Focus mode: every practice problem from the chapter, one after another.
Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have?
You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $1.02, with at least one coin of each type. How many dimes must you have?
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse?
Joe has a collection of 23 coins, consisting of 5-cent coins, 10-cent coins, and 25-cent coins. He has 3 more 10-cent coins than 5-cent coins, and the total value of his collection is 320 cents. How many more 25-cent coins does Joe have than 5-cent coins?
Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she could have made on the third test?
Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and 100, inclusive. Laila received the same score on the first four tests, and she received a higher score on the last test. Her average score on the five tests was 82. How many values are possible for Laila's score on the last test?
Mr. Patrick teaches math to 15 students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was 80. After he graded Payton's test, the test average became 81. What was Payton's score on the test?
Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?
(A) 76531 (B) 86724 (C) 87431 (D) 96240 (E) 97403
Laura added two three-digit positive integers. All six digits in these numbers are different. Laura's sum is a three-digit number . What is the smallest possible value for the sum of the digits of ?
What is the largest power of 2 that is a divisor of ?
Students guess that Norb's age is 24, 28, 30, 32, 36, 38, 41, 44, 47, and 49. Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb?
Josh went to the store with a number of dollars between 50 and 100, both inclusive. He spent a third of his money on lunch. He then tipped 15 dollars. After that, he deposited two-thirds of his remaining money in his bank account. After that, he donated a fifth of his remaining money to charity. He was then left with an integer number of dollars. How many dollars did he have at the beginning?
In a tournament there are six teams that play each other twice. A team earns 3 points for a win, 1 point for a draw, and 0 points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?
Bryan chooses a number between 1 and 1000. He gives a few conditions about the number:
Find the sum of all possible numbers Bryan could choose based on the conditions.
In eight games this season, Kelly's basketball team scored 22, 30, 33, 44, 50, 55, 61 and 66 points, respectively. They exactly tripled their opponent's score three times and exactly doubled their opponent's score three times. They lost two games by 4 points each. How many points did their opponents score altogether?
What fraction of the first 100 triangular numbers are evenly divisible by 7? Express your answer as a common fraction.
Find the arithmetic mean of all the three-digit palindromes. (Recall that a palindrome is a number that reads the same forward and backward, such as 777 or 383.)
The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of ?
A scientist walking through a forest recorded as integers the heights of 5 trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?
| Tree | Height |
|---|---|
| Tree 1 | ___ meters |
| Tree 2 | 11 meters |
| Tree 3 | ___ meters |
| Tree 4 | ___ meters |
| Tree 5 | ___ meters |
| Average height | ___.2 meters |
If C is a digit such that the product of the three-digit numbers 2C8 and 3C1 is the five-digit number 90C58, what is the value of C?
I am thinking of a number between 1000 and 9999, inclusive. It satisfies the following conditions
What number am I thinking of?