To apply at Duke, you only need to take the ACT and that too without writing
But at an ivy (say Yale), if you take the ACT, you have to take it with the writing component and you're not waived from SAT subject tests.
All candidates for admission must complete one of the following standardized testing options and arrange to have official test score reports sent to Duke:
The test of the ACT, including the writing exam
You must submit scores from either:
The SAT and any two SAT Subject Tests - or -
The ACT Plus Writing Test