3, the remainder are 0, 1, and 1, respectively.

Quantity A

The remainder when a+b is divided by 3

Quantity B

The remainder when a-c is divided by 3
In the sequence of numbers, each number after the first numbers is $$\frac{1}{3}$$ of the preceding number. T is the least number in the sequence that has a value greater than 1.

999, 333, 111, ......

Quantity A

T

Quantity B

3
If k, n, and $$\frac{k}{n}$$ are integers greater than 1, which of the following could be the value of kn?
All of the codes used to unlock a certain type of jewelry box are different arrangements of the letters iin the name "MARSHA," where both the first and last letters in each code are "A"s. How many such 6-letter codes are possible?
The function f is defined by f(x)=|x-a|-|b-x| for all numbers x, where a and b are positive costants. What is the value of f(-4)?
A box contains small toys, and each toy is worth either $3 or $6. If a toy is selected at random from the box, the probability that the selected toy will be worth $6 is 0.25. Which of the following could be the total value of all the toys in the box?

Indicate all such values.
In a certain portfolio 70 percent of the stocks declined in value last month. Of the stocks that declined in value, 40 percent were in large corporations. What percent of the stocks in the portfolio declined in value last month but were not in large corporations?
Thomas' daughter plans to begin college 6 years from now. Thomas plans to open a new college savings account that pays interest at the annual rate of 2.2 percent, compounded annually. Which of the following is closest to the amount of the initial deposit that Thomas should make if he plans to have $20,000 in the account at the end of 6 years, provided that there will be no ransactions in the account other than the initial deposit and the interest payments?
n is a four-digit positive integer such that its four digits are all different and each digit is either 4, 7, 8, or 9.

Quantity A

The remainder when n is divided by 5

Quantity B

The remainder when n is divided by 9
How many noncongruent triangles are there such that the length of each side of each triangle is an integer and the perimeter of each triangle is 15?
Each day for 25 days, the number of people who used a certain library that day was recorded. The standard deviation of the 25 recorded numbers is 12.

Which of the following statements individually provide(s) sufficient additional information to determine the mean of the 25 recorded numbers?

Indicate all such statements.
List A: 1, 5, 9, 13, 4

List B: 1, 5, 9, 13, 9

List C: 1, 5, 9, 13, 7

List D: 1, 5, 9, 13, 6

The standard deviation of n numerical data $$ x_{1}, x_{2}, x_{3}, ..., x_{n}$$, With mean $$\bar{x}$$ is equal to $$\sqrt{\frac{S}{n}}$$, where S is the sum of the squared differences $$(x_{i}-\bar{x})^{2}$$, for 1 ≤ i ≤ n.

Which of the following shows lists A, B, C, and D in order from the list with the least standard deviation to the list with the greatest standard deviation?


The figure above represents one of two pairs of identical support legs that will be part of the frame of a swing set, which is to be constructed on level ground using metal pipe. Each pair of support legs will have a horizontal bar 1.5 meters above ground level, and the triangle formed by the bar and support legs will be equilateral. Each support leg will extend below ground level by 0.5 meter. The frame will be completed by a horizontal bar, 5 meters in length and 3 meters above ground level, that will connect the tops of the two pairs of support legs. Approximately what is the total length, in meters, of the metal pipe needed to construct the entire frame?
The number 24 has the property that it is divisible by its units digit, 4. How many of the integers between 10 and 70 are divisible by their respective units digits?

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