Which of the following sequences is most likely to be cut by a restriction enzyme?
The answer is AATATT
TTATAA
I need an explanation why.

The restriction enzymes are the endonucleases that are found in the prokaryotes and cleave a  DNA sequence in a specific manner. They are present as a part of the defense mechanism in bacteria and archaea.

The correct answer is:

5'TTATAA3'    3' AATATT 5'

This can be explained as:

5' ---TTA    TAA--- 3'

3' ---AAT    ATT--- 5'

Therefore, the restriction enzyme will cleave blunt or sticky ends.

To learn more about restriction enzymes follow the link:

link

The sequence 5'TTATAA3'   3' AATATT 5'  will be recognized by the  Aan 1 enzyme and blunt ends can be produced.

Explanation:

In prokaryotes the restriction enzyme and restriction sites are seen. Restriction enzyme will either produce a  sticky end as eco R1 or blunt end. The single strand of DNA will have overhangs which can combine with the other strand by complementary base pairing  and ligase enzyme to get replicated.

The recognition sequence 5'TTATAA3'      3' AATATT 5'  is present in AaRl enzyme. The cut will be blunt.

5' ---TTA   TAA--- 3'

3' ---AAT   ATT--- 5'

Restriction enzymes are used in recombinant DNA technology.