GRE考满分·题库

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A stone was dropped into a still pond and produced concentric circular ripples on the surface of the water. The radius of the outermost ripple increased at a constant rate of x feet per second. If the area of the circular region enclosed by the outermost ripple was 400π square feet 10 seconds after the stone hit the water, what is the value of x?
S={1, 3, 5, 7,.............,397, 399}

Set S consists of the odd numbers from 1 to 399, inclusive. How many different ordered pairs (p, t) can be formed, where p and t are numbers in S and p < t? (Note: The sum of the integers from 1 to n, inclusive, is given by the formula $$\frac{n(n+1)}{2}$$ for all positive integers n.)
$$d$$ is the greatest common divisor of 36 and 60, $$m$$ is the least common multiple of 36 and 60.

Quantity A

$$\frac{36}{d}$$

Quantity B

$$\frac{m}{60}$$
If a=$$(-\frac{1}{37})^{12}$$, which of the following equals to $$37^{-12}$$?
If a set S has a total of 6 subsets that consist of 2 members each, then S consists of how many members?
Dr. Mosher call the roll ten days in a row. If Candy attended 8 times, Sam attended 7 times, and Amy attended 6 times. If they show in class simultaneously in only one day, and at least 1 student attend each day`s course, how many days in which exactly two of them attended?
There are 5!, or 120, ways of arranging 5 different solid-colored flags side by side. If the colors of the flags are red, blue, yellow, green, and orange, how many of those arrangements have either the red flag or the blue flag in the middle position?
40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. In how many ways can these DVDs be arranged?

Quantity A

The number of tenths equal to 1.4

Quantity B

The number of hundredths equal to 1.3
Vladimir invested $10,000 for one year.He invested some of the amount at 4 percent simple annual interest and the rest of the amount at 6 percent simple annual interest.

If the total interest earned for the year was between $450 and $550, which of the following statements must be true?.

Indicate all such statements.
All of the 80 science students at a certain school are enrolled in at least one of three science courses: biology, chemistry, and physics. There are 60 students enrolled in biology, 50 students enrolled in chemistry, and 35 students enrolled in physics. None of the students are enrolled in all three courses. Which of the following could be the number of students enrolled in both chemistry and physics?
Indicate all such numbers.
Eugene and Penny started a job in sales on the same day. Eugene's sales for the first month were r dollars and each month after the first his sales for that month were twice his sales for the preceding month. Penny's sales for the first month were 10r dollars, and each month after the first her sales for that month were 10r dollars more than her sales for the preceding month. Which of the following statements are true?
Indicate all such statements.
A telephone system has $$n$$ telephone lines. For each of the $$n$$ lines, the event that the line will fail during a certain reliability test has probability 0.3, and these $$n$$ events are independent. If the probability that at least one of the n lines will not fail during the reliability test is greater than 0.99, what is the minimum value of $$n$$?
During each run of a computer simulation, either the letter X or the letter Y is displayed. For each run of the simulation, if the letter X is displayed, then the probability that X will be displayed in the next run is 0.3. Also for each run of the simulation, if the letter Y is displayed, then the probability that Y will be displayed in the next run is 0.4.

In 7 consecutive runs of the simulation, if X is displayed in the 5th run, what is the probability that X will be displayed in the 7th run?
n > 10,000

Quantity A

The thousands digit of $$\frac{n}{8}$$

Quantity B

7
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.
If x, y and z are consecutive positive integers and if x+y+z is even, how many of the four integers xy, yz, zx, and xyz are even?
X=1!+2!+3!+4!+5!+6!+7!+8!+9!+10!

What is the remainder when X is divided by 20?
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.

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