5 and 4

Logic Level 3

There is a 5 digit number, $A$ . One of its digits is removed, giving the number $B$ . If $A +B = 52713$ , then find the sum of the digits of $A$ .

The answer is 23.

3 solutions

Adarsh Kumar
Jul 3, 2014

Let us say that the original 5 digit number is (abcde).Now the last digit needs to be removed because if any other digit is removed and the two numbers are added the units digit can't be 3 because that is an odd number.That implies the last digit has been removed.

But how did you find the sum of the original no.?

Erza Scarlet - 6 years, 1 month ago

From above, we know that $B = \lfloor \frac{A}{10} \rfloor$ , so $10 B \leq A < 10B + 10$ . Combined with $A + B = 52713$ , we get that $B \approx \frac{ 52713}{11} \approx 4792$ . Testing some values, we see that $B = 4792 ,A = 47921$ will work.

Calvin Lin Staff - 6 years, 1 month ago

B = [A/10] if one removed is last digit, but why do you know it is last digit?

Bình Bình - 6 years, 1 month ago

@Bình Bình – because if we remove any other digit, the total will be an even number

Arpan Sarangi - 6 years ago

@Arpan Sarangi – EXACTLY! GOOD JOB!

Adarsh Kumar - 6 years ago

Justine Allen Arciga
Apr 23, 2015

We know that the last digit was the one removed. We start with the first digit and work backwards to the last digit. The first digit cant be 5 because theres no number that when added to 5 the sum is 2. So the first digit is 4. Then to get the second digit you subtract (4 + 1) from 12 (2 + 10), the result is 7. Next, to get the third digit, you subtract 7 + 1 from 17 (7+10), the result is 9. To get the fourth digit, you subtract 9 from 11 (1+10), the result is 2. And for the last number you subtract 2 from 3 and the result is 1. So the number is 47921. Adding the digits gives 23.

Elijah Frank
Dec 7, 2020

Only do this: 52712/2 = 26356 -> B and (52712/2)+1 = 26357 added 0 for the 5th digit = 2+6+3+5+7 = 23 -> A question.

5 and 4

The answer is 23.

3 solutions

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