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

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

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10 Nov 2015, 12:00
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45% (medium)

Question Stats:

61% (01:10) correct 39% (01:07) wrong based on 294 sessions

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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.
[Reveal] Spoiler: OA

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Re: 2/3 of all the people who attended a certain party arrived by 8:00 PM. [#permalink]

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10 Nov 2015, 16:53
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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.

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

Cheers,
Brent
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Re: 2/3 of all the people who attended a certain party arrived by 8:00 PM. [#permalink]

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09 Dec 2016, 00:01
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Re: 2/3 of all the people who attended a certain party arrived by 8:00 PM. [#permalink]

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15 May 2017, 03:31
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

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

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21 May 2017, 03:45
Isushant wrote:
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

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

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Re: 2/3 of all the people who attended a certain party arrived by 8:00 PM. [#permalink]

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26 Aug 2017, 11:19
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

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Re: 2/3 of all the people who attended a certain party arrived by 8:00 PM.   [#permalink] 26 Aug 2017, 11:19
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