Tag Archives: Number Theory

SAT/ACT problem of the week, October 20, 2016

Problem of the Week, , , , , ,

There are 15 classrooms in Sunny Skies High School, numbered 1 through 15. Between classrooms 1 through 10, there are 250 math textbooks. Between classrooms 6 through 15 there are 300 math textbooks. Which of the following could be the total number of math textbooks in classrooms 1 through 15?

  1. 400
  2. 500
  3. 600
  1. I only (check answer)
  2. II only (check answer)
  3. I and II only (check answer)
  4. II and III only (check answer)
  5. I, II, and III (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 26th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.

SAT/ACT problem of the week, October 20, 2016 solution

Problem of the Week, , , , , ,

Hint for process of elimination: Draw a fast picture of the rooms and try to distribute the books in a way that gives you a total of 400, 500, and 600 books. You may quickly realize that there cannot be a total 600 books in these classrooms, and you may also gain enough intuition about this situation to solve the problem.

Read on for a full solution.

Continue reading →

SAT/ACT problem of the week, October 06, 2016

Problem of the Week, , , , ,

An integer $latex x $ has $latex n $ zeros at the end if and only if it is divisible by $latex 10^n $. For example, 12,500,000 is divisible by $latex 10^5 $ but not by $latex 10^6 $.

How many zeros are at the end of $latex 1 \times 2 \times 3 \times \cdots \times 100$?

  1. 1 (check answer)
  2. 3 (check answer)
  3. 10 (check answer)
  4. 20 (check answer)
  5. 24 (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 12th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.

SAT/ACT problem of the week, September 29, 2016 solution

Problem of the Week, , , ,

Hint for process of elimination: Though this problem has a “None of the above” option, choosing a random value for $latex z &s=1$ satisfying the simple conditions that $latex z &s=1$ is odd, such as $latex z=3 &s=1$, would immediately eliminate three of the choices because the answers are odd.

A second benefit of choosing a random value of $latex z &s=1$ is that the process may increase your intuition of what the answer should be.

Read on for a full solution.

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SAT problem of the week, September 29, 2014

Problem of the Week, , , ,

If $latex z &s=1$ is an odd integer, which of the following is an even integer?

  1. $latex z+2 &s=1$ (check answer)
  2. $latex z-2 &s=1$ (check answer)
  3. $latex z^2 – 3z &s=1$ (check answer)
  4. $latex (z+2)(z-2) &s=1$ (check answer)
  5. None of the above (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 5th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.

SAT problem of the week, October 20, 2014 solution

Problem of the Week, , , , ,

Hint for process of elimination: Draw a fast picture of the rooms and try to distribute the books in a way that gives you a total of 400, 500, and 600 books. You may quickly realize that there cannot be a total 600 books in these classrooms, and you may also gain enough intuition about this situation to solve the problem.

Read on for a full solution.

Continue reading →

SAT problem of the week, October 20, 2014

Problem of the Week, , , , ,

There are 15 classrooms in Sunny Skies High School, numbered 1 through 15. Between classrooms 1 through 10, there are 250 math textbooks. Between classrooms 6 through 15 there are 300 math textbooks. Which of the following could be the total number of math textbooks in classrooms 1 through 15?

  1. 400
  2. 500
  3. 600
  1. I only (check answer)
  2. II only (check answer)
  3. I and II only (check answer)
  4. II and III only (check answer)
  5. I, II, and III (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 26th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.

SAT problem of the week, October 06, 2014

Problem of the Week, , , ,

An integer $latex x $ has $latex n $ zeros at the end if and only if it is divisible by $latex 10^n $. For example, 12,500,000 is divisible by $latex 10^5 $ but not by $latex 10^6 $.

How many zeros are at the end of $latex 1 \times 2 \times 3 \times \cdots \times 100$?

  1. 1 (check answer)
  2. 3 (check answer)
  3. 10 (check answer)
  4. 20 (check answer)
  5. 24 (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 12th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.