GRE考满分·题库

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题目内容
What is the greatest prime divisor of $$3^{100}$$- $$3^{97}$$?
If the perimeter of the isosceles right triangle is (1+$$\sqrt{2}$$), what is the area of the triangular region?
Give your answer as a fraction.
The number of points of intersection between an equilateral triangle and a square could be (such that none of the sides would be overlapping)?
Indicate all that is/are true.
The sequence $$a_{1},a_{2},a_{3}.....a_{n}$$....is defined by $$a_{1}=2$$, $$a_{2}$$=3, and $$a_{n}$$=$$(a_{n-1})(a_{n-2})$$ for all integers n greater than 2. What is the value of $$a_{8}$$?
Sample P: 0.8, 0.9, 0.9, 1.0

Sample Q: 1.0, 1.0, 1.0, 1.0

Sample R: 0.8, 0.8, 1.0, 1.0

Sample S: 0.7, 0.7, 0.9, 0.9

Sample T: 0.9, 1.0, 1.0, 1.1

Five samples of 4 washers each were taken from a production line. The inside diameter of each washer was recorded to the nearest 0.1 centimeter, as shown above. For which of the samples is the standard deviation of the measurements greater than the standard deviation of the measurements for sample P?

Indicate all such samples.
Five gift cards will be distributed among 10 people so that no person receives more than one gift card. The gift cards consist of one $100 gift card, one $50 gift card, one $25 gift card and two $10 gift cards. How many different distributions of the five gift cards among the 10 people are possible if the two $10 gift cards are considered to be identical?
From a group of 100 people including Alice and Bob, 40 people are to be randomly selected at the same time to win movie tickets. What is the probability that both Alice and Bob will be selected to win movie tickets?
Give your answer as a fraction.
Three coins-two 10-cent coins and one 5-cent coin--are to be flipped simultaneously. For each of the three coins, the probability that the coin will land heads up is $$\frac{1}{2}$$. What is the probability that the total value of the coins that will land heads up is 15 cents?
Give your answer as a decimal.


In the sum above, if X and Y each denote one of the digits from 0 to 9, inclusive, then X=?
For each value x in a list of values with mean m, the absolute deviation of x from the mean is defined as |x-m|.

A certain online course is offered once a month at a university. The number of people who register for the course each month is at least 5 and at most 30. For the past 6 months, the mean number of people who registered for the course per month was 20. For the numbers of people who registered for the course monthly for the past 6 months, which of the following values could be the sum of the absolute deviations from the mean?

Indicate all such values.
n=1234567891011.........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?

Quantity A

The number of odd integers between $$\sqrt{12}$$ and $$12^{2}$$

Quantity B

70
Let $$\frac{1}{3}$$+$$\frac{1}{5}$$+$$\frac{1}{7}$$+$$\frac{1}{9}$$+$$\frac{1}{11}$$=$$\frac{m}{(3)(5)(7)(9)(11)}$$, where m is a positive integer. What is the remainder when m is divided by 5?
If $$p$$ is an prime number greater than 5, and if 5 is a factor of $$p+p^{2}$$,which of the following might be the remainder when $$p$$ is divided by 5?

Indicate all such numbers.
The price of a stock increased by 10% from January to February, decreased by n% from February to March, and then increased by 25% from March to April. If the company`s stock increased by 5% from January to April in total, then what is the value of n?

Give your answer to the nearest 0.1.
The speed of light is $$3·10^{8}$$ meters per second, rounded to the nearest $$10^{8}$$ meters per second. A "light-hour" is the distance that light travels in an hour.



Quantity A

The number of kilometers in a light-hour

Quantity B

$$10^{10}$$


Tickets for a carnival are sold either individually or in packages of 10 tickets or 20 tickets at the costs shown in the table. A group of friends bought n tickets for the least possible total cost. A second group of friends bought more than n tickets for a total cost that was less than the first group`s total cost. Which of the following could be the value of n?

Indicate all such values.
y+5 > x

Quantity A

y+2

Quantity B

x-2
On her walk today, Emma walked along a straight path between the entrance to her house, H, and the entrance to library, L, passing a crosswalk sign, J, and then a crosswalk sign, K. First Emma walked from H to J and then turned around and walked back from J to H. Then she walked directly from H to L, stopping briefly at J and K on her way. The total distance that Emma walked from H to J and back from J to H was $$\frac{2}{9}$$ of the distance that she walked directly from H to K and $$\frac{1}{6}$$ of the distance that she walked directly from H to L. If Emma walked a total of 420 meters during her walk today. what was the distance, in meters, that she walked from K to L?
If x is an integer, then what is the least possible value of $$3^{x}$$ + $$3^{-x}$$ ?

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