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03 Dec 2021, 10:37
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
49% (02:36) correct
51%
(02:41)
wrong
based on 134
sessions
History
Date
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Result
Not Attempted Yet
How many numbers are there between 1 and 30 including both the numbers such that n! is divisible by (n + 1)?
A. 17
B. 20
C. 18
D. 30
E. 19
A. 17
B. 20
C. 18
D. 30
E. 19
19 Dec 2021, 00:00
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We can solve by the following method:-
1 can be written as 1!/1+1 i.e 1/2 which is not properly divisible
2 can be written as 2*1/3 which is also not properly divisible
3 can be written as 3*2*1/4 or 3*2*1/2*2 which is also not properly divisible
4 cab be written as 4*3*2*1/5 which is also not properly divisible.
From this we can say that if n+1 is a prime no., we can eliminate that no. from the possible no. which can divide n! by n+1. So the no. we can eliminate are 1,2,4,6,10,12,16,18,22,28 & 30. So we already know 3 can also be eliminated from the no. that can divide n! by n+1. So total 12 numbers are there that cannot divide n! by n+1 properly
So our answer will be 18 no. between 1 to 30 that n! is divisible by n+1
1 can be written as 1!/1+1 i.e 1/2 which is not properly divisible
2 can be written as 2*1/3 which is also not properly divisible
3 can be written as 3*2*1/4 or 3*2*1/2*2 which is also not properly divisible
4 cab be written as 4*3*2*1/5 which is also not properly divisible.
From this we can say that if n+1 is a prime no., we can eliminate that no. from the possible no. which can divide n! by n+1. So the no. we can eliminate are 1,2,4,6,10,12,16,18,22,28 & 30. So we already know 3 can also be eliminated from the no. that can divide n! by n+1. So total 12 numbers are there that cannot divide n! by n+1 properly
So our answer will be 18 no. between 1 to 30 that n! is divisible by n+1
