Factors, multiples, prime and composite numbers Transitional Reasoning Download PDF

Questions

1. 1.

   A cybersecurity club designs an entry challenge where members must find the access code for a server rack. The code is a two-digit whole number strictly between 40 and 75 that has exactly six positive factors. If the code is not divisible by 3 and the sum of its distinct prime factors equals 15, which number is the access code?

   • A) 44
   • B) 50
   • C) 68
   • D) 52
2. 2.

   A school club is preparing gift bags for an event using 75 identical notebooks and 105 identical pens. All items must be completely distributed into identical gift bags such that each bag contains the same number of notebooks and the same number of pens. If the total number of gift bags is a composite number, how many total items (notebooks and pens combined) are in each gift bag?

   • A) 12
   • B) 15
   • C) 36
   • D) 60
3. 3.

   An art student is designing a rectangular mosaic using exactly 120 identical square tiles placed side by side without gaps or overlaps. To ensure the design meets specific framing guidelines, both the width and the length of the rectangle (measured in tile units) must be composite numbers strictly greater than 4. What is the difference, in tile units, between the maximum possible perimeter and the minimum possible perimeter of the rectangles that can be formed under these conditions?

   • A) 4
   • B) 14
   • C) 24
   • D) 8
4. 4.

   A school robotics team labels its storage bins with two-digit numbers based on specific code rules. A bin's number is a multiple of 6 that is strictly less than 50, has exactly 8 positive factors, and has digits whose sum is a prime number. Which of the following is the number on this storage bin?

   • A) 30
   • B) 24
   • C) 42
   • D) 12