Which of the following is equal to the value of \(2^5+ 2^5 + 3^5 + 3^5 + 3^5?\)

Each of 10 machines works at the same constant rate doing a certain job.  The amount of time needed by the 10 machines, working together, to complete the job is 16 hours.  How many hours would be needed if only 8 of the machines, working together, were used to complete the job?

The sequence \(a_1, a_2, a_3, . . . , a_n\) of n integers is such that \(a_k = k\) if k is odd and \(a_k = -a_{k – 1}\) if k is even. Is the sum of the terms in the sequence positive?

(1) n is odd.

(2) \(a_n\) is positive.

If x is an integer, is (\(x^2\) + 1)(x + 5) an even number?

(1) x is an odd number.

(2) Each prime factor of \(x^2\) is greater than 7.

A boat traveled upstream a distance of 90 miles at an average speed of (v – 3) miles per hour and then traveled the same distance downstream at an average speed of (v + 3) miles per hour.  If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet.  Which of the following gives the maximum number of different stocks that can be designated with these codes?

If the speed of x meters per second is equivalent to the speed of y kilometers per hour, what is y in terms of x ?

(1 kilometer = 1,000 meters)

At a certain company, the average (arithmetic mean) number of years of experience is 9.8 years for the male employees and 9.1 years for the female employees. What is the ratio of the number of the company’s male employees to the number of the company’s female employees?

(1) There are 52 male employees at the company.

(2) The average number of years of experience for the company’s male and female employees combined is 9.3 years.

If 0 < x < y, what is the value of \((x+y)^2\)/\((x-y)^2\)?

(1) \(x^2 + y^2\) = 3xy

(2) xy = 3

A 4-person task force is to be formed from the 4 men and 3 women who work in Company G’s human resources department.  If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

The points A, B, C, and D are on a number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D ?

(1) The distance between C and A is the same as the distance between C and B.

(2) A is to the left of D on the number line.

An integer greater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?

(1) The tens digit of n is a factor of the units digit of n.

(2) The tens digit of n is 2.

 If \((5^{21})(4^{11}) = 2(10^n)\) what is the value of n?

The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of k?

(1) \(3^2\) is a factor of k.

(2) \(7^2\) is not a factor of k.

If n is a positive integer and r is the remainder when 4 + 7n is divided by 3, what is the value of r ?

(1) n + 1 is divisible by 3.

(2) n > 20

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present.  If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

On the number line, if the number k is to the left of the number t, is the product kt to the right of t ?

(1) t < 0

(2) k < 1

Is (x+1)/(x-3)<0?

(1) -1 < x < 1

(2) \(x^2\) – 4 < 0

Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees.  If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?

If d is the standard deviation of x, y, and z, what is the standard deviation of x + 5, y + 5, and z + 5 ?