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

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

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.

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

Hints for problem of elimination: You might get an intuitive feeling that 1 and 3 are too small, leaving you with three choices. Even if you don’t know the full answer, you must guess at this point.

Read on for a full solution.

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

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

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

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

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

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

Read on for a full solution.

# SAT problem of the week, September 29, 2014

If $z$ is an odd integer, which of the following is an even integer?

1. $z+2$ (check answer)
2. $z-2$ (check answer)
3. $z^2 - 3z$ (check answer)
4. $(z+2)(z-2)$ (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

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.

# SAT problem of the week, October 20, 2014

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 solution

Hints for problem of elimination: You might get an intuitive feeling that 1 and 3 are too small, leaving you with three choices. Even if you don’t know the full answer, you must guess at this point.

Read on for a full solution.

An integer $x$ has $n$ zeros at the end if and only if it is divisible by $10^n$. For example, 12,500,000 is divisible by $10^5$ but not by $10^6$.
How many zeros are at the end of $1 \times 2 \times 3 \times \cdots \times 100$?