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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?
The standard deviation of $$n$$ numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean $$\overline{x}$$ is equal to $$\sqrt{\frac{s}{n}}$$, where $$S$$ is the sum of the squared differences $$(x_{i} - \overline{x})^{2}$$ for 1 ≤ i ≤ n.

For what value of $$x$$ is the standard deviation of the numbers $$6$$, $$14$$, $$16$$, and $$x$$ least?
When a certain stock exchange closed on Tuesdays, $$\frac{1}{5}$$ of the stocks closed at the same price as on the previous 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 a result of a chemical reaction between compounds A and B. $$\frac{1}{4}$$ of each compound was transformed into an equal amount of the other compound, while the remaining $$\frac{3}{4}$$ 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 $$k$$=?
When $$(5n+1)$$ is divided by $$3$$ and $$4$$, the remainder is $$2$$ and $$1$$, respectively.

Quantity A

$$n$$

Quantity B

$$3$$
Consider all the permutations of the letters in the word $$MISSISSIPPI$$, where $$I$$ is a vowel and the other letters are consonants.

Quantity A

The number of permutations in which all the vowels are next to each other

Quantity B

The number of permutations in which all the consonants are next to each other
Two balls are to be randomly selected from a bag, one at a time and without replacement. The probability that the first ball selected will be red is $$\frac{5}{8}$$. If the first ball selected is not red, the probability that the second ball selected will be red is $$\frac{2}{3}$$. What is the probability that the first or the second ball selected will be red (that is, one red ball either in the first attempt, or in the second attempt, but not both)?

Give your answer as a $$\underline{fraction}$$.


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?
One cup of a certain type of yogurt contains 9 grams of protein, which is equal to x percent of the recommended daily consumption of protein. How many grams is the recommended daily consumption of protein in terms of x?
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?
List S: 21, 22, 23, 25, 27, 32

List T: 221, 222, 223, 225, 227, 232

If the standard deviation of the numbers in list S is x, what is the standard deviation of the numbers in list T?
0 < a < b < c

a, b, and c are positive integers and the average (arithmetic mean) of a and c is 15. Which of the following could be the value of b?

Indicate all such values.
Rhonda has 2 different jackets, 3 different skirts, 2 different blouses, and 4 different scarfs that can be worn as part of an outfit. If an outfit consists of a jacket, a skirt, and a blouse with or without a scarf, how many different outfits can Rhonda wear?
If P is the product of all of the 100 different numbers of the form $$\frac{m+1}{m}$$, where m is an integer and 1 ≤ m ≤ 100, which of the following statements about P is true?

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