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28 Dec 2024, 03:34
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (01:15) correct
16%
(01:04)
wrong
based on 293
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The superfactorial of a positive integer n is defined to be (1!)(2!) ... (n!). What is the result when the superfactorial of 5 is divided by 6! ?
(Note: If n is a positive integer, n! = (1)(2) ... (n).)
A. \(\frac{1}{6}\)
B. \(\frac{5}{6}\)
C. 20
D. 48
E. 2,880
Hi,
Posting a PS question which appeared on GMAT official mock
GMAT-Club-Forum-cqxwhq3p.png [ 36.21 KiB | Viewed 1769 times ]
(Note: If n is a positive integer, n! = (1)(2) ... (n).)
A. \(\frac{1}{6}\)
B. \(\frac{5}{6}\)
C. 20
D. 48
E. 2,880
Hi,
Posting a PS question which appeared on GMAT official mock
Attachment:
GMAT-Club-Forum-cqxwhq3p.png [ 36.21 KiB | Viewed 1769 times ]
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28 Dec 2024, 03:58
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Pretty easy IMHO, I did it the ye olde fashioned way:
Let us define -- Superfactorial (S!) = \(1!2!3!...n!\)
As per question, \(\frac{ S!(5)}{6!} = \frac{1!2!3!4!5!}{6!}\)
i.e., \(\\
\frac{\\
1!2!3!4!5!}{5!6\\
\\
}\\
\\
\)
Crossing out the 5! and simplifying
i.e., \(\frac{2.6.24}{6}\)
=48
The answer is 48
Let us define -- Superfactorial (S!) = \(1!2!3!...n!\)
As per question, \(\frac{ S!(5)}{6!} = \frac{1!2!3!4!5!}{6!}\)
i.e., \(\\
\frac{\\
1!2!3!4!5!}{5!6\\
\\
}\\
\\
\)
Crossing out the 5! and simplifying
i.e., \(\frac{2.6.24}{6}\)
=48
The answer is 48
22 Apr 2026, 16:19
Kudos
Bookmarks
The superfactorial of a positive integer n is defined to be (1!)(2!) ... (n!). What is the result when the superfactorial of 5 is divided by 6! ?
(Note: If n is a positive integer, n! = (1)(2) ... (n).)
The superfactorial of 5:
5!4!3!2!1!
The superfactorial of 5 divided by 6!:
\(\frac{5!4!3!2!1!}{6! }\)
Cancel and then multiply what remains:
\(\frac{5!4!3!2!1!}{6(5!)}\)
\(\frac{4!3!2!1!}{6}\)
\(4!2!1!\)
\(4!2! = 24 × 2 = 48\)
A. \(\frac{1}{6}\)
B. \(\frac{5}{6}\)
C. 20
D. 48
E. 2,880
Correct answer: D
(Note: If n is a positive integer, n! = (1)(2) ... (n).)
The superfactorial of 5:
5!4!3!2!1!
The superfactorial of 5 divided by 6!:
\(\frac{5!4!3!2!1!}{6! }\)
Cancel and then multiply what remains:
\(\frac{5!4!3!2!1!}{6(5!)}\)
\(\frac{4!3!2!1!}{6}\)
\(4!2!1!\)
\(4!2! = 24 × 2 = 48\)
A. \(\frac{1}{6}\)
B. \(\frac{5}{6}\)
C. 20
D. 48
E. 2,880
Correct answer: D
