Can't figure this out!

[eclaym2003]

I have been going over problems that I missed during some practice tests that I have been doing. Here's one that I cannot figure out:

Henry and Eleanor are waiting in line for a movie. If Henry is fourth in line and there are n people in front of Eleanor, where n>4, how many people are between Henry and Eleanor?

n-5
n-4
n-3
n+3
n+4

The answer is n-4 but I don't understand why this is the answer though.
Here is the explanation that the book gives?

There are n people in front of Eleanor. One of them is Henry. Three more of them are in front of Henry (since Henry is fourth in line). So that makes four people that are not behind Henry. All the rest, or n-4, are behind Henry andin front of Eleanor, so n-4 is the answer.

Yeah, so if someone could help me understand this better I would greatly appreciate it.

[luvaduva]

If I told you that there are three points on a line: A, B, and C.

The distance from A to B is 10 units and the distance from A to C is 15 units.

What is the distance from B to C?

[skj]

If we mark Henry's position in the line with H=4 and Eleanor's position with E, then the number of people in front of Eleanor is n=E-1. The number of people between Eleanor and Henry is x=E-H-1. Since E-1=n, then x=n-H and since H=4 then x=n-4.

[Stuart@KaplanGMAT]

I have been going over problems that I missed during some practice tests that I have been doing. Here's one that I cannot figure out:

Henry and Eleanor are waiting in line for a movie. If Henry is fourth in line and there are n people in front of Eleanor, where n>4, how many people are between Henry and Eleanor?

n-5
n-4
n-3
n+3
n+4

The answer is n-4 but I don't understand why this is the answer though.
Here is the explanation that the book gives?

There are n people in front of Eleanor. One of them is Henry. Three more of them are in front of Henry (since Henry is fourth in line). So that makes four people that are not behind Henry. All the rest, or n-4, are behind Henry andin front of Eleanor, so n-4 is the answer.

Yeah, so if someone could help me understand this better I would greatly appreciate it.

This type of question is vastly simplified by picking numbers.

We know that Henry is 4th.

Let's say that Eleanor is 7th, so that gives us n=6, since there are 6 people in front of Eleanor.

Well, if E is 7th and H is 4th, there are 2 people between H and E (the ones who are 5th and 6th).

Now let's plug n=6 into the choices and see which one gives us the correct answer of "2".

n-5 = 1
n-4 = 2
n-3 = 3
n+3 = lots
n+4 = lots

Only n-4=2: pick (b).

Picking numbers is a great way to make complicated problems with variables in the answer choices much less complicated. Someone adept at picking numbers (just like anything else, it takes practice to become an expert) could answer this particular question in about 30 seconds.

[gmatinjuly]

I got n-4 here is the explaination

Say | is start of line
* is each person
$ is Henry
% is Eleanor (assuming Eleanor is in 8th position)

| * * * $ * * * %

1. If E is in 8th position then he has 7 people in front ..
So if he has n people in from he is in n+1 position

2. H is in 4th position E is in n+1 position number of people between them
(not including any one of them)
[(n+1 ) - 4 ] - 1
= n-4

Now look at example above and put values
7 people in from so n= 7
so [8-4]-1 = 3 which is as in diagram above.

[Scott@TargetTestPrep]

I have been going over problems that I missed during some practice tests that I have been doing. Here's one that I cannot figure out:

Henry and Eleanor are waiting in line for a movie. If Henry is fourth in line and there are n people in front of Eleanor, where n>4, how many people are between Henry and Eleanor?

n-5
n-4
n-3
n+3
n+4

The answer is n-4 but I don't understand why this is the answer though.
Here is the explanation that the book gives?

There are n people in front of Eleanor. One of them is Henry. Three more of them are in front of Henry (since Henry is fourth in line). So that makes four people that are not behind Henry. All the rest, or n-4, are behind Henry andin front of Eleanor, so n-4 is the answer.

Yeah, so if someone could help me understand this better I would greatly appreciate it.

If n = 5, there are 5 people ahead of Eleanor (which means that Eleanor is 6th in line). Since Henry is the fourth person, there is only 1 person between Henry and Eleanor. Looking at the choices, we see that only n - 4 yields the result of 1 when n = 5, so that is the correct answer.

Answer: B

[Brent@GMATPrepNow]

Henry and Eleanor are waiting in line for a movie. If Henry is fourth in line and there are n people in front of Eleanor, where n>4, how many people are between Henry and Eleanor?

A) n-5
B) n-4
C) n-3
D) n+3
E) n+4

We call this a Variables In The Answer Choices (VIAC) question.
This question type can be solved algebraically or solved using the INPUT-OUTPUT approach where we test values.
Let's use the INPUT-OUTPUT approach.

Let's say n = 9, which means there are 9 people ahead of Eleanor.
We got the following: _ _ _ H _ _ _ _ _ E
In this case, there are 5 people between Henry and Eleanor.
In other words, when we INPUT n = 9, the answer to our question (i.e., the OUTPUT) is 5

Now we'll check the answer choices to see which one yields an output of 5 when we input n = 9.
A. 9 - 5 = 4. No good. We want an output of 5.
B. 9 - 4 = 5. PERFECT!
C. 9 - 3 = 6. No good. We want an output of 5.
D. 9 + 3 = 12. No good. We want an output of 5.
E. 9 + 4 = 13. No good. We want an output of 5.

Answer: B