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Rounding me to the nearest thousand makes me 8000.the sum of my digits is 24.if you red me forward and backward,i am still the same.what number am i?

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Rounding me to the nearest thousand makes me 8000 = From here we could say that the thousands digit is 7 or 8. So, 7BCD or 8BCD.

The sum of my digits is 24 = 7+B+C+D = 24 or 8+B+C+D = 24. So, B+C+D = 17 or 16.

If you read me forward and backward,i am still the same = It is a Palindromic number. So A=D and B=C. Then it could be 7557 or 8448.

Checking:

Round off 7557 is 8000.

Round off 8448 is 8000.

7+5+5+7=24

8+4+4+8=24

So it could be 7557 or 8448.