Types of Numbers

A treasure chest contains 3,125 gold coins. Three pirates decide to split the gold coins equally among themselves. However, after dividing the coins, they discover there are some coins left over. They decide to bury the remainder. If the number of leftover coins is a prime number less than 20, how many coins does each pirate receive, and how many are buried?

• Each pirate receives 1042 coins, and 5 coins are buried.
• Each pirate receives 1041 coins, and 2 coins are buried.
• Each pirate receives 1040 coins, and 3 coins are buried.
• Each pirate receives 1043 coins, and 7 coins are buried.

A factory produces widgets in quantities represented by natural numbers each day over a week: 120, 130, 140, 150, 160, 170, and 180. Select all that could be the sum of the production quantities for any two days of the week.

• 250

• 270

• 310

• 340

• 360

A triangular park has side lengths given by three consecutive natural numbers. The sum of the two shorter sides equals the length of the longest side. This triangle is a valid geometric triangle.

• True
• False

A rectangle has a perimeter of 96 units, and the length of one side is a natural number. If the length of the longer side is 26 units, the length of the shorter side is ________.

A computer encrypts a secret code using a sequence of natural numbers. The encryption works by taking the sum of all two-digit natural numbers that are divisible by 3 or 5 but not by both. What is the sum of these numbers, and how can you verify your result using divisibility rules?

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Lila has three boxes of pencils. Each box contains 120 pencils. She distributes them equally among 15 classrooms. How many pencils does each classroom receive?

• 8
• 16
• 32
• 24

A school library has 784 books and decides to donate 15 books to each of the 32 classrooms. They also keep 160 books aside for a special event. Which of the following are correct about the library's actions?

• The library will have fewer than 200 books left after the donations and setting books aside for the event.

• The total number of books donated to the classrooms is a multiple of 5.

• The number of books left in the library is more than half of what they originally had.

• The library donated an odd number of books to each classroom.

Lina is organizing her book collection into stacks of 15 books each. If she has 245 books in total, she can create exactly 16 stacks without any books left over.

• True
• False

A bookstore had 3,248 books in stock. On a sale day, they sold 1,179 books. Later, they received a new shipment of 956 books. The total number of books now in stock is ________.

A ticket seller is distributing tickets for a concert. The prices of tickets are $25, $50, and $75. A total of 200 tickets were sold, generating $10,000 in revenue. How many tickets of each type were sold? Devise a method to find all possible solutions.

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