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# SAT/ACT problem of the week, January 12, 2017 solution

Hint for process of elimination: This is considered a difficult problem to solve on the SAT directly, since the test makers don’t necessarily expect you to know logarithms. However, they do expect you to know the equation for percent growth, so you should have an equation to plug into. The equation is described below in the full solution.

Notice that the investment grows from \$10,000 to \$100,000, which is a tenfold increase in value of the investment. In this case, you might get a hint that the growth rate of the investment is pretty big. If the investment grows at a rate of 20% per year, then it takes less than 5 years for the value of the investment to double. That means it takes less than 15 years for the investment to double three times, which is a factor of $2^3 = 8$. To grow by a factor of 10, it really should not take more than 15 years, at the roughest estimate. This leaves choices A (5 years), B (10 years), and C (12.6 years). Clearly 5 years is too short. After all, an investment that grows at 20% per year cannot grow 1000% in five years. This leaves choice B and C, giving you a 50% chance of getting the answer right. Even if you can’t decide on which answer is correct at this point, you should still give an answer.

Read on for a full solution.

# SAT/ACT problem of the week, January 12, 2017

A \$10 thousand investment in a stock is expected to achieve a rate of return of 20% per year. At this rate, approximately how much time is expected to pass for the investment expected to be valued at \$100 thousand?

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on January 18th. 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, December 29, 2016 solution

Hint for process of elimination: The largest part of the student body population consists of girls. Therefore, the population of girls is greater than $\dfrac{1}{3}$, or 33.3%, of the total population. This at least eliminating choice A. But the ratio of girls to girls plus boys is $\dfrac{150\%}{150\%+100\%}=3/5$, or 60%. Therefore the population of girls is under 60%. That at least eliminates both D and E. Answer C is too nice for this particular complex situation, and is also meant to draw your eye since the number $50\%$ appears twice in the problem, so I lean towards B.

Read on for a full solution.

# SAT/ACT problem of the week, December 29, 2016

The Funny Clowns High School student body consists of human boys, human girls, and chimpanzees of undetermined gender. The number of girls is 50% more than the number of chimpanzees. The number of chimpanzees is 50% more than the number of boys. What percentage of the student body is girls?

Have a solution? Hint? Question? We’d love to hear from you. A full solution will be posted on January 4th. 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, December 22, 2016 solution

Hint for process of elimination: First, pay close attention to which set is contained in which set and their pairwise relative size. This can help you get a good estimate of what the answer to this question is, or possibly lead you to the exact answer. Second, draw a picture of this system. That might give you a visual representation of how large set A is compared to set C. Third, the answer choices range from a low of 4% to a high of 96%. This massive range in percent values is about as big as a range can or will get on an SAT. Enormous differences in sizes of the answer choices should allow you to eliminate some of them. Fourth, The answer should be lower than 20%, so use that to eliminate choices.

Read on for a full solution.

# SAT/ACT problem of the week, December 22, 2016

Set A is 20% of set B, and set B is 20% of set C. What percent of set C is set A?

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on December 30th. 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, December 01, 2016 solution

Hint for process of elimination: Whenever an SAT gives a question that is realistic, it attempts to make sure that the solution is realistic. Therefore, if you happen to know anything about New York City, use that.

Also, notice that the ratio of the population of NYC to the population of the rest of New York is $8:11$. That means that a bit less than half of all New Yorkers live in New York City. Therefore, you should expect the answer to be a little under $50\%$. That leaves one or maybe two choices.

Read on for a full solution.

# SAT/ACT problem of the week, December 01, 2016

The ratio of the population of New York City to the population of the rest of New york is $8:11$. What percentage of the population of New York lives in New York City?

1. $27.2\%$ (check answer)
2. $37.5\%$ (check answer)
3. $42.1\%$ (check answer)
4. $57.9\%$ (check answer)
5. $72.7\%$ (check answer)

Have a solution, hint or question? Share it with us! A full solution will be posted on December 7th. 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 12, 2015 solution

Hint for process of elimination: This is considered a difficult problem to solve on the SAT directly, since the test makers don’t necessarily expect you to know logarithms. However, they do expect you to know the equation for percent growth, so you should have an equation to plug into. The equation is described below in the full solution.

Notice that the investment grows from \$10,000 to \$100,000, which is a tenfold increase in value of the investment. In this case, you might get a hint that the growth rate of the investment is pretty big. If the investment grows at a rate of 20% per year, then it takes less than 5 years for the value of the investment to double. That means it takes less than 15 years for the investment to double three times, which is a factor of $2^3 = 8$. To grow by a factor of 10, it really should not take more than 15 years, at the roughest estimate. This leaves choices A (5 years), B (10 years), and C (12.6 years). Clearly 5 years is too short. After all, an investment that grows at 20% per year cannot grow 1000% in five years. This leaves choice B and C, giving you a 50% chance of getting the answer right. Even if you can’t decide on which answer is correct at this point, you should still give an answer.

Read on for a full solution.