This question is testing PARALLELISM and SUBJECT/VERB agreement.
When there is a closed parallel marker such as BOTH X AND Y, the part of the sentence that follows "both" must be parallel to the part that follows "and."
In each of the answer choices, I've highlighted what comes after each marker:
A. is both unhealthy and cost a lot of money
Not parallel - both [adjective] and [verb]
B. are both unhealthy and costs a lot of money
Not parallel.
C. are both unhealthy and cost a lot of money
Same.
D. is both unhealthy and costs a lot of money
Same.
E. is both unhealthy and costly
Both [adjective] and [adjective] - correct!
We also could have used SUBJECT/VERB agreement to eliminate answer choices. "Smoking" is singular, so we cannot use "are" or "cost." That would have eliminated A, B, and C.
The answer is E.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education