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18 Mar 2022, 02:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:31) correct
36%
(01:27)
wrong
based on 347
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If \(n! = n*(n - 1)*(n - 2)*...*1\), where n is a positive integer, which of the following is (are) true?
I. 26 is not a factor of 25!
II. 29 is a factor of 25!
III. 1,000,000 is a factor of 25!
A. None
B. III Only
C. I and II only
D. II and III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
I. 26 is not a factor of 25!
II. 29 is a factor of 25!
III. 1,000,000 is a factor of 25!
A. None
B. III Only
C. I and II only
D. II and III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
20 Mar 2022, 23:29
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If \(n! = n*(n - 1)*(n - 2)*...*1\), where n is a positive integer, which of the following is (are) true?
All prime numbers greater than n will not be factors of n!
I. 26 is not a factor of 25!.......26=2*13, so will be a factor
II. 29 is a factor of 25!..........29 > 25 and prime, so will not be a factor
III. 1,000,000 is a factor of 25!.......This will depend on number of 5 in 25! as 1000000 contains \(5^6\)
=> 25/5 +5/5 = 5+1 =6, so yes it is a factor.
ONLY III is true.
B
All prime numbers greater than n will not be factors of n!
I. 26 is not a factor of 25!.......26=2*13, so will be a factor
II. 29 is a factor of 25!..........29 > 25 and prime, so will not be a factor
III. 1,000,000 is a factor of 25!.......This will depend on number of 5 in 25! as 1000000 contains \(5^6\)
=> 25/5 +5/5 = 5+1 =6, so yes it is a factor.
ONLY III is true.
B
21 Mar 2022, 06:42
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Bunuel
I. 26 is not a factor of 25!
2*13 is a factor of 25!
II. 29 is a factor of 25!
29 is a prime number and only happen if till 29! happens therefore not a factor
III. 1,000,000 is a factor of 25!
Yes since 5^6 is a factor and 2^19 is a factor
Therefore IMO B
