Directions: Read the following information carefully and answer the question that follows.

A survey was conducted among a group of 150 college students regarding their usage of three streaming services: Netflix, Hulu, and Prime Video. The ratio of students who use only Netflix to those who use only Hulu is 5:4. The number of students who use only Prime Video is equal to the number of students who use both Netflix and Hulu only. A total of 21 students use all three streaming services. The number of students who use both Netflix and Prime Video only is 40% more than the number of students who use both Hulu and Prime Video only. The number of students who use both Hulu and Prime Video only is 30, which is double the number of students who use only Netflix.

Determine the difference between the total number of students who use Prime Video and the total number of students who use Netflix.

The correct option is 15.

Let us break down the given survey data for 150 college students across the three streaming services: Netflix, Hulu, and Prime Video.

Step 1: Determine students using Hulu and Prime Video only
It is given that the number of students who use both Hulu and Prime Video only is 30.

$\text{Hulu \& Prime Video only}=30$

Step 2: Determine students using only Netflix
The number of students using both Hulu and Prime Video only (30) is double the number of students using only Netflix.

$\text{Only Netflix}=\frac{30}{2}=15$

Step 3: Determine students using only Hulu
The ratio of students using only Netflix to those using only Hulu is 5:4.

$\frac{\text{Only Netflix}}{\text{Only Hulu}}=\frac{5}{4}$

$\frac{15}{\text{Only Hulu}}=\frac{5}{4}$

$\text{Only Hulu}=\frac{15\times 4}{5}=12$

Step 4: Determine students using Netflix and Prime Video only
The number of students who use both Netflix and Prime Video only is 40% more than the number of students who use both Hulu and Prime Video only (30).

$\text{Netflix \& Prime Video only}=30+(0.40\times 30)=30+12=42$

Step 5: Students using all three services
A total of 21 students use all three services.

$\text{All three services}=21$

Step 6: Determine students using only Prime Video and Netflix & Hulu only
Let $x$ be the number of students who use only Prime Video. The problem states that this is equal to the number of students who use both Netflix and Hulu only.

$\text{Only Prime Video}=x$

$\text{Netflix \& Hulu only}=x$

Step 7: Solve for x using the total number of students (150)
Summing all seven disjoint regions of the Venn diagram:

$\text{Only Netflix}+\text{Only Hulu}+\text{Only Prime Video}+\text{Netflix \& Hulu only}+\text{Hulu \& Prime Video only}+\text{Netflix \& Prime Video only}+\text{All three}=150$

$15+12+x+x+30+42+21=150$

$120+2x=150$

$2x=30$

$x=15$

So, $\text{Only Prime Video}=15$ and $\text{Netflix \& Hulu only}=15$.

Step 8: Calculate total Prime Video users

$\text{Total Prime Video users}=\text{Only Prime Video}+\text{Netflix \& Prime Video only}+\text{Hulu \& Prime Video only}+\text{All three}$

$\text{Total Prime Video users}=15+42+30+21=108$

Step 9: Calculate total Netflix users

$\text{Total Netflix users}=\text{Only Netflix}+\text{Netflix \& Hulu only}+\text{Netflix \& Prime Video only}+\text{All three}$

$\text{Total Netflix users}=15+15+42+21=93$

Step 10: Calculate the required difference

$\text{Difference}=\text{Total Prime Video users}-\text{Total Netflix users}$

$\text{Difference}=108-93=15$

The difference between the total number of students who use Prime Video and the total number of students who use Netflix is 15.