Amy and Jed are among 35 people, who are standing in a line, on behind

We are told that Jed is standing behind Amy.

Let x = number of people behind Jed
Let y = number of people ahead of Jed but behind Amy
Let z = number of people ahead of Amy


So, our diagram looks like this: BACK|-----x people----JED------y people------AMY----z people------|FRONT

Amy and Jed are among 35 people
We can write: x + y + z + Jed + Amy = 35 people
In other words, x + y + z + 2 = 35
Simplify: x + y + z = 33

The number of people in front of Amy plus the number of people behind Jed is 24.
We can write: x + z = 24

There are 15 people behind Amy, including Jed
x + y + Jed = 15
In other words: x + y + 1 = 15
Or: x + y = 14

Take:
x + y + z = 33
x + z = 24

Subtract the bottom equation from the top equation to get: y = 9

Take: x + y = 14
Since y = 9, we know that x = 5

Take: x + y + z = 33
Since y = 9 and x = 5, we know that z = 19

We have: BACK|-----5 people----JED------9 people------AMY----19 people people------|FRONT

How many people are in front of Jed?
The number of people in front of Jed = y + AMY + z
= 9 + AMY + 19
= 29

Answer: D

Cheers,
Brent

Given

• There are 35 people including Amy and Jed
• Amy is in front of Jed, not necessarily in immediate front.

Let's say the line looks as follows

-------x people------- Amy ------- z people ------- Jed ------- y people-------

Question = z + x + 1 ?

Amy and Jed are among the 35 people

x + y + z + 2 = 35

x + y + z = 33 ---(1)

The number of people in front of Amy plus the number of people behind Jed is 24

x + y = 24 ---(2)

There are 15 people behind Amy, including Jed

z + 1 + y = 15

z + y = 14 ---(3)

(1) + (2)

x + y + z + y = 38

y = 38 - 35 = 5

x = 24 - 5 = 19

Therefore 19 + 5 + 1 = 29

IMO D

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