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If n! and (n + 1)! have the same units digit, then n can be which of t

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If n! and (n + 1)! have the same units digit, then n can be which of t [#permalink]

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If n! and (n + 1)! have the same units digit, then n can be which of the following?

I. n = 10
II. n = 1
III. n = 0

A. I only
B. II only
C. III only
D. I and III
E. I, II, and III
[Reveal] Spoiler: OA

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Re: If n! and (n + 1)! have the same units digit, then n can be which of t [#permalink]

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New post 21 Apr 2016, 01:08
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Bunuel wrote:
If n! and (n + 1)! have the same units digit, then n can be which of the following?

I. n = 10
II. n = 1
III. n = 0

A. I only
B. II only
C. III only
D. I and III
E. I, II, and III


Given: n! and (n + 1)! have the same units digits
Let us first write down the factorials of different numbers:

0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720

If we notice here, all the numbers after 4! will end with a 0.
Here is why:

If we multiply any number by 10, a 0 is added to that number
And a 10 is formed by a 5 and a 2, 10 = 5*2
Till 4!, we do not have a "5" in multiplication. But after that, we will have atleast one "5" in the multiplication.

Hence the units digits will be same after 5! and for 0! and 1!
Now checking the statements


I. n = 10
Yes, the units digits of 10! and 11! are same and = 0. TRUE

II. n = 1
units digit f 1! = 1 and units digit of 2! = 2. FALSE

III. n = 0
Units digit of 1! = 1 and units digit of 0! = 1. TRUE

Correct Option: D
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Re: If n! and (n + 1)! have the same units digit, then n can be which of t [#permalink]

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New post 21 Apr 2016, 10:14
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Re: If n! and (n + 1)! have the same units digit, then n can be which of t [#permalink]

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New post 21 Apr 2016, 16:14
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0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10!=3628800

All the numbers after 4! will end with a 0 as we have atleast one "5" in the multiplication.

Hence the units digits will be same after 5! and for 0! and 1!
Now checking the statements

I. n = 10
Yes, the units digits of 10! and 11! are same.
TRUE

II. n = 1
units digit f 1! = 1 and units digit of 2! = 2.
FALSE

III. n = 0
Units digit of 1! = 1 and units digit of 0! = 1.
TRUE

Correct Option: D
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Re: If n! and (n + 1)! have the same units digit, then n can be which of t [#permalink]

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New post 22 Apr 2016, 12:15
Bunuel wrote:
If n! and (n + 1)! have the same units digit, then n can be which of the following?

I. n = 10
II. n = 1
III. n = 0

A. I only
B. II only
C. III only
D. I and III
E. I, II, and III


2 rules to make factorials easy

1. Any factorial greater than ( and including ) 5 will always have units digit as 0
2. 0! = 1! = 1


This question only tests the above two factorial rules...

Answer will definitely be (D)

PS : IMHO this problem can also be solved at a glance if the above properties are known to the test takers.
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Re: If n! and (n + 1)! have the same units digit, then n can be which of t [#permalink]

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New post 19 May 2017, 12:00
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Re: If n! and (n + 1)! have the same units digit, then n can be which of t   [#permalink] 19 May 2017, 12:00
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