If x is a positive integer, is the value of $y-z$ at most twice the value of $3^x-5^x$ ?

1. $y=3^{x+\mathrm{<font\; color="\#FE8080">1</font>}}$ and $z=5^{x+\mathrm{<font\; color="\#FE8080">1</font>}}$
2. $x=5$

The profits of a new company were x percent higher in the second year than the first year and y percent lower in the third year than the second year. Were the profits higher in the third year than the first year?

1. $\mathrm{<font\; color="\#FE8080">1</font>}-x<\mathrm{<font\; color="\#FE8080">1</font>}-y$
2. $\frac{xy}{100}<x-y$

At a company's awards ceremony, $\frac{3}{5}$ of the attendees were company employees and the remaining attendees were staff hired for the event. If $\frac{\mathrm{<font\; color="\#FE8080">1</font>}}{5}$ of the employees were managers, what was the number of employees who were not managers?

1. There were 125 attendees.
2. There were 50 staff hired for the event.

In a lecture hall, what is the ratio of the number of women to the number of men?

(1) There are twice as many women as men in the lecture hall.

(2) The number of men is  of the number of men and women in the lecture hall.

In each of two rows, a series of statues is ordered by height. On the bottom row, the shortest statue is 14.1 centimeters tall. On the top row, the tallest statue is 14.01 centimeters tall. What is the median height out of all the statues in both rows?

1. There are 14 statues in the lower row.
2. There are 15 statues in the upper row.

If e, f, g, and h are positive numbers, and $f\ne h$, is $\frac{e}{f}<\frac{g}{h}$?

1. $\frac{e-g}{h-f}$ is negative.
2. $fg{\left(\frac{eh}{fg}\right)}^2<eh$

What is the value of $\left|w\right|$?

1. $w^2=16$
2. $w=-\left|w\right|$

Each week Paige deposits $100 plus 10 percent of her weekly earnings over $1,000 into a savings account. What is the total amount Paige saved last week?

1. The total amount Paige saved last week was equal to 10 percent of the amount she earned last week.
2. Paige's earnings last week totaled $2,000.

How many integers are there between integers i and k, inclusive?

1. $k-i=22$
2. There are 21 integers between, but not including, $i+\mathrm{<font\; color="\#FE8080">1</font>}$ and $k+\mathrm{<font\; color="\#FE8080">1</font>}$.

Pete has taken 10 tests for a particular class. If his lowest score is 80, is the average (arithmetic mean) score of the 10 tests greater than 90?

(1) The average (arithmetic mean) of his seven highest test scores is 95.

(2) The average (arithmetic mean) of his four lowest test scores is 85.

Penelope has coins worth either $0.10 or $0.50. If she has more than five $0.50 coins, how many coins does she have?

1. Penelope has fewer than 10 coins worth $0.10 each.
2. The total value of Penelope's coins is $4.70.

If the tick marks shown on the line above are equally spaced, what is the value of m?

1. $k=\frac{13}{11}$
2. $\frac{\left(k+m\right)}{3}+\frac{\mathrm{<font\; color="\#FE8080">1</font>}}{33}=\mathrm{<font\; color="\#FE8080">1</font>}$

What is the cube root of z?

1. The 5th root of z is 243.
2. The 25th root of z is 3.

Last year, if a company spent a total of $1,200,000 on marketing, salaries, and administrative costs, how much did it spend on salaries?

1. Last year, the total amount that the company spent on salaries and administrative costs was 50 percent of the amount that it spent on marketing.
2. Last year, the amount that the company spent on salaries was 25 percent of the total amount it spent on marketing and administrative costs.

Pat invested $4,000 at a percent simple annual interest and a different amount at p percent simple annual interest for the same period of time. What amount did Pat invest at p percent simple annual interest?

1. The total amount of interest earned by Pat's investments in one year was $400.
2. Pat invested the $4,000 at 4 percent simple annual interest.

If m is an integer, is m odd?

1. $\mathrm{<font\; color="\#FE8080">1</font>}+m^2$ is an odd integer.
2. $5m-2$ is an even integer.

Three programmers , , and working simultaneously and independently at their respective constant rates, can write 10,000 lines of code in 3 hours. How long does it take Programmer , working alone at a constant rate, to write all lines of the code?

(1) Programmers and , working simultaneously and independently at their respective constant rates, can write all lines of the code in 4 hours.

(2) Programmers and , working simultaneously and independently at their respective constant rates, can write all lines of the code in 6 hours.

What is the value of ?

(1)

(2)

A cyclist rides a bike at a constant speed of 15 kilometers per hour. If the cyclist completes one lap around a city park, is that distance less than 800 meters? (1 kilometer = 1,000 meters)

(1) It takes the cyclist more than 2.5 minutes to complete one lap.

(2) It takes the cyclist less than 3 minutes to complete one lap.

If the set consists of six consecutive positive integers, what is the sum of these six integers?

(1) The integer 15 is in , but 14 is not in .

(2) The sum of the even integers in is 54.