DS - What is the value of (2T+T-X) / (T-X)

[J.140]

I answered this correctly as "A" (statement 1 sufficient), however I solved it as a Combo. OG 2018 and Manhattan Navigator solves it as "Direct Algebra."

Can this be solved as a combo? I cleaned the statement from (2T+T-X) / (T-X) to "2T" by cancelling out (T-X) on top and bottom of the fraction. My cleaned up statement was "What is the value of 2T"? Statement 1 was: 2T / T-X = 3. I cross multiplied to get my combo 2T = 3T-3X and I decided statement 1 was sufficient.

Is it mathematically correct to clean up the statement into "2T"?
Can a Combo equal an expression with variables? My combo equaled 2T = 3T -3X

Thank you.

[Sage Pearce-Higgins]

Please read the forum guidelines before posting. This looks like a problem from the 2018 OG, meaning that it's copyrighted and we can't reprint it on a public forum. You're lucky I know the problem well; we request that you post the full text of the problem to make the thread easy for everyone to understand.

However, on a brief note, your two errors cancelled themselves out for you (luckily!). You can't simply cancel the (t-x) from top and bottom (although trying to rephrase the combo question is a good move). Consider the following fraction (4 + 2) / 2. This is equal to 3. However, if you cancel the 2s on the top and bottom you'd get 4 - showing how it's an illegal move. Check out the fractions chapter in the Foundations of Math for more about cancelling.

You other error was to conclude that finding that 2t = 3t - 3x makes statement (1) sufficient. When a question asks for a value, then a statement must provide a single number to make it sufficient. Knowing that "3t - 3x" is not a value.