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# How many people are standing in line?

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Intern
Joined: 01 Sep 2010
Posts: 19
How many people are standing in line?  [#permalink]

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04 Oct 2010, 06:12
1
6
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Difficulty:

55% (hard)

Question Stats:

54% (01:00) correct 46% (00:45) wrong based on 243 sessions

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How many people are standing in line?

(1) Three people are standing in front of Alan and three people are standing behind David.

(2) Two people are standing between Alan and David.
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Joined: 02 Sep 2009
Posts: 60687
How many people are standing in line?  [#permalink]

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04 Oct 2010, 06:21
Hi all,

Please consider the following DS problem that I have been struggling with:

How many people are standing in line?

1. Three people are standing in front of Alan and three people are standing behind David.

2. Two people are standing between Alan and David.

Obviously each statement alone is not sufficient. When taken together we can have following two cases:

1. XXXDXXAXXX --> so in this case there are 10 people in the line;
2. AXXD --> so in this case there are 4 people in the line.

Two different answers, hence not sufficient.

Hope it helps.
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Re: How many people are standing in line?  [#permalink]

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04 Oct 2010, 06:24
Wow Bunuel - that was fast.

I didn't consider the possible options for overlaps between David and Alan.

Thank you.
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Re: How many people are standing in line?  [#permalink]

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16 Oct 2010, 07:22
Tricky...i missed one situation...
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23 Jun 2014, 03:34
Chandra and Ken are waiting in line for concert ticket s. If each person takes up 2 feet of space in the line,
how long is the line?
1) There are three people in front of Chandra and three people behind Ken
2) Two people are standing between Chandra and Ken
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Re: How many people are standing in line?  [#permalink]

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23 Jun 2014, 03:40
parassagi wrote:
Chandra and Ken are waiting in line for concert ticket s. If each person takes up 2 feet of space in the line,
how long is the line?
1) There are three people in front of Chandra and three people behind Ken
2) Two people are standing between Chandra and Ken

thats easy,

you dont know if Chandra stands infront of Ken or behind him.
Using the tewo scenarios, you will get 2 different ans, even if you combine the 2 choices.

Hence E
Math Expert
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Posts: 60687
How many people are standing in line?  [#permalink]

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23 Jun 2014, 03:41
parassagi wrote:
Chandra and Ken are waiting in line for concert ticket s. If each person takes up 2 feet of space in the line,
how long is the line?
1) There are three people in front of Chandra and three people behind Ken
2) Two people are standing between Chandra and Ken

Merging similar topics. Please refer to the solutions above.

Similar question to practice: pam-and-ed-are-in-a-line-to-purchase-tickets-how-many-98651.html

Hope it helps.

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Re: How many people are standing in line?  [#permalink]

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31 Dec 2015, 21:03
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

How many people are standing in line?

(1) Three people are standing in front of Alan and three people are standing behind David.

(2) Two people are standing between Alan and David.

In the original condition, because we have to know the number of “key” people in line, there are numerous variables. In order to match the number of variables and the number of equations, we need numerous equations as well. Since both the condition 1) and 2) has 1 equation, there is high chance E is the answer.
Using both the condition 1) and 2), we cannot know who is in front between David and Alan. Therefore, the correct answer is E.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: How many people are standing in line?  [#permalink]

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14 Jan 2017, 17:30
48. In order to determine the length of the line, we need to know how many people are standing in it. Thus, rephrase the question as follows: How many people are standing in the line?
Statement (1) says that there are three people in front of Chandra and three people behind Ken. Consider the following different scenarios: The line might look like this:
(Back) X X X Ken X Chandra X X X (Front)

OR The line might looks like this: (Back) Chandra X X Ken (Front)

The number of people in the line depends on several factors, including whether Chandra is in front of Ken and how many people are standing between Chandra and Ken. Since there are many different scenarios, statement (1) is not sufficient to answer the question.

Statement (2) says that two people are standing between Chandra and Ken. Here, we don't know how many people are ahead or behind Ken and Chandra. Since there are many different scenarios, statement (2) is not sufficient to answer the question.

Taking both statements together, we still don't know whether Chandra is in front of Ken or vice versa, and therefore we still have two different possibilities:
The line might look like this: (Back) X X X Ken X X Chandra X X X (Front)
OR The line might look like this: (Back) Chandra X X Ken (Front)
Therefore, the correct answer is (E): Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: How many people are standing in line?  [#permalink]

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04 Sep 2018, 23:42
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Re: How many people are standing in line?   [#permalink] 04 Sep 2018, 23:42
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