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31 Dec 2023, 08:59
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Which of the following has the greatest value?
A. \(400!*80!\)
B. \(480!\)
C. \(360!*120!\)
D. \((120!)^4\)
E. \((240!)^2\)
A. \(400!*80!\)
B. \(480!\)
C. \(360!*120!\)
D. \((120!)^4\)
E. \((240!)^2\)
31 Dec 2023, 08:59
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Official Solution:
Which of the following has the greatest value?
A. \(400!*80!\)
B. \(480!\)
C. \(360!*120!\)
D. \((120!)^4\)
E. \((240!)^2\)
Let's compare A and B:
\(480! = 400! * 401 * 402 * ... * 480\). Since \(401 * 402 * ... * 480\), the product of 80 numbers from 401 to 480, inclusive, is more than \(80!\), he product of 80 numbers from 1 to 80, inclusive, then B > A.
Similarly, we can conclude that B > C.
Option D, \(120!^4 = 120! * 120! * 120! * 120!\). While option B, \(480! = 120! * (121 * ... * 240) * (241 * ... * 360) * (361 * ... * 480)\). Obviously, B > D.
Similarly, we can conclude that B > E.
Therefore, among the options, B, \(480!\), has the greatest value.
Answer: B
Which of the following has the greatest value?
A. \(400!*80!\)
B. \(480!\)
C. \(360!*120!\)
D. \((120!)^4\)
E. \((240!)^2\)
Let's compare A and B:
\(480! = 400! * 401 * 402 * ... * 480\). Since \(401 * 402 * ... * 480\), the product of 80 numbers from 401 to 480, inclusive, is more than \(80!\), he product of 80 numbers from 1 to 80, inclusive, then B > A.
Similarly, we can conclude that B > C.
Option D, \(120!^4 = 120! * 120! * 120! * 120!\). While option B, \(480! = 120! * (121 * ... * 240) * (241 * ... * 360) * (361 * ... * 480)\). Obviously, B > D.
Similarly, we can conclude that B > E.
Therefore, among the options, B, \(480!\), has the greatest value.
Answer: B
03 Sep 2024, 05:32
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I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Adding "obviously" to a statement is not an explanation
