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There isn't one. The only two digit numbers whose sum of digits is 12 are: 39, 48, 57, 66. (I didn't include 75, 84, or 93 since interchanging their digits and subtracting from the original number will be a negative result.) None of the four remaining numbers will exceed the original by 25. 66 won't work since the difference will be zero. Using 39, the new number (93) will exceed the original by 54; using 48 the difference will be 36; and using 57 the difference will be 18

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Q: If the sum of a two digit number is 12 and the digits interchange their places the new number exceeds the original number by 25 what is the number?

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-- "The sum of a two-digit number" is unclear. I took it to mean"The sum of the digits of a two-digit number."-- "... the product ?" is unclear. Are you looking for the product of the two digits,or the product of the forward and backward numbers ?-- It's not possible to write a number whose two digits sum to 12 and whosereverse exceeds it by 25. The tens digit would have to be 4.611... and the unitsdigit would have to be 7.388... .Then(4.611...) + (7.388...) = 12(46.111...) + (7.388...) = 53.5(73.888...) + (4.611...) = 78.5Difference = 25So, the number can't be written, but ...The product of its two digits is 34.071 (rounded)The product of the forward and reverse numbers is 4,199.75 (rounded)

17

Integers of 6 digits are normally greater than integers of 5 digits

The number 11 is prime and has two identical digits.

105 is not a prime number. You can readily see that 3 and 5 go into it, and 7 goes into it too. The number ends in 5, and 5 goes into any number ending in 0 or 5. The sum of the digits is 6, and when the sum of the digits is divisible by 3, then so is the original number.

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-- "The sum of a two-digit number" is unclear. I took it to mean"The sum of the digits of a two-digit number."-- "... the product ?" is unclear. Are you looking for the product of the two digits,or the product of the forward and backward numbers ?-- It's not possible to write a number whose two digits sum to 12 and whosereverse exceeds it by 25. The tens digit would have to be 4.611... and the unitsdigit would have to be 7.388... .Then(4.611...) + (7.388...) = 12(46.111...) + (7.388...) = 53.5(73.888...) + (4.611...) = 78.5Difference = 25So, the number can't be written, but ...The product of its two digits is 34.071 (rounded)The product of the forward and reverse numbers is 4,199.75 (rounded)

To total 17 the two digits must be 8 and 9! The original number was 98.

83 A+

19

45

The original number is 58.

The original number would be 28. Swapped around, the number's digits are 82. The difference between the two numbers is 54.

45

45

39

Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.

3 and 6

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