i am a 2 digit odd number. I am between 50-100. The difference of my digits is 3. i do not have a remainder when divided by 7.

Question

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Answer 1

You must be between 51 and 99 then and you have to be a multiple of 7.

(Thank you Kenneth S. for pointing that out!)

 

This leaves you with 7*8 = 56, 7*9 = 63, 7*10 = 70, 7*11 = 77, 7*12 = 84, 7*13 = 91, 7*14 = 98

 

But since the answer must be odd, you can eliminate all of the even multiples of 7:

7*8 = 56, 7*9 = 63, 7*10 = 70, 7*11 = 77, 7*12 = 84, 7*13 = 91, 7*14 = 98

 

 

Now looking for a difference of 3 in the digits:

6-3 = 3, this satisfies the final condition so the answer is 63.

 

To make sure and eliminate the others, 7-7 = 0, 9-1 = 8. Neither equals 3, so the ONLY answer is 63.

 

Hope this helped!