Should I submit both of my new test scores?

In the spring of my junior year I took the ACT and the SAT and received scores that were decent but a ways from my goals. I had both scores set to automatically send to 4 schools on my college list. I recently retook both tests and scored considerably better. My ACT score was higher in both instances, so I would like my new ACT to be the score considered. Since I have already submitted both my lower SAT and ACT scores to those colleges, should I submit both my ACT and my SAT retakes so they will see that I improved both scores? I have learned that it is better to submit just one test, but I am not sure if there is any way to ask a school to only review certain scores that they receive. I know I can select which scores to report on CommonApp, but I do not know if schools will only review scores that are listed on CommonApp. Any insight would be much appreciated!

I feel like I may have made the wording a little confusing, please let me know if there is any way I can clarify. In short, I am asking if reporting only my ACT on the CommonApp will cause schools to review only my ACT scores and disregard the SAT scores that I sent via collegeboard. If not, should I submit my higher SAT in addition to my higher ACT so they can see that I improved both scores?

You should submit which ever score was the highest. Colleges only care about the highest score. It would be useful to tell us what those scores are.

For the benefit of other users, it is not always a good idea to take advantage of the free sending service, in light of the very scenario described above. Unless you are very confident you will do well the first time, it’s best to wait and see what your scores are before sending them.

I would send the higher scores. It doesn’t matter that they were not listed on the Common App.
Good luck.

@Lindagaf My initial scores were 31 and 1380, my retakes were 33 and 1460. ACT superscore is 34 and SAT superscore is 1460.
Thanks for the replies!

34 is better, for sure.