Tag Archives: Sets

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.

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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?

  1. 25% (check answer)
  2. 47% (check answer)
  3. 50% (check answer)
  4. 77% (check answer)
  5. 90% (check answer)

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.

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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?

  1. 4% (check answer)
  2. 5% (check answer)
  3. 10% (check answer)
  4. 40% (check answer)
  5. 96% (check answer)

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 problem of the week, December 29, 2014 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.

Continue reading

SAT problem of the week, December 29, 2014

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?

  1. 25% (check answer)
  2. 47% (check answer)
  3. 50% (check answer)
  4. 77% (check answer)
  5. 90% (check answer)

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 problem of the week, December 22, 2014 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.

Continue reading

SAT problem of the week, December 22, 2014

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

  1. 4% (check answer)
  2. 5% (check answer)
  3. 10% (check answer)
  4. 40% (check answer)
  5. 96% (check answer)

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.