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What is the units digit of (5!*4! + 6!*5!)/31?

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Bunuel
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What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   19 Apr 2016, 03:15
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What is the units digit of \(\frac{(5!*4! + 6!*5!)}{31}\)?

A. 4
B. 3
C. 2
D. 1
E. 0
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E
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   19 Apr 2016, 03:39
(5!*4! + 6!*5!)/31
=5!(4! + 6!)/31
=120 ( 24 + 720)/31
=(120 * 744)/31
= 120 * 24

Units digit of the above product will be equal to 0

Answer E
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   19 Apr 2016, 04:36
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Bunuel wrote:
What is the units digit of (5!*4! + 6!*5!)/31?

A. 4
B. 3
C. 2
D. 1
E. 0


Hi,
the moment the Q asks us the units digit of \(\frac{(5!*4! + 6!*5!)}{31}\), we know 5!*4! + 6!5! is a multiple of 31..
Also due to 5! in each, the term/sum is a multiple of 10.. so units digit is 0
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   19 Apr 2016, 10:51
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Hi

Any factorial above 4 will have 0 as a units digit. Therefore, it's a units digit of 0 divided by another units digit rendering a 0 as the outcome's units digit.
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   23 Nov 2016, 11:40
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Bunuel wrote:
What is the units digit of (5!*4! + 6!*5!)/31?

A. 4
B. 3
C. 2
D. 1
E. 0


\(\frac{(5!*4! + 6!*5!)}{31}\)

\(= \frac{5!(4! + 6!)}{31}\)

\(= \frac{5!(4! + 6*5*4!)}{31}\)

\(= \frac{5!*4!(1 + 6*5)}{31}\)

\(= \frac{5!*4!(31)}{31}\)

\(= 5!*4!\)

5! alone will have units digit as 0 , so the units digit of \(\frac{(5!*4! + 6!*5!)}{31}\) will be (E) 0
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   24 Nov 2016, 03:32
I say (E) as well.

The numerator adds up to zero (the units digit of 5! and 6! is zero) so the answer can only be zero.

PS: Always appreciate questions that you can solve by using logic rather than doing a lot of math! lol
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   23 Jan 2017, 18:29
Great Question.
Here is what i did in this one -->
(5!*4! + 6!*5!)/31 => 5!*4!(31)/31 => 5!*4!
Hence it will always end with a zero due to the presence of a 2 and a 5.

Hence E.
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   23 Jan 2017, 19:49
Harshit401 wrote:
E

Sent from my Lenovo A6020a46 using GMAT Club Forum mobile app

2880×31=89280
86400+2880=89280
6!*5!=86400
5!*4!=2880

Sent from my Lenovo A6020a46 using GMAT Club Forum mobile app
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink] New post   20 Apr 2020, 13:15
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Re: What is the units digit of (5!*4! + 6!*5!)/31? [#permalink]
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