VJesus12 wrote: ↑

Fri Dec 17, 2021 10:13 am

2/3 of all the people who attended a certain party arrived by 8:00 PM. How many people arrived by 8:00 PM?

(1) 9 people arrived after 9:00 PM.

(2) 21 people arrived between 8:00 PM and 9:00 PM, and by 9:00 PM 90% of all the people who attended the party had arrived.

Answer: B

Source: Manhattan GMAT

Target question: How many people arrived by 8:00 PM?

Given: 2/3 of all the people who attended a certain party arrived by 8:00 PM

IMPORTANT: To answer the target question, we need to know the TOTAL number of people who attended the party.

Statement 1: 9 people arrived after 9:00 PM
This doesn't help because we don't know how many people arrived between 8pm and 9pm. During this period it's possible that no one arrived, or it's possible that millions of people arrived.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 21 people arrived between 8:00 PM and 9:00 PM, and by 9:00 PM 90% of all the people who attended the party had arrived.
Let T = TOTAL number of people who attended the party
Given: 2/3 of all the people who attended a certain party arrived by 8:00 PM
So, we can say that (2/3)T = number of people who arrived by 8:00 PM

21 people arrived between 8:00 PM and 9:00 PM.....
So, at 9pm, the number of people at the party = (2/3)T + 21

....by 9:00 PM 90% of all the people who attended the party had arrived.
In other words, at 9pm, the number of people at the party = (9/10)T

So, we have two different ways to express the number of people at the party at 9pm.
We can write: (2/3)T + 21 = (9/10)T

At this point, we need only recognize that we COULD solve this equation and find one unique value of T, which means we COULD determine how many people arrived by 8:00 PM
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent