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

Question

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.

BrentGMATPrepNow · Accepted Answer

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

Isushant · Answer

Hi - I have a doubt in the first statement. As it is give that 2/3 of the people who attended the party arrive by 8 pm and 9 after 9 pm, then can't we say that the 9 who arrived later were 1/3 as 2/3 are already in the party. Therefore, by this total number of people are 27. Please suggest

KM2018AA · Answer

No you cannot say that since we do not know how many people arrived between 8:00 PM and 9:00 PM. Assume if 3 people had arrived between 8-9 PM then the \(\frac{1}{3}\) of total number of attendees = 9+3 = 12. only If you had known somehow that 0 people had arrived between 8-9 PM then and only then you could conclude that \(\frac{1}{3}\) of total no. of attendees = 9+0=9

Hope this is clear

Hope this is clear

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Zoser · Answer

I got confused with the wording of "21 people arrived between 8:00 PM and 9:00 PM"

Can't between 8:00 and 9:00 include those who reached by 8:00?

Thanks

sid993 · Answer

2/3 people arrived by 8:00 pm. Convert this into %,which makes 66% roughly.
Now 21 people arrived after 8:00pm and before 9:00pm. At 9 pm there were 90% guests present.
Difference =90-66= 25%
Let total guests be T 
25%T= 21
We can find T and hence 2/3T

Gylmitul · Answer

Hi, I have a doubt here. It is written that 21 people arrived between 8-9 p.m.. Are we assuming that between 8-9 p.m. includes 8 p.m. and 9.pm.. Since, it is not explicitly mentioned.
21 people could have also arrived by 8.59 p.m.

inigofga · Answer

I have a doubt regarding statement 2. If I understand, the statement says that 2/3T + 21 = 0.90 T, hence we are able to solve for variable T, and then multiply it by 2/3 to answer the question, hence sufficient.

But how do we actually know that the people that arrived at 8:00pm and between 8:00-9:00 pm represent the 90% of the total. Could we not have had, for instance, 4 people that arrived at 7:00pm? This will change the equation to the following: 4 + 2/3 T + 21 = 0.90 T. I believe that by not knowing if there were people that arrived to the party before 8:00pm we can not draw an accurate equation, thus insufficient.

SFischer · Answer

Hey Inigofga,
not sure if you received an answer to your question yet, thus here's quickly my thought. I think the the difference is in the wording. The stem says that "2/3 of all the people who attended a certain party arrived BY 8:00 pm." Thus, they could have arrived at 7:59 pm or at 5:30 pm, but it's only important hat they arrived BEFORE 8:00 pm. The statement does not state that they arrived AT 8:00 pm, which would mean that they arrived at exactly 8:00 pm. However, to avoid that meaning "by" is used and not "at".

Hope it helps!

Best,
Seb

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

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