The other tutor's answer is wrong because the
clue says it's greater than 1, so it can't be 1.

The clue:

"Multiply me by 3 and the product is less than
20."

Since 3 times 7 = 21 tells us that it's 6 or
less

The clue:

"I'm a whole number greater than 1."

Now we know it's one of these

6,5,4,3,2

The clue "Divide me by 3 and the remainder is 1".
So we divide all the possibilities by 3 and look at the
remainders:


  2      1      1      1      0
3)6    3)5    3)4    3)3    3)2
  6      3      3      3      0
  0      2      1      0      2

We see that 4 is the only one that has a remainder of 1 
when divided by 3.

So the answer is 4.

Edwin