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

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

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

As attached in the picture.

Answer should be C.

----(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

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).

Answer: C

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)

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

(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.

Answer: C

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.

I've solved it slightly differently for those with a similar thought process.
Let the order be as below -
X (People before Adam)....A (Adam)....Z (People between Adam and beth)....B (Beth).....Y(People after Beth)
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.

Video solution from Quant Reasoning:
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\(-----x----Beth---y---Adam---z----\)

Let,
\(x\) people behind Beth
\(y\) people in front of Beth and behind Adam
\(z\) people in front of Adam

Given that, \(x+z=18\)

(1) \(x+y+z + 2=32\) ( The two are Beth and Adam)

\(⇒ x+y+z=30\)

\(⇒ y=30-(x+z)=30-18=12\); Insufficient

(2) \(x+y+1=23\)

\(⇒ x+y=22\); Insufficient.

Considering Both:

\(⇒ x+y=22\)

\(⇒ x+12=22\)

\(∴ x=10;\) Sufficient.

The answer is \(C\)[/quote]

Answer: Option C

Video solution by GMATinsight



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