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# The people in a line waiting to buy tickets to a show are standing one

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Math Expert
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The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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26 Jun 2017, 01:19
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36
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Difficulty:

35% (medium)

Question Stats:

77% (02:02) correct 23% (01:58) wrong based on 1535 sessions

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The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.
(2) 23 people in the line are behind Adam.

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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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31 Jul 2017, 06:54
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Bunuel wrote:
The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.
(2) 23 people in the line are behind Adam.

Target question: How many people in the line are behind Beth?

Given: Beth is standing behind Adam with a number of people between them. The number of people in front of Adam plus the number of people behind Beth is 18
So, we have: FRONT.....x people...ADAM......y people.....BETH......z people......BACK
We can write: x + z = 18
NOTE: Our goal is to determine the value of z

Statement 1: There are a total of 32 people in the line
We can write: x + y + z + 2 = 32 (the 2 represents Adam and Beth)
Simplify: x + y + z = 30
Is this information, along with x + z = 18, enough to determine the value of z?
No. There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 1, y = 12 and z = 17. In this case, z = 17
Case b: x = 2, y = 12 and z = 16. In this case, z = 16
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 23 people in the line are behind Adam
We can write: y + z + 1 = 23 (the 1 represents Beth)
Simplify: y + z = 22
Is this information, along with x + z = 18, enough to determine the value of z?
No. There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 2, y = 6 and z = 16. In this case, z = 16
Case b: x = 3, y = 7 and z = 15. In this case, z = 15
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y + z = 30
Statement 2 tells us that y + z = 22
Plus, it's given that x + z = 18
Since we have three different equations with 3 variables, we COULD solve this system for x, y and z, which means we COULD determine the value of z (the number of people behind Beth) . Of course, we're not going to waste valuable time solving the system, since our sole goal is to determine the sufficiency of the statements.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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26 Jun 2017, 03:17
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Bunuel wrote:
The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in from of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.
(2) 23 people in the line are behind Adam.

The queue is like this:
(a people standing here) .. Beth .. (b people standing here) .. Adam .. (c people standing here)

We have $$a+c=18$$

(1) We have $$a+b+c+2=32 \implies a+b+c=30 \implies b = 12$$. However, we dont know $$c$$, so we can't know $$a$$. Insufficient.

(2) We have $$a+b+1=23\implies a+b=22$$. Like (1), we can't know the value of $$a$$. Insufficient.

Combine (1) and (2) we have
$$a+b+c=30 \implies b=12$$
$$a+b+1=23\implies a+b=22$$
Hence $$a=10$$. Sufficient.

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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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Updated on: 26 Jun 2017, 08:18
2
Let X,Y,Z be three variables such that
X: No of people standing in front of Adam
Y: No of people standing in between Adam and Beth
Z: No of people standing behind Beth

From the data
$$X+Y=18; Z=?$$

St1: $$X+A+Y+B+Z= 32$$
NS

St2:$$Y+B+Z=23$$
NS

St 1+2:A,B=1;
Three variables three equations and three unknowns so it's solvable

Hence C
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Originally posted by RaguramanS on 26 Jun 2017, 07:28.
Last edited by RaguramanS on 26 Jun 2017, 08:18, edited 1 time in total.
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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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26 Jun 2017, 07:52
3
I might be missing something. But isnt the answer A?

We have three sections.

After B, between B and A and before A.

We know after B+before A is 18.

If the total is 32, as given by I, then 32-18-2=12 people should be between Adam and Beth?

Edit:
Found my misstake!

Misread the stem to ask for between a and b and not behind b. :/

Posted from my mobile device

Posted from my mobile device
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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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02 Jul 2017, 23:31
2
As attached in the picture.

Attachments

IMG_20170703_125544-2.jpg [ 54.81 KiB | Viewed 16714 times ]

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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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08 Aug 2017, 08:11
Bunuel wrote:
The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.
(2) 23 people in the line are behind Adam.

a + b = 18
b = ?

1) a + adam + n + beth + b = 32
=> adam + n + beth = 14

Then, a = 9, b = 9 or a = 10, b = 8. 2 different values. Insufficient.

2) n + beth + b = 23
Total people in line = ??
Insufficient. We don't have enough information to determine the value of b.

1+2)
a + b = 18
a + adam + n + beth + b = 32
and n + beth + b = 23
=> a = 9
=> b = 9
Sufficient.

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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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15 Nov 2017, 16:24
1
1
Bunuel wrote:
The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.
(2) 23 people in the line are behind Adam.

We need to determine the number of people in the line who are behind Beth, given that Beth is standing behind Adam and the number of people in front of Adam plus the number of people behind Beth is 18. If we know the number of people who are in front of Adam and the number of people who are strictly between Adam and Beth, then we can determine the number of people who are behind Beth.

Statement One Alone:

There are a total of 32 people in the line.

Since there are a total of 32 people in the line, subtracting Adam, Beth, and the 18 people who are either in front of Adam or behind Beth, we know that there are 12 people between Adam and Beth. However, since we don’t know the exact number of people who are in front of Adam, we can’t determine the number of people who are behind Beth. Statement one alone is not sufficient.

Statement Two Alone:

23 people in the line are behind Adam.

We are given that 23 people in the line are behind Adam. However, since we don’t know the number of people who are between Adam and Beth, we can’t determine the number of people who are behind Beth. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we know that there are a total of 32 people in the line and that 23 people in the line are behind Adam. Thus, there must be 32 - 23 - 1 = 8 people who are in front of Adam (note the number 1 is for Adam). From statement one, we also know that 12 people are between Adam and Beth. Thus, there are 32 - 8 - 12 - 2 = 10 people behind Beth (note the number 2 is for Adam and Beth).

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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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04 Oct 2018, 19:28
Bunuel wrote:
The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.
(2) 23 people in the line are behind Adam.

Queue: [X]+A+[Y]+B+[Z]
[X]+[Z]=18
Find [Z]=?

(1) [X]+A+[Y]+B+[Z] = 32
[Y] = 12

(2) [Y]+B+[Z] = 23
[Y]+[Z] = 22

(1)+(2)
[Y]=12 & [Y]+[Z]=22
[Z]=10 (sufficient)
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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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13 Nov 2019, 07:58
Let us visualize the stem this way.

———B——————A——
We know there are people behind adam, between beth and adam, and in front of adam. We do not know how many.

People behind beth = x
People between beth and adam = y
People in front of adam = z
Z+X=18
What is X?

1) X+Y+Z +beth + adam = 32 or X+Y+Z = 30.
Z+X = 18 Y+18=30
Y=12
Insuff.
2) B+X+Y=23
X+Y= 22
Insuff.

Combined we have:
X+Y=22
Y=12
X=10
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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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06 Jul 2020, 00:18
Bunuel wrote:
The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.
(2) 23 people in the line are behind Adam.

(1) Total number of people are 32.
Not much can be inferred from that , we can infer that there are 12 people in between A and B. Number of people number of people in front of Adam plus the number of people behind Beth cannot be inferred correctly. I could be 13+5 or 9+9, etc.

(2) 23 people behind A will mean, B+22 are behind A.

(1&2) Now we know people behind A=23, people in front of A=32-23=9. Therefore people behind B can found, which is 9.

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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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19 Jul 2020, 23:13
Bunuel wrote:
The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.
(2) 23 people in the line are behind Adam.

Here's how I did it.

There is an N variables rule, which says to solve for n variables, you need n distinct equations.
Exceptions:
1. When there is a combination of variables and you can substitute for that, you do not need as many equations to solve.
2. If the variables cancel out – you do not need as many equations.
3. If the equations are identical – you cannot solve.

Let people in front Adam be X, between Adam and Beth Y, and behind Beth Z.

We are given x+z=18 (this is our equation number 1)
(1) x+y+z=32 (the equation number 2)
(2) z=23 (the equation number 3)

So we have 3 equations and 3 variables so the correct answer is C.
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Re: The people in a line waiting to buy tickets to a show are standing one  [#permalink]

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31 Jul 2020, 05:29
I've solved it slightly differently for those with a similar thought process.
Let the order be as below -
We know that, X+Y = 18. We need to find Y.

Statement 1
X+A+Z+B+Y=32
Equating X+Y we get => A+Z+B=14
This is not sufficient to answer

Statement 2
Z+B+Y=23
This is not sufficient

Combining
Subtracting equation in Statement 1 from 2 =>
Z+B+Y-Z-B-A=23-14 =>
Y-A=9
A is actually Adam and the count for Adam is obviously 1 since he is one person.
=>Y=9+1=> Y (people after Beth) =10

Hope this helps.
Re: The people in a line waiting to buy tickets to a show are standing one   [#permalink] 31 Jul 2020, 05:29