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# At a certain baseball game attended by 2,000 people, 800 people like

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Math Expert
Joined: 02 Sep 2009
Posts: 54375
At a certain baseball game attended by 2,000 people, 800 people like  [#permalink]

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06 Apr 2016, 01:16
3
4
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:57) correct 43% (02:10) wrong based on 155 sessions

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At a certain baseball game attended by 2,000 people, 800 people like eating popcorn, and 300 people like eating both popcorn and peanuts. At most, how many people like eating peanuts?

(1) At least 700 people do not like eating popcorn or peanuts.
(2) At least 1,200 people do not like eating peanuts.

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Joined: 12 Aug 2013
Posts: 44
Re: At a certain baseball game attended by 2,000 people, 800 people like  [#permalink]

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06 Apr 2016, 02:38
Like Popcorn Don't like Popcorn

Like Peanuts 300 ?
Don't like peanuts 500 B
---------------------------------------------------
1800 A 2000

Now as per Statement 1 :- A+B > 700 which does not say anything about ?
Statement 2 :- B >= 1200 which again does not confirm the number of people like peanuts

combining both statements again does not say anything about ?

Hence E should be the answer
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At a certain baseball game attended by 2,000 people, 800 people like  [#permalink]

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06 Apr 2016, 03:01
Popcorn(only) + Peanuts(only) + Both + Neither = 2000 --- (1)
Popcorn(only) + Both = 800
Both = 300 --> Popcorn(only) = 800 - 300 = 500

N(Peanuts) = Peanuts(only) + Both = ?

St1: Neither >= 700. Since question asks atmost, fix the value of Neither to 700.
Substitute in (1) --> Peanuts(only) + Both = 2000 - (500 + 700) = 800.
Sufficient

St2: Popcorn(only) + Neither >= 1200
Popcorn(only) = 500 --> Neither >=700 --> Peanuts(only) <= 500

Since the question asks atmost(maximum) how many like peanuts, we have to fix the value of 'Neither' to minimum --> Neither = 700
Hence, Peanuts(only) + Both = 500 + 300 = 800
Sufficient

Math Expert
Joined: 02 Aug 2009
Posts: 7563
Re: At a certain baseball game attended by 2,000 people, 800 people like  [#permalink]

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06 Apr 2016, 04:16
ravisinghal wrote:
Like Popcorn Don't like Popcorn

Like Peanuts 300 ?
Don't like peanuts 500 B
---------------------------------------------------
1800 A 2000

Now as per Statement 1 :- A+B > 700 which does not say anything about ?
Statement 2 :- B >= 1200 which again does not confirm the number of people like peanuts

combining both statements again does not say anything about ?

Hence E should be the answer

Hi,

we are looking for EXACT number but AT THE MOST..
so relook in your solution and you will find you both statements are sufficient
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Joined: 20 Oct 2014
Posts: 37
GMAT 1: 740 Q49 V42
Re: At a certain baseball game attended by 2,000 people, 800 people like  [#permalink]

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07 Apr 2016, 09:12
ravisinghal wrote:
Like Popcorn Don't like Popcorn

Like Peanuts 300 ?
Don't like peanuts 500 B
---------------------------------------------------
1800 A 2000

Now as per Statement 1 :- A+B > 700 which does not say anything about ?
Statement 2 :- B >= 1200 which again does not confirm the number of people like peanuts

combining both statements again does not say anything about ?

Hence E should be the answer

Both the statements are enough to find the MAXIMUM value, which is 800. The answer should be (D).
Intern
Joined: 05 Jun 2016
Posts: 19
Re: At a certain baseball game attended by 2,000 people, 800 people like  [#permalink]

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26 Nov 2016, 15:35
Can someone please explain how statement 2 adds additional info? The info provided in the q stem alone is sufficient to derive info provided in statement 2, is it not?

From the q stem alone (black : given info from q stem; red : info you can derive from q stem).

................. PopCorn...........Not PopCorn...... Total
Peanuts............300.........
Not Peanuts........500
Total...............800........... 1200..................2000
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Joined: 05 Jul 2006
Posts: 1702
Re: At a certain baseball game attended by 2,000 people, 800 people like  [#permalink]

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02 Jan 2017, 06:19
relations in 2 overlapping sets

when "neither" is maxed overlap is maxed and thus both is maxed and accordingly "only set A" and "only set B" are both minimised , and vice versa.

let Peanuts set = A and pop set = B and Peanuts only = a and Pop only = b

Total = a+b+both+neither

(a+b) = total -both -neither , total = 2000, both = 300, b= 500

thus a = 2000-500-300-neither and to max a we need min neither

from 1

neither min = 700 thus a = 500.... suff

from 2

min (b+neither ) = 1200 thus min neither is 1200-500 = 700 ... same info as in 1.... suff

D
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Joined: 14 Nov 2012
Posts: 23
GMAT 1: 740 Q51 V38
Re: At a certain baseball game attended by 2,000 people, 800 people like  [#permalink]

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07 Sep 2017, 00:18
Pop + Pea - Both + Neither = 2000
Both = 300
Pop = 800
=> Pea + Neither = 2000 + 300 - 800 = 1500

(1) At least 700 people do not like eating popcorn or peanuts.

--> Neither >= 700
--> 1500 - Pea >= 700
--> Pea =< 800

Max(Pea)=800
Suff.

(2) At least 1,200 people do not like eating peanuts.
--> Min (Pea) = 1200
Also, Max(Pea)= Max(1500 - Neither)= 1500 with Neither = 0

Suff.

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Re: At a certain baseball game attended by 2,000 people, 800 people like   [#permalink] 07 Sep 2017, 00:18
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