In each of five taste tests, each of 51 participants chose

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Princeton Review

In each of five taste tests, each of 51 participants chose either Brand \(X\) or Brand \(Y\). The brand chosen by the majority of participants in a taste test was the winner of that taste test, and the brand that won the majority of the taste tests was deemed the better brand. Which of the brands was deemed the better brand?

1) Brand \(X\) was chosen by a total of 155 participants.
2) One brand won three of the first four taste tests.

OA E
Source: — Data Sufficiency |

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edited:

by deloitte247 » Sat Aug 31, 2019 1:17 am

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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