To win the contest a brand has to win majority of the 5 taste tests.
A brand winning 3 or more tests can be termed as a winner.
Total number of participant = 51
Each of the participants chose a brand per test
Total votes = 51 * 5 = 255

Statement 1 => Brand X was chosen by a total of 155 participants
If brand X was chosen by all 51 participants in 3 tests,
Total votes for brand X = 155 in 3 tests + for brand X total votes = over 100.
With these statistics, brand X is the winner.
It is also possible for brand X to have register 24 votes in 3 tests while brand Y registered 27 votes in them with X getting the remaining votes in last 2 tests.
So, brand X will be winning 2 tests while brand Y will be winning 3 out of 5 test making brand Y the winner since the information given is providing more than one solution.
Then statement 1 is NOT SUFFICIENT.

Statement 2 => One brand won three of the first four taste tests.
This can be either brand X or brand Y since the specific brand was not mentioned. Statement 2 is NOT SUFFICIENT

Combining both statements together,
From statement 1, we have brand X winning either 3/5 or 2/5 test and brand Y winning either 3/5 or 2/5 tests as well and either of them could have won the three of the first four taste tests; either brand X or brand Y could still be the winning brand.

Both statements together do not provide a definite answer.
Hence, both statements together are not SUFFICIENT
Answer = option E