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# Tag Archives: Algebra

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

**Hint for process of elimination:** Taking test values such as $latex a=3 $ and $latex b=5 $ and carefully using order of operations will help you eliminate most or all answers. If your own choice of values of $latex a $ and $latex 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 $latex 5a + 3b -(5b -2) $?

- $latex 5a $ (check answer)
- $latex 5a – 2b +2 $ (check answer)
- $latex 5a – 10b $ (check answer)
- $latex 5a – 15b^2 – 6b $ (check answer)
- $latex 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 $latex y &s=1$ and $latex xy &s=1$ are both positive, $latex x &s=1$ is also positive. Therefore $latex y-x<y=15 &s=1$. This eliminates choice E, leaving you with four choices. Some awareness about how big or small the answer should be, for example noting that $latex x=8 &s=1$, 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 $latex xy = 120 &s=1$ and $latex y = 15 &s=1$, then $latex y-x= &s=1$

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 $latex a &s=1$. 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 $latex 8a &s=1$. 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 $latex a &s=1$ dollars at the shoe store. The shoe store pays $latex b &s=1$ dollars for a box of eight pairs of shoes wholesale. If the cost of eight pairs of shoes purchased wholesale is $latex c &s=1$ dollars less than the cost of eight pairs of shoes at the shoe store, which of the following equations must be true?

- $latex a-8b+c=0 &s=1$ (check answer)
- $latex 8a-b+c=0 &s=1$ (check answer)
- $latex a-b-c=0 &s=1$ (check answer)
- $latex 8a-b-c=0 &s=1$ (check answer)
- $latex a+8b-c=0 &s=1$ (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 $latex a=3 $ and $latex b=5 $ and carefully using order of operations will help you eliminate most or all answers. If your own choice of values of $latex a $ and $latex 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 $latex 5a + 3b -(5b -2) $?

- $latex 5a $ (check answer)
- $latex 5a – 2b +2 $ (check answer)
- $latex 5a – 10b $ (check answer)
- $latex 5a – 15b^2 – 6b $ (check answer)
- $latex 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 $latex y &s=1$ and $latex xy &s=1$ are both positive, $latex x &s=1$ is also positive. Therefore $latex y-x<y=15 &s=1$. This eliminates choice E, leaving you with four choices. Some awareness about how big or small the answer should be, for example noting that $latex x=8 &s=1$, may help you eliminate choice D for being too big, and choice A for being too small.

Read on for a full solution