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The number 50 can be expressed as the sum of different prime numbers; for example, as a sum of four different prime numbers: 3+7+17+23=50.

Quantity A

The least possible number of different prime numbers whose sum is 50

Quantity B

$$3$$
If $$x$$, $$y$$, and z are integers greater than $$1$$ and $$xyz=231$$, what is the value of $$x+y+z$$?
What is the product of the distinct positive prime factors of 52?
If $$b$$ and $$p$$ are positive integers and $$b$$ is a prime number such that $$(b^4)(2^p)=2,592$$, what is the value of $$b+p$$?
If $$x$$ is the product of all the different prime factors of 60, then $$x=$$?


The table above shows the values of one share of stock for companies $$A B$$, and c at the close of the stock market yesterday, where $$x$$ is in dollars and $$x > 2$$. Which of the following statements individually provide(s) sufficient additional information to determine the value of $$x$$? Indicate all such statements.
There are $$10$$ packages of candy on a shelf, $$4$$ that are filled with blue candies and 6 that are filled with red candies. If $$3$$ packages are to be chosen at random from the shelf without replacement, what is the probability that at least one of the $$3$$ packages will be filled with blue candies?
A student is to be selected at random from a certain class. The probability that the student will be a female is $$p$$, the probability that the student will be under the age of $$19$$ is $$r$$, and the probability that the student will be a female and under the age of $$19$$ is $$0.3$$. Which of the following could be the values of $$p$$ and $$r$$? Indicate all such values.

Quantity A

The number of integers between 10 and 100 whose least positive prime factor is 7

Quantity B

$$3$$
If an accurate 12-hour clock shows exactly 4 o'clock at a certain time, what time will the clock show exactly 1,195 hours later?
x and y are two consecutive positive odd integers.

Quantity A

The remainder when $$x^2+y^2$$ is divided by $$4$$

Quantity B

$$2$$
The reciprocal of $$x+5$$ is $$x-5$$, and $$x > 0$$.

Quantity A

$$x$$

Quantity B

$$5$$
The number of feet in the perimeter of a rectangular game board is equal to the number of square feet in the area of the game board.

Quantity A

The width of the game board

Quantity B

2 feet
A game involves $$52$$ playing chips, which are either blue, red, or white. The number of blue chips is $$\frac{1}{2}$$ the number of red chips, and the number of white chips is $$\frac{2}{3}$$ the number of red chips. Which of the following statements are true? Indicate all such statements.
Actual non-work-related expenditures in the three categories of entertainment/restaurants, groceries, and clothing include a sales tax of $$5$$ percent of the cost of the items in these categories. Of the following, which is the closest approximation to the total of the before-tax costs of the items in these three categories?
If $$23.75$$ percent of actual work-related expenditures for lunch and snacks was for soft drinks, what percent of total actual work-related expenditures was for soft drinks?
For how many of the $$14$$ categories shown did actual expenditures differ from budgeted expenditures by more than $$20$$ percent of budgeted expenditures?

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