Jim and Beth are in a ticket line along with 43 other people, and Jim

Question

Jim and Beth are in a ticket line along with 43 other people, and Jim is ahead of Beth in the line. If there are 20 people behind Jim and 30 people ahead of Beth, how many people in the line are between Beth and Jim?

A. 5
B. 7
C. 10
D. 13
E. 15

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Attachment:

Jim.png

gmatophobia · Accepted Answer

Jim and Beth are in a ticket line along with 43 other people, and Jim is ahead of Beth in the line. If there are 20 people behind Jim and 30 people ahead of Beth, how many people in the line are between Beth and Jim?

A. 5
B. 7
C. 10
D. 13
E. 15

I always try to avoid double counting as I usually forget subtracting 1 or 2 later at the end and fall for the trap answers.

What worked for me:

______X____ Beth ______Y_____ Jim _____Z______

X = people behind Beth
Y = people between Beth and Jim (This is what we need to find out)
Z = people ahead of Jim

Now, Total people in the line = Jim + Beth + 43 = 45.

People behind Jim = 20
X + Beth + Y = 20 ........ (1)

People ahead of Beth = 30
Y + Jim + Z = 30 .......... (2)

Adding (1) and (2)
X + Beth + Y + Y + Jim + Z = 50
Y + (X + Beth + Y + Jim + Z) = 50
Y + Total people = 50
Y + 45 = 50
Y = 5

Answer: A.

MartyMurray · Answer

Jim and Beth are in a ticket line along with 43 other people, and Jim is ahead of Beth in the line. If there are 20 people behind Jim and 30 people ahead of Beth, how many people in the line are between Beth and Jim?

A. 5
B. 7
C. 10
D. 13
E. 15

Show Spoiler

Attachment:

Jim.png

First, let's get a more complete picture of the scenario by determining how many people are in the line.

Jim and Beth are in a ticket line along with 43 other people

Jim + Beth + 43 = 45 people in the line

Now, let's use the facts we have to determine how many people are between Beth and Jim.

Jim is ahead of Beth in the line

there are 20 people behind Jim

So, there must be 45 - (Jim + 20) = 24 people ahead of Jim in the line.

there are ... 30 people ahead of Beth

We already have Jim + 24 = 25 ahead of Beth.

For there to be a total of 30 ahead of Beth. there must be 30 - 25 = 5 more people between Jim and Beth.

Now, we just have to make sure we chose the correct answer because we could still fall for a trap by including Jim and Beth in our total and choosing 7.

The question asks how many people in the line are between Beth and Jim. So, the correct number is 5.

a) 5
b) 7
c) 10
d) 13
e) 15

Correct answer:  (A)

sanebeyondone · Answer

I think MartyMurray's solution makes better sense than gmatophobia's.

By definition:
As X is not supposed to be 25 but 24
Z is not supposed to be 15 but 14

But these mistakes are covered up by letting Y be 5 instead of 7.

If the question ask further how many people are in front of Jim, the right answer is X=24 not X=25.

J must be 1 and B must be 1

X+J+Y+B+Z=45
X+1+Y+1+Z=45
Not 
X+Y+Z=45

Posted from my mobile device

sayan640 · Answer

I think x + y + z should be 43 . Jim and beth should not be included .  Bunuel   MartyMurray

sayan640 · Answer

Considering your current diagram ,

it should be ,

x + 1 +y +1 +z = 45
x +y +z = 43

y +1 +z = 20
y+z = 19---------(2)

x +1 +y = 30
x+y = 29--------------(3)
Adding (2) and (3) , we get , x +2y + z = 48

Solving we get, x + 2*y  + z - (x +y +z ) = 48 -43 = 5

Am I right in my approach ?  KarishmaB   MartyMurray

MartyMurray · Answer

Yes, exactly, x + y + z should be 43.

MartyMurray · Answer

Yes, that approach is spot on.

Bunuel · Answer

KarishmaB · Answer

Always make a small diagram for such questions. Total 45 people so 1 to 45. Since 20 people are behind Jim, it means he is at 25th place (26 to 45 behind him) Since 30 people are ahead of Beth, it means she is at 31st place. Screenshot 2024-06-23 at 4.56.13 PM.png Between them are 26 - 30 i.e. 5 people. Answer (A)

Tushar2804 · Answer

Note 1: Jim is ahead of Beth in the line. 
20 people behind Jim indicates that Jim is at the 25th position in the line. 
30 people ahead of Beth indicates that Beth is at the 31st position.

Which means that the number of people between them are positions - 26, 27, 28, 29 and 30 - 5 people.

thekingslay · Answer

Think about the questions in the below way -->

Jim & Beth and there "with 43 people"
That makes it 45 people line in total.

As the line is of 45 people,
&, the question talks about 20 and 30 people behind & ahead.
So the number of people between Jim and Beth has to be ending with digit "5". as -> ('X'5-'Y'0='Z'5)

This leads to options A and E.

Now make a number line and use 5 and 15 between Jim and Beth. 
You will end up with "A"- the answer.

mbaprepavi · Answer

Total are 43
But 30 ahead of beth and 20 behind Jim means there is an overlap of 7 people

But note, these 7 people also have J and B included
Therefore there are 5 people  between  J and B

Yasho1998 · Answer

I solved it using set theory, where Total = A + B - Both.

Hence, 45 = 30 + 20 - Both
Both = 50 - 45
Both = 5

IMO A

purse1234 · Answer

I'm not sure if my method is correct, but I used a venn diagram to solve this question.

There are 45 people (include Jim and Beth)
Jim and number of people behind him= 21 people
Beth and number of people ahead of her= 31 people
x is the overlapping people (including Jim and Beth)

Applying the formula, we will get

45 = 21 + 31 - x
x = 7 (This means there are 7 people total in the overlap, including Jim and Beth.)

Therefore, the the number of people between J and B will be 7-2 = 5 people

SudsMeister · Answer

I always try to avoid double counting as I usually forget subtracting 1 or 2 later at the end and fall for the trap answers.

What worked for me:

______X____ Beth ______Y_____ Jim _____Z______

X = people behind Beth
Y = people between Beth and Jim (This is what we need to find out)
Z = people ahead of Jim

Now, Total people in the line = Jim + Beth + 43 = 45.

People behind Jim = 20
X + Beth + Y = 20 ........ (1)

People ahead of Beth = 30
Y + Jim + Z = 30 .......... (2)

Adding (1) and (2)
X + Beth + Y + Y + Jim + Z = 50
Y + (X + Beth + Y + Jim + Z) = 50
Y + Total people = 50
Y + 45 = 50
Y = 5

Answer: A.

juliansorre · Answer

Consider it as an "overlapping sets" problem:

Let A be the number of people (including Jim) ahead of Beth, and B the number of people behind Jim (including Beth). The intersection of the two sets is exactly the number of people between Jim and Beyh.

We have:

A + B -x = 45 (1)

solving for x:

x= 30+20-45 = 5.

nisiat · Answer

I see all these complicated solutions and I wanted to share my line of thinking, which I find more intuitive.

- There are 45 people in the line. 
- Jim is number 21 (since there are 20 people behind him) 
- Beth is number 15 (since there're 30 people ahead of her)
- people in between them: 16th, 17th, 18th, 19th, 20th.

You can think about it as a arithmetic sequence with n = 45 if you like (a1, a2,..., a45).

GMATGuruNY · Answer

One approach is to PLUG IN THE ANSWERS, which represent the number of people between B and J.
When the correct answer is plugged in, there will be 43 people in addition to Beth and Jim.

D: 13 --> B + 13 + J
Since there are 20 people behind Jim (including B) and 30 people ahead of Beth (including J), the line looks as follows:
6 + B + 13 + J + 16 --> 6+13+16 = 35
The number of additional people is too small.

B: 7 --> B + 7 + J
Since there are 20 people behind Jim (including B) and 30 people ahead of Beth (including J), the line looks as follows:
12 + B + 7 + J + 22 --> 12+7+22 = 41
The number of additional people is stiil too small.

As the answer choices DECREASE in value, the number of additional people INCREASES.
Implication:
For the number of additional people to increase to 43, the correct answer must be smaller than option B.

A

A: 5 --> B + 5 + J
Since there are 20 people behind Jim (including B) and 30 people ahead of Beth (including J), the line looks as follows:
14 + B + 5 + J + 24 --> 14+5+24 = 43
Success!

kevincan · Answer

Jim and Beth are in a ticket line along with 43 other people, and Jim is ahead of Beth in the line. If there are 20 people behind Jim and 30 people ahead of Beth, how many people in the line are between Beth and Jim?

A. 5
B. 7
C. 10
D. 13
E. 15

Show Spoiler

Attachment:

Jim.png

45 people in total . If 20 people are behind Jim, there are 24 ahead of him, so he’s the 25th person in line . As 30 people are ahead of Beth , she’s 31st in line . People in positions 26 to 30 are between them, thus 5 people are between them

Jim and Beth are in a ticket line along with 43 other people, and Jim

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Jim and Beth are in a ticket line along with 43 other people, and Jim

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