A number is said to be a “digifac�

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A number is said to be a "digifac" if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?

(A) 5
(B) 7
(C) 9
(D) 10
(E) 14

The OA is D .

I don't know how can I solve this PS question. Experts, may you clarify this to me? Thanks in advance.
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by [email protected] » Sat Nov 25, 2017 11:43 am
Hi M7MBA,

We're given the definition of a "digifac" number - each of its DIGITS is a factor of the number itself. We're asked for the sum of the missing two digits of the following five-digit digifac: 9, 5, 3 _ _ ? This question is based on several Number Property Rules.

For '5' to be a factor of this 5-digit number, the number must end in either a 0 or a 5.
For '9' to be a factor of this 5-digit number, the digits must SUM to a number that is divisible by 9.
Any number that is divisible by 9 will also be divisible by 3, so no extra work is required here.

IF.... the 5-digit number was....
9 5 3 _ 0 .... then the sum of the digits would be 17 and the missing digit would need to be a 1. However, with 95310.... '0' is NOT a factor of 95310, so this is NOT a possible solution.

9 5 3 _ 5 .... then the sum of the digits would be 22 and the missing digit would need to be a 5. With 95355, the sum of the digits is 27 and all of the digits IS a factor of the 5-digit number. Thus, the sum of the missing digits is 5+5 = 10

Final Answer: D

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