How many four-digit numbers are divisible by 9 ?
In arithmetic progression problems
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Answer:
5503500
Step-by-step explanation:
The smallest one is 1008, the largest one is 9999. The difference is 8991, which means 999 intervals of 9. In consequence, there are 1000 4 digits numbers divisible by 9.
Now, if you pair 1008 and 9999, the sum is 11007. If you pair the second smallest one with the second largest one, you remove 9 on one side just to add it on the other, so the sum is still 11007. If you keep pairing numbers like that, you will have 500 pairs, where the sum is always 11007.
The sum of all these numbers is therefore 11007*500 = 5503500.
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