- D Since triangle ABC is inscribed in a semicircle, it must be a right triangle.
The area of the triangle is thus^12 × 10 × 24 = 120. Using the Pythagorean
Theorem, the diameter of the circle = AC = 26. The area of the circle is thus (π)
r^2 = (π)13^2 = (π)169. The area of the semicircle is thus 169π 2 = 84.5π. The area of
the shaded region = area of the semicircle − area of the triangle. This can be
expressed as 84.5π − 120. - E Plug the given values into the R × T = D formula. The rate is 2.6 million
feet per day and the distance is 10.2 million feet. Thus: 2.6 million × T =
10.2 million → T = 10.2 million2.6 million = approximately 4 days. Now, convert days to
seconds. 1 day = 24 hours = 60(24) minutes = 60(60)(24) seconds = 86,400
seconds. So, the number of seconds in 4 days is 86,400 × 4 = 345,600 seconds.
The closest answer is 350,000. - B The number of students majoring in Philosophy in 2015 was 1.11(1,000) =
1,110. The number of students majoring in Philosophy in 2017 was thus
(.97)(1,110) = 1,076.7 or approximately 1,077. - A and B The easiest way to confirm each choice is to plug in numbers.
Choice A: Choose 1,000 for the number of Psychology majors in 2015.
The number of Psychology majors in 2017 was thus 1,000(.9)(1.1) = 990.
Choice A is correct.
Choice B: Choose 1,000 for the number of Mathematics majors in 2015.
The number of Mathematics majors in 2017 was thus 1,000(1.06)(1.11) =
1,176. The change was 176. 176 is more than 17% of 1,000, Thus, choice B
is correct.
Choice C: We have no values for any of the majors, so we cannot infer any
relationships about the number of students in each major. - 117% Choose values. Let the number of English majors in 2015 = 1,000. The
number of biology majors in 2015 was thus 2,000. The number of Biology
majors in 2017 was thus (2,000)(.88)(1.08) = 1,900.8. The number of English
majors in 2017 was (1,000)(.97)(.9) = 873. Now, use the percent greater
formula: % greater = % of − 100%. Plug in the numbers: (1,900.8/873) × 100 −
100% = 117%. - 23 Plug in numbers: Let 1,200 = population of State X and 600 = population of
State Y. Let the population concentration of State X = 12, and the population
concentration of State Y = 4. The area of State X is thus populationarea = 1,200area
= 12 → area = 100. The area of State Y is thus populationarea = area^600 = 4 → area = 150.
The ratio of the area of State X to the area of State Y is thus^100150 =^23.
570 PART 5 ■ GRE PRACTICE TESTS05-GRE-Test-2018_463-582.indd 570 23/01/18 11:22 AM