All posts by Juan Rodriguez

SAT/ACT problem of the week, November 10, 2016

If Sophie can run 0.03 km in 0.12 minutes, in how many minutes can Sophie run 5 km?

  1. $latex 0.15 $ (check answer)
  2. $latex 20 $ (check answer)
  3. $latex 33 \frac{1}{3} $ (check answer)
  4. $latex 45 $ (check answer)
  5. $latex 360 $ (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on November 16th. 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, November 03, 2016

$latex f $ and $latex g $ are functions such that $latex f(6) = 5 $ and $latex g(6) = -3 $. What is the value of $latex f(g(6)) $?

  1. $latex -15 $ (check answer)
  2. $latex 2 $ (check answer)
  3. $latex 5 $ (check answer)
  4. $latex 12 $ (check answer)
  5. It cannot be determined from the information given. (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 16th. 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 27, 2016 solution

Hint for process of elimination: You need to know that “integers” are the positive and negative whole numbers, “nonnegative” means the numbers are not negative, and “distinct” means the list does not repeat any numbers. If the arithmetic mean of the five numbers is 7, then either all five numbers are 7, or at least one of the numbers is greater than 7. This helps you to eliminate two choices.

Another hint: They want to know the maximum value of the largest number is. The maximum value of the largest number occurs when the other four numbers are as small as possible. So instead of searching for the largest number, choose the other four numbers as small as possible, and use that to get the largest number, or at least an idea of how large the largest number could be.

Read on for a full solution.

Continue reading

SAT/ACT problem of the week, October 27, 2016

The product and average (arithmetic mean) of five distinct nonnegative integers are 0 and 7, respectively. What is the maximum value of the largest number?

  1. 5 (check answer)
  2. 7 (check answer)
  3. 19 (check answer)
  4. 29 (check answer)
  5. 35 (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on November 2nd. 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

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.

Continue reading

SAT/ACT problem of the week, October 13, 2016

A portion of the following sentence is underlined. Below the sentence are five ways of rewording the sentence by replacing the underlined material. If you feel the underlined word produces a more correct sentence than any other alternative, choose A.

As computers continue to advance at breakneck speeds, many computer scientists have asked whether it will become so advanced and replacing the need for humans to work.

  1. it will become so advanced and replacing (check answer)
  2. it will become so advanced, replacing (check answer)
  3. they will become so advanced that they will replace (check answer)
  4. they will become so advanced, they will replace (check answer)
  5. they will become so advanced, replace (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 19th.