Mathematics
titou 04
-
quendistu Posted messages 102 Registration date Status Membre -
quendistu Posted messages 102 Registration date Status Membre -
Hello, who can help me solve this problem: I am an odd number greater than 7000. I have 4 digits. My digit
in the tens place is half of the one in the thousands place. The sum of my digits is 16. Who am I?
in the tens place is half of the one in the thousands place. The sum of my digits is 16. Who am I?
Configuration: Windows XP Internet Explorer 6.0
2 réponses
8341 and 8143. Indeed:
The number is between 7001 and 9999,
the thousands digit is therefore 7, 8, or 9.
For half of the thousands digit to be an integer,
that digit must be even,
so it can only be 8.
The tens digit is half of that, which is 4.
The sum of the thousands digit and the tens digit is therefore 12.
The total sum of the 4 digits being 16,
the sum of the hundreds digit and the units digit is 4 (16-12).
Thus, the hundreds digit and the units digit can only be
(0,4), (1,3), (2,2), (3,1), or (4,0)
The number being odd, the units digit is therefore also odd.
So, among the pairs mentioned, only (1,3) and (3,1) remain.
So the hundreds digit is 1 and the units digit is 3, or vice versa.
Thus, there are two solutions:
8341 and 8143.
--
Thank you for marking the problem or question as resolved if applicable.
The number is between 7001 and 9999,
the thousands digit is therefore 7, 8, or 9.
For half of the thousands digit to be an integer,
that digit must be even,
so it can only be 8.
The tens digit is half of that, which is 4.
The sum of the thousands digit and the tens digit is therefore 12.
The total sum of the 4 digits being 16,
the sum of the hundreds digit and the units digit is 4 (16-12).
Thus, the hundreds digit and the units digit can only be
(0,4), (1,3), (2,2), (3,1), or (4,0)
The number being odd, the units digit is therefore also odd.
So, among the pairs mentioned, only (1,3) and (3,1) remain.
So the hundreds digit is 1 and the units digit is 3, or vice versa.
Thus, there are two solutions:
8341 and 8143.
--
Thank you for marking the problem or question as resolved if applicable.