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

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

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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.
[Reveal] Spoiler: OA

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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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New post 26 Jun 2017, 04:17
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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.

The 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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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
A: Adam; B: 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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Last edited by RaguramanS on 26 Jun 2017, 09:18, 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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New post 26 Jun 2017, 08:52
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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. :/

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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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New post 03 Jul 2017, 00:31
As attached in the picture.

Answer should be 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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New post 31 Jul 2017, 07:54
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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

Answer:
[Reveal] Spoiler:
C


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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New post 08 Aug 2017, 09:11
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 people ahead of adam)--- Adam---- (N people between Adam and Beth) ---- Beth -------- (b people behind beth)
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.

C is the answer
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Re: The people in a line waiting to buy tickets to a show are standing one   [#permalink] 08 Aug 2017, 09:11
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