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Passwords for a certain computer consist of 5 symbols typed on a computer keyboard. Each password consists of one @ symbol, two # symbols, and two $ symbols, typed in any order. For example, @#$$# and $#$#@ are two different passwords for the computer. What is the total number of different passwords for the computer?
$$a$$ = $$3^{11}$$+$$3^{16}$$+$$3^{19}$$+$$3^{23}$$)?

What is the units digit of $$a$$?

Quantity A

The number of positive factors of 97

Quantity B

The number of positive factors of 87

Quantity A

The number of unique prime factors of 27

Quantity B

The number of unique prime factors of 12
How many integer values of n satisfy the inequality | 3-n | ≤ 4 ?
$$x \geq 0$$

Quantity A

$$2^{x}$$+$$2^{x}$$+$$2^{x}$$+$$2^{x}$$

Quantity B

$$4^{x}$$+$$4^{x}$$
The length of the three sides of a triangle is 9, 12 and 16.

Quantity A

The angle opposite to the longest side of the triangle

Quantity B

90°

PQ=QR=QS

Quantity A

PS

Quantity B

RS
Of the people surveyed about the effectiveness of various treatments for insomnia, 65 percent reported that prescription drugs were effective and 48 percent reported that exercise was effective. If 22 percent of those surveyed reported that prescription drugs were effective but did not report that exercise was effective,what percent of those surveyed reported that exercise was effective but did not report that prescription drugs were effective?

_____%

The figure above shows a rectangle inscribed in a large circle. Inside the rectangle is a small circle of radius 2 that is tangent to two sides of the rectangle. If the length of the rectangle is twice its width, what is the area of the large circle?
A certain number of toys were packed into $$x$$ boxes so that each box contained the same number of toys, with no toys left unpacked. If $$3$$ fewer boxes had been used instead, then $$12$$ toys would have been packed in each box, with $$5$$ toys left unpacked. What is the value of $$x$$?


The figure above shows a normal distribution with mean $$m$$ and standard deviation $$d$$, including approximate percents of the distribution corresponding to the six regions shown.

A survey of 5,500 book readers found that the number of books read per year was approximately normally distributed with mean 19.0 and standard deviation 2.0. Which of the following is the best description of the numbers of books read per year by the 880 book readers who read the most books?
C and M have to take pictures together with five other people. C has to stand in one of the three positions in the middle, M has to stand besides C, while the other five people can stand as they want. In how many ways can they stand in total?
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 $$n$$?
$$0 \lt a \lt b \lt 1$$

$$c$$ and $$d$$ are positive integers such that $$c \lt d$$

Quantity A

$$a^{c-d}$$

Quantity B

$$b^{d-c}$$
In a certain sequence of numbers, the $$1^{st}$$ term is equal to 1 and each term after the $$1^{st}$$ term is equal to 12 times the square of the preceding term. If the $$5^{st}$$ term of the sequence is equal to $$12^{n}$$, what is the value of n?
If a two-digit number that has x as the tens digit and y as the units digit is multiplied by 5, then the value of the product is
If k, n and p are consecutive positive even integers and k < n < p, which of the following must be an integer?
$$n$$ is an integer such that $$111 \leq n \leq 114$$.

Quantity A

The remainder when $$n$$ is divided by $$31$$

Quantity B

$$16$$
R=$$3^{7}$$ $$5^{11}$$ $$7^{15}$$

W=$$2^{3}$$ $$5^{15}$$ $$7^{19}$$

What is the units digit of R-W?

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