If Alex and Keanu received the same total number of attempts during a

Yes that's what I thought at first, but I could not find a constraint which states that the daily number of attempts has to be the same for Keanu and Alex. I guess the constraint refers to the total number of attempts of the two-day archery competition. (So the number of attempts on Day 1 and Day 2 could vary between Keanu and Alex as long as they are the same in total)

Please correct me if I'm getting this totally wrong.

Greetings
Max

Percentage usually is misleading

(1) On the first day, Alex hit bull's-eyes on a higher percentage of shots than Keanu did.

Let Alex percentage is 50% and Keanu's is 30%

If Alex has to 10 total attempts, then he got 5
If Keanu has to 100 total attempts, then he got 30

keanu shot more.

If Alex has to 100 total attempts, then he got 50
If Keanu has to 10 total attempts, then he got 3

Alex shot more

Insufficient

(2) On the second day, Alex hit bull's-eyes on a higher percentage of shots than Keanu did.

Use the same example above
Insufficient

Combing 1 & 2

Still 2 cases
Insufficient

Answer: E

clearly both are insuff

so will work with together statement

Let on first day Alex got 10 trials and hit 6 of them =60% hit
first day Keanu got 2 trials and hit only 1 of them = 50%

Second day Alex got 1 trial and hit 1 = 100%
so keanu got 9 trials and let he hits 7 of them <100%

Total of two days
Alex score 7/11
Keanu scores 8/11

clearly keanu wins....

But if may also happen that alex got all hits correct on both days
so two possibilities

insuff

Ans E

We are given that Alex and Keanu received the same total number of attempts during a two-day archery competition and need to determine whether Alex hit more bull's-eyes than Keanu did.

Statement One Alone:

On the first day, Alex hit bull's-eyes on a higher percentage of shots than Keanu did.

Without having any information regarding the number of bull’s-eyes hit on day two, we cannot answer the question. Statement one is not sufficient to answer the question.

Statement Two Alone:

On the second day, Alex hit bull's-eyes on a higher percentage of shots than Keanu did.

Without having any information regarding the number of bull’s-eyes hit on day one, we cannot answer the question. Statement two is not sufficient to answer the question.

Statements One and Two Together:

Using the information from statements one and two, we still cannot answer the question.

For instance, let's say Alex hit on 9 of 10 attempts (90%) on day one and 8 of 10 attempts (80%) on day 2 while Keanu hit on 8 of 10 attempts (80%) on day 1 and 7 of 10 attempts (70%) on day 2. In that scenario, Alex would have hit more bull’s-eyes than Keanu did [Alex’s 17 hits in 20 attempts (85%) in two days vs. Keanu’s 15 hits in 20 attempts (75%) in two days].

However, if Alex hit on 20 of 200 attempts (10%) on day one and 90 of 100 attempts (90%) on day 2 while Keanu hit on 9 of 100 attempts (9%) on day 1 and 171 of 200 attempts (85.5%) on day 2, then Keanu would have hit more bull’s-eyes than Alex did [Keanu’s 180 hits in 300 attempts (60%) in two days vs. Alex’s 110 hits in 300 attempts (~36%) in two days].

Answer: E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.