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2021年GRE数学新170难题
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题目列表
题目内容
In the rectangular coordinate plane, how many points (x, y), where both x and y are integers, satisfy the equation $$x^{2}+y^{2}=5$$?
What is the units digit of ($$4^{32}$$ - $$3^{32}$$)?
Set A includes all the positive multiples of 6. Set B includes all the positive multiples of 8. how many integers from 1 to 100, inclusive, are included in both Set A and Set B?
The top surface of a certain 1-inch-thick oak board is 8 inches wide and has an area of 960 square inches. What is the price of this board? (1 foot=12 inches)
For the 6-inch-wide boards listed, which of the following is closest to the ratio of the price per linear foot of the least expensive type of board to the price per linear foot of the most expensive type of board?
The price of one maple board that is 8 inches wide and n feet long is $1.50 less than the price of 2 maple boards that are each 4 inches wide and n feet long. What is the value of n?
A set consists of all three-digit positive integers with the following properties. Each integer is of the form JKL, where J, K, and L are digits; all the digits are nonzero; and the two-digit integers JK and KL are each divisible by 9. How many integers are in the set?
Set D consists of the numbers of the form $$\frac{1}{2^{n}}$$ , where n is an integer from 1 to 10. What is the hundredths digit in the decimal representation of the product of 8,000 and the sum of the numbers in D?
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?
A campaign director can divide the campaign workers into 10 or 11 teams. When the workers are divided into 11 teams, each of 10 of the teams has x workers and 1 team has 6 workers. When the workers are divided into 10 teams, each of 9 of the teams has x+1 workers and 1 team has 5 workers. How many campaign workers are there?
During archery practice, Kyle made 50 attempts to hit a target. After each attempt, his success rate was calculated as the number of successful attempts to hit the target as a percent of the number of attempts up to that time. After the 20th attempt, his success rate was 45 percent. After the 40th attempt, his success rate was 55 percent. Which of the following statements must be true?
Indicate all such statements.
The odds against the occurrence of an event are defined to be the ratio of the probability that the event will not occur to the probability that the event will occur. An integer is to be selected at random from the set of integers from k to n, where k < n. The odds against the event that the integer selected will be an even integer are 1 to 0.95. Which of the following could be the integers k and n, respectively?
For what value of x does the standard deviation of the numbers in the list x, 6, 14, and 16 have the least value?
When a certain stock exchange closed on Tuesdays, $$\frac{1}{5}$$ of the stocks closed at the same price as on the pretious day. Of the remaining stocks, 3 stocks closed at a higher price for every 4 stocks that closed at a lower price. What fraction of all the stocks on this exchange closed at a higher price than on the previous day?
As aresult of a chemical reaction between compounds A and B. 1/4 of each compound was transformed into an equal amount of the other compound, while the remaining 3/4 of each compound was not transformed. If the amount of B was initially 4 times the amount of A. what was the ratio of the amount of A to the amount of B after the reaction?
Suppose a, b, c are different integers, and the repeating decimal $$0.\overline{abc}$$=$$\frac{m}{n}$$, where 0 < m < n < 100 and both m and n are positive integers, then
Quantity A
n
Quantity B
39
If c < b < a < 0, which of the following is equal to |a-b-c|-|b+c|?
All the chairs in a certain cargo have the same weight, and all the tables in the cargo have the same weight. There are 6 times as many chairs as there are tables. The weight of each table is 9 times the weight of each chair. If the total weight of the tables is 1,200 kilograms, then the total combined weight of the chairs and tables is how many kilograms?
For a certain type of can, the number of grams of aluminum per can decreased by 20 percent from 1994 to 1998, while the cost per gram of aluminum decreased by 60 percent. If the cost of the aluminum in y cans in 1994 was equal to the cost of aluminum in ky cans in 1998, then k=?
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