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21 Jun 2022, 01:30
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The area of a circle with radius \(a\) is less than the area of a square with sides of length \(ka\). Which of the following could be the value of k?
I. \(\frac{5}{3}\)
II. \(\frac{6}{3}\)
III. \(\frac{7}{3}\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
I. \(\frac{5}{3}\)
II. \(\frac{6}{3}\)
III. \(\frac{7}{3}\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
21 Jun 2022, 02:35
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pi*a^2 < (ka)^2
=> (pi - k^2)*a^2<0
Because a^2 is not negative,
pi - k^2 < 0
k^2 > pi
pi is approximately 3.14
I. (5/3)^2=25/9 < 3
II 2^2 = 4 > pi
III (7/3)^2 > 2^2 > pi
The answer is thus (D).
=> (pi - k^2)*a^2<0
Because a^2 is not negative,
pi - k^2 < 0
k^2 > pi
pi is approximately 3.14
I. (5/3)^2=25/9 < 3
II 2^2 = 4 > pi
III (7/3)^2 > 2^2 > pi
The answer is thus (D).
21 Jun 2022, 23:11
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Bunuel
The area of a circle with radius \(a\) is less than the area of a square with sides of length \(ka\). Which of the following could be the value of k?
I. \(\frac{5}{3}\)
II. \(\frac{6}{3}\)
III. \(\frac{7}{3}\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
I. \(\frac{5}{3}\)
II. \(\frac{6}{3}\)
III. \(\frac{7}{3}\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
\(\pi * a^2 < k^2 * a^2\)
\(k^2 > \pi \approx 3.14\)
I. \(k = \frac{5}{3}\); \(k^2 = \frac{25}{9} < 3 < 3.14\). Therefore, \(k \neq \frac{5}{3}\)
II. \(k = \frac{6}{3} = 2\); \(k^2 = 4 > 3.14\). Therefore, k could be \(\frac{6}{3}\).
III. \(k = \frac{7}{3}\); k could be \(\frac{7}{3}\) because \(\frac{7}{3} > \frac{6}{3}\).
Show SpoilerAnswer
D
