Hi All,
This question can be solved with a little math and a bit of 'brute force.'
We're told that D is a positive DIGIT (meaning 1-9, inclusive). We're asked for the value of D.
1) D.D + DD = (D.D)(DD)
While this might look complex, if you substitute in a value for D, you'll find that math to be rather straight-forward....
IF.... D = 1, we have...
1.1 + 11 = (1.1)(11)
Does that equation 'balance out?'
1.1 + 11 = 12.1
(1.1)(11) = 12.1
So YES, D could equal 1.
What about D = 2? Does....
2.2 + 22 = (2.2)(22)
You should be able to answer that question WITHOUT actually doing the math. On the left side, you're ADDING 10% of 22 to 22 and on the right side you're MULTIPLYING those values. The right side will clearly be a lot bigger than the left side. This means that D CANNOT equal 2.
Now how about D=3? D=4? Etc. You should see that you run into the same issue that you did when we worked through D=2: the right side is much bigger than the left side, so there's really no need to check all of those values. This means that D=1 is the ONLY possible solution.
Fact 1 is SUFFICIENT.
2) D is not a prime number
This tells us that D cannot be 2, 3, 5 or 7.... but that still leaves us with 5 other possibilities (1, 4, 6, 8 and 9)
Fact 2 is INSUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich