Difference between revisions of "2018 AMC 8 Problems/Problem 14"

(Solution(factorial))
(Video Solutions)
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120 is 5!, so we have 5,4,3,2,1. Now look for the largest digit which you multple numbers.
 
120 is 5!, so we have 5,4,3,2,1. Now look for the largest digit which you multple numbers.
  
(5)(4)(3)(2)(1)=120
+
(5)(4)(3)(2)(1) = 120
 
make the greatest integer  
 
make the greatest integer  
  
 
(5)(4 times 2)(3)(2 divided by 2)(1)
 
(5)(4 times 2)(3)(2 divided by 2)(1)
(5)(8)(3)(1)(1)
+
= (5)(8)(3)(1)(1) =120
  
 
8 is the largest value and will go in the front  
 
8 is the largest value and will go in the front  
Line 25: Line 25:
  
 
5+8+3+1+1 = 18
 
5+8+3+1+1 = 18
 +
 +
==Video Solution (CREATIVE ANALYSIS!!!)==
 +
https://youtu.be/zxEO6amczPU
 +
 +
~Education, the Study of Everything
  
 
==Video Solutions==
 
==Video Solutions==

Revision as of 14:18, 30 March 2023

Problem

Let $N$ be the greatest five-digit number whose digits have a product of $120$. What is the sum of the digits of $N$?

$\textbf{(A) }15\qquad\textbf{(B) }16\qquad\textbf{(C) }17\qquad\textbf{(D) }18\qquad\textbf{(E) }20$

Solution

If we start off with the first digit, we know that it can't be $9$ since $9$ is not a factor of $120$. We go down to the digit $8$, which does work since it is a factor of $120$. Now, we have to know what digits will take up the remaining four spots. To find this result, just divide $\frac{120}{8}=15$. The next place can be $5$, as it is the largest factor, aside from $15$. Consequently, our next three values will be $3,1$ and $1$ if we use the same logic. Therefore, our five-digit number is $85311$, so the sum is $8+5+3+1+1=18\implies \boxed{\textbf{(D) }18}$.


Solution(factorial)

120 is 5!, so we have 5,4,3,2,1. Now look for the largest digit which you multple numbers.

(5)(4)(3)(2)(1) = 120 make the greatest integer

(5)(4 times 2)(3)(2 divided by 2)(1)

= (5)(8)(3)(1)(1) =120

8 is the largest value and will go in the front so we can express it as 5,8,3,1,1

We don't even need the number just add

5+8+3+1+1 = 18

Video Solution (CREATIVE ANALYSIS!!!)

https://youtu.be/zxEO6amczPU

~Education, the Study of Everything

Video Solutions

https://youtu.be/IAKhC_A0kok

https://youtu.be/7an5wU9Q5hk?t=13

https://youtu.be/Q5YrDW62VDU

~savannahsolver

See Also

2018 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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