Unique Value/Divisibility Question Type

mattnyc15 wrote: My question is have you seen a question on the official GMAT or otherwise that has 2 prime numbers in this question type that is NOT sufficient with a total value? I ask because it takes me forever, up to 3:30 - 4:00 minutes, to solve -- and I'd like to know if and when a total value is introduced in conjunction with two prime values that statement would most always be sufficient?

No, I have never seen a question like that. I won't swear that you'll never see such a question...

Consider:
I bought $2 apples and $3 oranges and spent a total of $20.
Well, I could have bought 4 apples and 4 oranges for $8 and $12 respectively, or I could have bought 1 apple and 6 oranges for $2 and $18 respectively.

But... it's highly unlikely that the GMAT would do this to you, especially with large numbers. What the GMAT is really testing is whether you'll fall for the assumption that "I always need 2 equations for 2 variables." They want to trick the student who blindly follows the rules and doesn't think. For that reason, it's highly unlikely that they'd ever make you do all of that work to get to the same answer that someone who blindly followed the rule would have gotten to.

So, save yourself the 4:00 min and just bet on a single equation being sufficient, as long as the coefficients don't share any factors.

For another example, see OG2015 DS #132:

Joanna bought only $0.15 and $0.29 stamps. How many $0.15 stamps did she buy?
(1) She bought $4.40 worth of stamps.
(2) She bought the same number of $0.15 and $0.29 stamps.

And for more, see here: https://www.manhattanprep.com/gmat/blog ... ons-rules/