Work for Naitik

The digits 2, 3, 4, and 5 can be used to form 24 different 4-digit numbers containing four distinct digits. What is the arithmetic mean of these 24 numbers? Express your answer as a decimal to the nearest tenth.

• 3988.5

• 3788.5

• 3888.5

• 6348.5

Chelsea has written an interesting four-digit number. Each digit is a prime number. The hundreds digit is the sum of the units and the tens digit. The thousands digit is two more than the hundreds digit and the units digit is greater than the tens digit. What number did Chelsea write?

Two standard dice are rolled. What is the probability that the sum of the two numbers rolled is not a prime number?

• 5/12

• 7/12

• 5/6

• 11/12

Leah writes the positive integers from 1 through 15, inclusive, in a row, in ascending order. What is the smallest number that Leah can cross off so that the sum of the numbers to the left of the crossed-off number is at least the sum of the numbers to the right of the crossed-off number?

• 9

• 10

• 11

• 12

Shane makes three pastries in 12 minutes. Tyasia makes four of the same pastries in 9 minutes. If they work together for 288 minutes, how many pastries will they make?

• 196

• 200

• 202

• 204

A right rectangular prism measures 5n inches x 6n inches x 4n inches. The volume of the prism is 3240 in³. What is the value of n?

• 2

• 3

• 4

• 5

If (5x - 7)² = ax² + bx + c, then what is a + b + c?

• 4

• 144

• 111

• 14

Among the 24 arrangements of the letters in the word TEAM, how many have either the letters A, T, and E in that order from left to right (not necessarily adjacent), or the letters T, E, A in that order from left to right (not necessarily adjacent)?

• 4

• 8

• 10

• 12

A palindrome is a positive integer that does not end in 0 and reads the same forward and backward. What is the least three-digit positive integer that is neither a palindrome nor the sum of two palindromes?

• 102

• 201

• 301

• 402

What is the sum of the positive integer factors of 2025?

• 2052

• 2751

• 3751

• 3851