If the five-digit number 5DDDD is divisible by 6, then : PS Archive
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# If the five-digit number 5DDDD is divisible by 6, then

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If the five-digit number 5DDDD is divisible by 6, then [#permalink]

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27 May 2006, 14:07
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If the five-digit number 5DDDD is divisible by 6, then determine the digit D.
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27 May 2006, 14:12
D=4

Only 5 options for D - 0,2,4,6,8, and 5+4*D should be divisible by 3
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27 May 2006, 14:12
4.
its divisible by 2 , hence the digit could be one of 2,4,6,8,0

and the sum of 5 + 4*D should be divisible by 3 . hnec the solution is 4
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31 May 2006, 10:45
For divisiblity by 6, sum of digits has to be a mutiple of 3 and last digit even.

Test 2

52222 - does not work since sum of digits is 13

Test 4

54444 - works - sum of digits is divisible by 3 and last digit is even
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31 May 2006, 12:17
Hi-
could someone explain "5+4*D should be divisible by 3?"

I just figured it had to be even- then tried 4 b/c 54/6 is an integer...
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31 May 2006, 14:11
kook44 wrote:
Hi-
could someone explain "5+4*D should be divisible by 3?"

I just figured it had to be even- then tried 4 b/c 54/6 is an integer...

There's a shortcut you can use when determining divisability. Basically, a number is divisble by 3 if the sum of all the digits is divisible by 3.

5+4*D is the sum of the digits.
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31 May 2006, 19:06
Yes should be 4.
Nice explainations above.
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31 May 2006, 19:59
Yeah, great explanation. Especially the sum of the digits one makes it so easy and clear.
31 May 2006, 19:59
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