Hi stevecult,
This DS question is all about Number Properties that are tied to specific numbers.
We're told that the DIGITS P, Q, R and S make up the 3-digit number PQP and the 4-digit number RQS5. We're asked for the value of R.
1) (PQP)(P) = RQS5
With Fact 1, we have the product of 2 numbers and the result. Notice how the units digits in the product are both "P"s - with the resulting digit a "5." How many digits can you multiply by themselves and end in a 5? There are only 10 options to consider:
(0)(0) = 0
(1)(1) = 1
(2)(2) = 4
(3)(3) = 9
Etc.
If you map them all out, you'll find that there's just ONE option: 5. This means that the "P" MUST be a 5. Substituting that in, we have...
(5Q5)(5) = RQS5
From here, it looks like the value of Q will impact the value of R, so let's see if we can define the range of possible outcomes by trying a couple of options...
Minimum:
Q=0... (505)(5) = 2525
Maximum:
Q=9... (595)(5) = 2975
Notice that the "R" will ALWAYS be a "2", so there's no more work to be done.
Fact 1 is SUFFICIENT.
2) P, Q, R and S are DISTINCT non-zero digits.
With this Fact, we know that the 4 digits represent 4 DIFFERENT integers, but we don't know exactly what R is.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
