help with a math question!

<p>so i was doing a practice test, and i came upon this question:



<p>Each of the four letters in the addition of the three-digit numbers above represents a different digit. What digit does D represent?</p>

<p>HOW DO I DO THIS!?!?!? lol
thanks! :D</p>

<p>I guess and checked, but I made educated guesses. I figured that C = 1, because there aren't two three-digit numbers whose sum would equal a number in the 2000s (999 + 999 = 1998). </p>

<p>So if C = 1, then I could make a guess on A and B. I started with A = 9 and B = 2, because 9 + 2 = 11 and this would give me a 1 in the ones digit:</p>




<p>This would work, but B and D are the same, and they must be different. I tried A = 8 B = 3, again because 8 + 3 = 11, giving me a 1 in the ones digit:</p>




<p>Now all the numbers are different and D = 2</p>

<p>the ones digit value for A+B is C. We can tell that A+B= a number >10 because otherwise the overall answer would be CCC.
This means that a "1" will be carried over and placed above the second B. Now when we add the tens digits,1+A+B, we get a "ones digit of D. This tells us that C+1=D.
Also, since the greatest number that can be carried over in the addition of two numbers is a "1" we can conclude that C=1.And because we know that C+1=D. D=2</p>

<p>hopefully this helps</p>

<p>OHHH, that makes sense. thanks guys!</p>

<p>i hope i dont see this type of question in october.. so freaking time consuming.</p>