Rates
Working alone, Alice can paint a room in 1 hour. Bob can paint the room in 2 hours alone. How many minutes will it take them to paint the room together?
40
How many ways are there for Coach Lewis to pick 4 of his basketball players out of his 10-player team?
210
The arithmetic mean of 9, 11, 13, x and 7 is 10. What is the value of x?
10
What is the 8th term of the sequence 3,7,11,...?
31
If ⚾ + ✈ = 14, and ⚾ − ✈ = 4, what is the value of ✈?
5
A recipe requires three cups of flour and two eggs to make eight servings of a cake. How many cups of flour are needed to make 20 servings of the same cake? Express your answer as a decimal to the nearest tenth.
7.5
How many ways are there to arrange the letters in the word REVIEW?
360
The combined number of chickens and cows on a farm is 100. There are a total of 260 feet on these animals. How many chickens are there?
70
Compute 812-792
320
Lolli’s Candy Store sells fruit-flavored candy rope, priced by length, at $4.00 per meter. At this rate, how much will it cost to buy 50 cm of candy rope?
$2.00
The ratio x:y is 4:5. The ratio of y:z is 7:15. What is the ratio of x:z?
28:75
Professor Pete has 5 lamps in a row. Each of his five lamps can be either red, green, or blue. If he randomly assigns a color to each lamp, what is the probability that no lamps are green?
32/243
A bag contains 4 blue, 5 green and 3 red marbles. How many green marbles must be added to the bag so that 75 percent of the marbles are green?
16
What is the sum of the first 15 positive odd integers?
225
A price is reduced by 10% and then increased by 10%. What percent of the original price is the new price?
99%
In Quaternion, the coin with the least value is the qua. Four quas equal one quab, four quabs equal one quac, four quacs equal one quad, four quads equal one quae and four quaes equal one quaf. What is the least number of coins that have a combined value of 2012 quas?
11
A six-sided die is weighted so that the probabilities of rolling a 1, 2, 3 or 4 are equal. The probabilities of rolling a 5 or 6 also are equal to each other. With this die, Kia is three times more likely to roll a 6 than a 2. What is the probability that she will roll a 4? Express your answer as a common fraction.
1/10
Three employees split a bonus valued at some number of dollars. Arman first receives $10 more than one third of the total amount. Bernardo then receives $3 more than one half of what was left. Carson receives the remaining $25. What is the total dollar value of the bonus?
99
The first three terms of an arithmetic sequence are p, 2p + 6 and 5p – 12. What is the 4th term of this sequence?
66
The digits of a 3-digit integer are reversed to form a new integer of greater value. The product of this new integer and the original integer is 91,567. What is the new integer?
721
A train traveling at 45 miles per hour enters a tunnel that is 1 mile long. The length of the train is 1/8 mile. How many minutes after the front of the train enters the tunnel does the back of the train exit the tunnel? Express your answer as a decimal to the nearest tenth.
1.5
Tiles numbered 1-6 are each placed randomly into one of three different boxes. What is the probability that each box contains 2 tiles? Express your answer as a common fraction.
10/81
A flower bouquet contains pink roses, red roses, pink carnations, and red carnations. One third of the pink flowers are roses, three fourths of the red flowers are carnations, and six tenths of the flowers are pink. What percent of the flowers are carnations?
70
Ana has $100,000 in her savings account. The first month she withdraws 100 dollars. Each month she withdraws 100 dollars more than the previous month. How much money will she have at the end of 37 months?
$27,700
Starting at 9:00 p.m., Joe watches three films consecutively, with no breaks in between. The first film is the same length as the third film, and the second film is 50% longer than each of the other two films. If Joe finishes the third film at 2:15 a.m., how many minutes long is the second film?
135