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Numbers

by knight247 » Fri Aug 05, 2011 4:12 am
D and F represents two distinct digits. If the number 457D89F is divisible by 36 then what is the value of (D+F)?

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by Frankenstein » Fri Aug 05, 2011 5:08 am
Hi,
For the number to be divisible by 36, it has to be divisible by 9 and 4.
457D89F is divisible by 4 -> 9F is divisible by 4. So, F can be 2 or 6
457D89F is divisible by 9 -> (4+5+7+D+8+9+F) is divisible by 9. So, 33+(D+F) should be divisible by 9
So, D+F can be 3 or 12
D+F = 3 => F = 2, D = 1
D+F = 12 =>F = 6, D = 6
As D and F are distinct, F=2, D=1 is the only solution.
So, D+F = 3.
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by tpr-becky » Fri Aug 05, 2011 10:29 pm
the above solution is correct, just wanted to put forth the concept that when a problem has crazy numbers and talks about divisibility you should always think about factoring and your divisibility rules first. You could have even started reasoning through the problem by realizing that F had to be even because 36 has a 2 in it but you would have needed the divisibility rules for 4 and 9 to solve the problem.
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