# SAT/ACT problem of the week, January 26, 2017 solution

Hint for process of elimination: Taking test values such as $a=3$ and $b=5$ and carefully using order of operations will help you eliminate most or all answers. If your own choice of values of $a$ and $b$ do not eliminate all choices, making a second choice (or in very extreme cases even a third choice) will finish off all remaining incorrect answers.

Another hint is, variables are never being multiplied with other variables, this eliminates choices D and E. Also, there is nothing in the original expression which can combine with and eliminate the number 2 from the expression. This eliminates choices A and C, leaving you with the correct answer, B.

Read on for a full solution.

# SAT/ACT problem of the week, January 26, 2017

Which of the following is equal to $5a + 3b -(5b -2)$?

1. $5a$ (check answer)
2. $5a - 2b +2$ (check answer)
3. $5a - 10b$ (check answer)
4. $5a - 15b^2 - 6b$ (check answer)
5. $8ab - 5b + 2$ (check answer)

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on February 1st. If you would like to learn how to enter fancy math formulas into this blog, visit the WordPress LaTeX tutorial page.

# SAT/ACT problem of the week, August 25, 2016 Solution

Hint for process of elimination: Since $y$ and $xy$ are both positive, $x$ is also positive. Therefore $y-x. This eliminates choice E, leaving you with four choices. Some awareness about how big or small the answer should be, for example noting that $x=8$, may help you eliminate choice D for being too big, and choice A for being too small.

Read on for a full solution

# SAT/ACT problem of the week, August 25, 2016

If $xy = 120$ and $y = 15$, then $y-x=$

Solutions, hints, and questions are welcomed. A full solution will be posted on the August 31st. 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, August 18, 2016 Solution

Hint for process of elimination: If we read carefully, we notice that the price of a single pair of shoes at the shoe store is $a$. The problem asks for the difference involving the cost of eight pairs of shoes at the shoe store. Therefore, the answer must have a term of $8a$. This eliminates choices A, C, and E.

You can now try to reason through choices B and D. Since you eliminated three choices, you are statistically likely to improve your score by not leaving the answer blank, so you have to choose either B or D.

Read on for a full solution.

# SAT problem of the week, August 18, 2014

A pair of shoes costs customers $a$ dollars at the shoe store. The shoe store pays $b$ dollars for a box of eight pairs of shoes wholesale. If the cost of eight pairs of shoes purchased wholesale is $c$ dollars less than the cost of eight pairs of shoes at the shoe store, which of the following equations must be true?

1. $a-8b+c=0$ (check answer)
2. $8a-b+c=0$ (check answer)
3. $a-b-c=0$ (check answer)
4. $8a-b-c=0$ (check answer)
5. $a+8b-c=0$ (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on August 24th. 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, January 26, 2015 solution

Hint for process of elimination: Taking test values such as $a=3$ and $b=5$ and carefully using order of operations will help you eliminate most or all answers. If your own choice of values of $a$ and $b$ do not eliminate all choices, making a second choice (or in very extreme cases even a third choice) will finish off all remaining incorrect answers.

Another hint is, variables are never being multiplied with other variables, this eliminates choices D and E. Also, there is nothing in the original expression which can combine with and eliminate the number 2 from the expression. This eliminates choices A and C, leaving you with the correct answer, B.

Read on for a full solution.

# SAT problem of the week, January 26, 2015

Which of the following is equal to $5a + 3b -(5b -2)$?

1. $5a$ (check answer)
2. $5a - 2b +2$ (check answer)
3. $5a - 10b$ (check answer)
4. $5a - 15b^2 - 6b$ (check answer)
5. $8ab - 5b + 2$ (check answer)

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on February 1st. If you would like to learn how to enter fancy math formulas into this blog, visit the WordPress LaTeX tutorial page.

# SAT problem of the week, August 25, 2014 Solution

Hint for process of elimination: Since $y$ and $xy$ are both positive, $x$ is also positive. Therefore $y-x. This eliminates choice E, leaving you with four choices. Some awareness about how big or small the answer should be, for example noting that $x=8$, may help you eliminate choice D for being too big, and choice A for being too small.

Read on for a full solution

If $xy = 120$ and $y = 15$, then $y-x=$