Results of the Ungraded Discrete Math Quiz

• Question 1: What is 2¹⁰ ?
  • Answer: 1024
  • Success rate: 66%
  • Note: about 1/2 of the correct answers showed math, while this is really a value you should know without writing down math. Even counting on your fingers is ok :)
• Question 2: Complete this sequence of increasing data size units: KB, MB, GB, __
  • Answer: TB
  • Success rate: 93%
• Question 3: What is 2^x x 2^y$ when written as a power of 2?
  • Answer: 2^x+y
  • Success rate: 60%
  • Note: this is really a huge concern that 40% of students could not do this :(
• Question 4: What is 2^x / 2^y when written as a power of 2?
  • Answer: 2^x-y
  • Success rate: 63%
• Question 5: I have a basket with x eggs in it, and a bunch of 6-egg boxes to fill. I need z boxes to store all the eggs. Give an expression for z.
  • Answer: ceil(x/6)
  • Success rate: 67%
  • Note: I counted as correct the answer x/6, even though it’s missing the ceiling to round up. Otherwise, the success rate would be more like 20%.
• Question 6: I have a basket with x eggs in it, and a bunch of 6-egg boxes. I fill boxes one after another. The last box is not empty and not full, and contains 0 < z < 6 eggs. Give an expression for z.
  • Answer: x mod 6
  • Success rate: 22%
  • Note: it’s very odd that this is such a lower success rate than the above question, since the two are tied (that is, the quotient and the remainder of the integer division).
• Question 7: If I am working with positive integers in base 2, and I can use 3 digits, how many different numbers can I write?
  • Answer: 8
  • Success rate: 30%
  • Note: there are 3 digits, I have 2 choices for each digits, so there are 2³ = 8 different possible combinations.
• Question 8: If I am working with positive integers in base 7, and I can use 4 digits, how many different numbers can I write?
  • Answer: 7⁴
  • Success rate: 30%
• Question 9: What is the power of two that is the closest to integer 450?
  • Answer: 512
  • Success rate: 49%
• Question 10: I am working with positive integers in base 2. I must write 67 different numbers all with the same number of digits, and using as few digits as possible. How many digits should I use?
  • Answer: 7
  • Success rate: 17%
  • With n bits I can describe 2ⁿ different numbers. With 6 bits I could have 2⁶ = 64 different numbers, but that’s not enough. So I need 7 bits.