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 = 18NOTE: 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 = 17Case b: x = 2, y = 12 and z = 16. In this case,

z = 16Since 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 = 16Case b: x = 3, y = 7 and z = 15. In this case,

z = 15Since 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 = 18Since 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:

Cheers,

Brent

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