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题目内容
A caterer has 20 liters of fruit punch that is 12 percent grape juice, by volume. How many liters of fruit punch that is 20 percent grape juice, by volume, must be added to the original 20 liters of fruit punch in order to create fruit punch that is 15 percent grape juice, by volume?
Every positive integer can be represented uniquely in base $$11$$ by

$$(a_n......a_2 a_1 a_0)_{11}$$= $$a_n(11^{n})+......a_2(11^{2})+a_1(11^{1})+a_0(11^{0})$$

for some nonnegative integer $$n$$. In the expression, the coefficient $$a_i$$ of $$11^i$$ is one of the digits from 0 to 9 or A, which represents 10, for $$0 ≤ i ≤ n$$, but $$a_n≠ 0$$. For example, $$(4A5)_{11}=599$$ because

$$(4A5)_{11}= 4(11^2)+10(11^1)+5(11^0)$$.

What is the value of $$(8,423)_{11}- (6,682)_{11}$$?

Quantity A

The expected value of X

Quantity B

The expected value of Y
A survey of voters who were either supporters of Candidate A or supporters of Candidate B showed that 64 percent of the supporters of Candidate A and 50 percent of the supporters of Candidate B were in favor of a progressive income tax.

Quantity A

The percent of the voters surveyed who were in favor of a progressive

Quantity B

57%
The average (arithmetic mean) weight of the packages in a certain shipment of 30 packages is 6.0 pounds. If 10 additional packages are added to the shipment, the average weight of the packages in the 40-package shipment will be between 0.5 pound and 1.2 pounds less than the average weight of the packages in the original shipment of 30 packages. Which of the following values could be the average weight, in pounds, of the 10 additional packages?

Indicate all such values.


ABCD is a rectangle.

x > 3

Quantity A

The perimeter of rectangle ABCD

Quantity B

6x-8

Quantity A

x

Quantity B

35
$$5k < 35 < 7k$$

Quantity A

k

Quantity B

4

Quantity A

$$(-5)^{94}$$

Quantity B

$$(-7)^{95}$$

Quantity A

$$3^{120}$$

Quantity B

$$6^{60}$$
The average (arithmetic mean) of 5 consecutive even integers is 20.

Quantity A

The least of the 5 integers

Quantity B

16
A sequence of numbers $$p_1, p_2, p_3, .........., p_n,.........$$. is generated by the rules $$p_1=1$$ and $$p_n= 24p_{n-1}+8$$ for each integer $$n ≥ 2$$.

Quantity A

The remainder when $$p_{66}$$ is divided by 6

Quantity B

4
Set $$S$$ is the set of all numbers of the form $$\frac{1}{n(n+1)}$$, where n is a positive integer less than 4.

Quantity A

The sum of all the numbers in $$S$$

Quantity B

$$\frac{2}{3}$$
A certain type of code is a list of 4 identical asterisks and 2 identical dots in any order. For example, **•*•* is one such code.

Quantity A

The number of possible codes of this type

Quantity B

15
Each person who attended a seminar on politics was either a Democrat, a Republican, or an independent. If a person had been selected randomly from those attending the seminar, the probability would have been 0.52 of selecting a Republican and 0.35 of selecting a Democrat. What was the ratio of the number of independents to the number of Republicans at the seminar?
List K: 0, 2, 3, 5, 10

List M: 1, 6, 8, 9, 11

Quantity A

The standard deviation of the numbers in list K

Quantity B

The standard deviation of the numbers in list M
A number is to be selected from the set {1, 3, 5, 7, 9}, and a number is to be selected from the set {2, 4, 6, 8, 10}. P is the product of the two numbers selected.

Quantity A

The number of different possible values of P

Quantity B

25

Quantity A

The area of the region enclosed by the polygon

Quantity B

$$42x$$
-4 < $$x$$ < 2 and -2 < $$x$$ < 4

Quantity A

$$|x|$$

Quantity B

2
A tour group in an art museum consisted of 40 people, some of whom were art students. Of the art students who were in the tour group, 5 were studying sculpting and the rest were studying painting.

Which of the following statements individually provide(s) sufficient additional information to determine the number of art students who were in the tour group?

Indicate all such statements.

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