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07 Apr 2020, 10:18
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:21) correct
33%
(01:25)
wrong
based on 196
sessions
History
Date
Time
Result
Not Attempted Yet
What is the largest value of \(n\) for which \(3^n\) is a factor of (1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!)?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
07 Apr 2020, 10:26
Kudos
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What is the largest value of n for which 3^n is a factor of (1!) (2!) (3!) (4!) (5!) (6!) (7!) (8!) (9!)?
no of factor of 3 in (1!) = 0
no of factor of 3 in (2!) = 0
no of factor of 3 in (3!) = 1
no of factor of 3 in (4!) = 1
no of factor of 3 in (5!) = 1
no of factor of 3 in (6!) = 2
no of factor of 3 in (7!) = 2
no of factor of 3 in (8!) = 2
no of factor of 3 in (9!) = 4
total no of factors of 3 = 13 (adding all)
so, largest value of n =13
correct answer D
no of factor of 3 in (1!) = 0
no of factor of 3 in (2!) = 0
no of factor of 3 in (3!) = 1
no of factor of 3 in (4!) = 1
no of factor of 3 in (5!) = 1
no of factor of 3 in (6!) = 2
no of factor of 3 in (7!) = 2
no of factor of 3 in (8!) = 2
no of factor of 3 in (9!) = 4
total no of factors of 3 = 13 (adding all)
so, largest value of n =13
correct answer D
07 Apr 2020, 10:27
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sjuniv32
The question should ask about the largest INTEGER value of n.
So, basically we should count the number of 3's in (1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!).
1! and 2! don't have any 3's.
3!, 4!, and 5! each has one 3. For example, 5! = 1*2*3*4*5. Total 3.
6!, 7!, and 8! each has two 3's. For example, 7! = 1*2*3*4*5*(2*3)*7. Total 6.
9! has four 3's: 9! = 1*2*3*4*5*(2*3)*7*8*(3*3). Total 4.
Grand total = 3 + 6 + 4 = 13.
Answer: D.
