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. $\frac{\left(k+m\right)}{3}+\frac{1}{33}=1$

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. $1+m^2$ is an odd integer.
2. $5m-2$ is an even integer.

In the table above, each entry will represent the frequent flyer miles awarded for flying one way between a pair of cities. As part of a promotion, the airline is awarding an additional 1000 frequent flyer miles for those flights that originate in City E. What is the least number of table entries that are needed to show the frequent flyer points awarded for flying between each city and each of the other five cities?

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.

If  and  represent the length and width, respectively, of a rectangle, then what is the perimeter?

(1)

(2)

If 20 percent of the students at a certain college take a writing class, what percent of the students at the college take a math class?

(1) 50 percent of the students who take a writing class also take a math class.

(2) 40 percent of the students who take a math class also take a writing class.

In the sequence  of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 4th term of ?

(1) The 5th term of  minus the 3rd term equals 8.

(2) The 5th term of  plus the 6th term equals 34.

In the sequence of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of ?

(1) The 5th term of plus the 6th term equals 26.

(2) The 6th term of minus the 4th term equals 10.

In the sequence of numbers, each term after the first two terms is the product of the two immediately preceding terms and no term is equal to 0. What is the 4th term of ?

(1) The 5th term of divided by the 3rd term equals 18.

(2) The 3rd term of multiplied by the 5th term equals 648.

On a certain day, each of students chose either pizza or chicken to eat and either milk or juice to drink for lunch. If one of these students is to be selected at random, is the probability less than that the student chose pizza and milk for lunch?

(1) Of the students, chose pizza.

(2) Of the students, chose milk.

A store received a shipment of coats. Each coat was either red or black, and there was at least one of each color coat. These coats have either buttons or a zipper. If one of these coats is to be selected at random, is the probability less than that a red coat with buttons is selected?

(1) Of the coats, are black.

(2) Of the coats, twice as many have a zipper than buttons.

Sasha flips a coin 4 times. What is the probability that she will flip exactly 2 heads and 2 tails?

A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have 1 boy and 3 girls?