Grades 5-6 Video Solutions 2025-2025_5-6

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17. Each of the cards shown below has two 3-digit numbers written on them, but some of the digits cannot be seen as they are covered in ink. On one of the cards, the sum of the  digits of both numbers is the same. On which card are those two numbers? Pause if you would like to try and solve it.  Let's see which of these cards we can have two numbers that have the same digit sum. If we look at the first one here, we can see that 5 plus 4 plus 3 is equal to 12. So the  sum of the digits of the first number is 12. And 1 plus 1 is 2, which means that the third digit would have to be 10. But obviously, 10 is not a digit. 10 is actually two digits.  So for that reason, we clearly can't have the first one have both numbers having the same sum, because there's no digit we can put here that will make this sum 12. So A  is not correct. Let's look at B. We have 5 plus 8 on this side, which is 13. And we have 1 plus 1, which  is 2. Now it doesn't even matter what this third one over here is, what this third digit over here is, because already we can't get even 13, let alone any number bigger than  that. Because in order to get up to 13 from 2, you need 11, which is two digits. So even  if we put a zero here, the smallest digit, then this sum would be 13. We still can't get any digit that will get us from 2 to 13. So B is also not correct.  Let's look at option C. Well, we have 9 plus 8 plus 2, which is 19. And we have 1 on this  side. So can we do it? Well, actually we can, right? Because we have two digits to get 19 minus 1, which is 18. So what two digits add up to 18? Well, 18 is equal to 9 plus  9. So if both of these digits are 9s, then the digit sum of the left side will be 19,  and the digit sum of the right side will also be 19. So C is actually our correct answer. And if you want, we can also quickly check the last two options to make sure. 2 plus  1 plus 1 is 4. And this is already 6, which is bigger than 4. So no matter what digit these are, even if this is 0 and 0, this side is always going to be bigger than this side.  So it can't be D. And then if we check E, 7 plus 7 plus 7 is 21. And 2, in order to  get from 2 to 21, we need to add 19. And even if both of these digits are 9, 9 plus 9 is  only 18. So there's no digits we can put here to get from 2 to 19. E is not correct. And so we can be sure that the correct answer is option C.

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