Data Sufficiency

Hi All,

We're told that in each of 5 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. We're asked which of the brands was deemed the better brand.

Before working on this question, it's worth noting that to win the 'majority' in a taste test, it only takes 26 of the 51 total votes - but a 'win' is any number from 26 to 51, inclusive. Thus, the TOTAL number of votes received across all 5 taste tests can be mis-leading, unless you know exactly how many votes were won in EACH of the 5 tests. This question can be solved by TESTing VALUES.

1) Brand X was chosen by a total of 155 participants.

IF....Brand X received...
51 votes in the 1st test,
51 votes in the 2nd test,
25 votes in the 3rd test,
25 votes in the 4th test,
and 3 votes in the 5th test, then Brand X would have won just 2 of the taste tests and Brand Y would have won the other 3 (and been determined the better brand).

IF....Brand X received...
26 votes in the 1st test,
26 votes in the 2nd test,
26 votes in the 3rd test,
26 votes in the 4th test,
and 51 votes in the 5th test, then Brand X would have won ALL 5 of the taste tests and been determined the better brand.
Fact 1 is INSUFFICIENT

2) One brand won three of the first four taste tests.

Fact 2 tells us nothing about which of the two brands actually won the 3 (of the first 4) taste tests.
Fact 2 is INSUFFICIENT

Combined, we know...
Brand X was chosen by a total of 155 participants.
One brand won three of the first four taste tests.

From the examples above, we can clearly see that Brand X could have won 2 or more of the 5 taste tests. With the information in Fact 2, we know the winner won either 3 or 4 of the 5 tests, so Brand X might have won or not.

For example:
Brand X scores 51, 51, 51, 1 and 1 - winning 3 of the first 4 and determined the better brand.
Brand X scores 25, 25, 25, 51 and 29 - meaning that Brand Y won 3 of the first 4 and determined the better brand.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

swerve wrote: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.

The OA is E.

Source: Princeton Review

Given: 5 state tests; to get the majority, the winner brand must win at least 3 tests.
Number of votes for 5 tastes = 5*51 = 255

We have to determine which of two brands was deemed the better brand.

Let's take each statement one by one.

(1) Brand X was chosen by a total of 155 participants.

Case 1: The number of votes Band X got in 5 tests are: 51, 51, 51, 1 and 1 (total 155); since Brand X won a greater number of tests than Brand Y, Brand X is the winner by the majority. The answer is Brand X.

Case 2: The number of votes Band X got in 5 tests are: 18, 18, 17, 51 and 51 (total 155); since Brand Y won a greater number of tests than Brand X, Brand Y is the winner by the majority. The answer is Brand Y. No unique answer.

(2) One brand won three of the first four taste tests.

From this information, it can be any of the brands. Insufficient.

(1) and (2) together

Both the cases discussed in Statement 1 are applicable here, too, resulting in no unique answer.

The correct answer: E

Hope this helps!

-Jay
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