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.

Find the number of students who use only one streaming service.

The correct answer is 42.

Step-by-step explanation:

Let us analyze the given information step-by-step using a Venn diagram breakdown for the three streaming services: Netflix, Hulu, and Prime Video.

1. Identify the given values:

• Total number of students surveyed = 150
• Number of students who use all three streaming services = 21
• Number of students who use both Hulu and Prime Video only = 30

2. Determine the number of students using only Netflix:

We are given that the number of students using both Hulu and Prime Video only (30) is double the number of students who use only Netflix.

$\text{Students using only Netflix}=\frac{30}{2}=15$

3. Determine the number of students using only Hulu:

The ratio of students using only Netflix to those using only Hulu is given as 5 : 4.

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

Substituting the value of Only Netflix (15):

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

$\text{Students using only Hulu}=\frac{15\times 4}{5}=12$

4. Determine the number of students using both 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).

$\text{Students using Netflix and Prime Video only}=30+(40\%\text{of}30)$

$\text{Students using Netflix and Prime Video only}=30+(\frac{40}{100}\times 30)=30+12=42$

5. Set up variables for the remaining unknown regions:

We are given that the number of students who use only Prime Video is equal to the number of students who use both Netflix and Hulu only.
Let this unknown value be $x$.

• Students using only Prime Video = $x$
• Students using both Netflix and Hulu only = $x$

6. Solve for x using total student count:

The sum of all 7 non-overlapping regions in the Venn diagram equals the total student count of 150:

$\left(\text{Only Netflix}\right)+\left(\text{Only Hulu}\right)+\left(\text{Only Prime Video}\right)+\left(\text{Netflix and Hulu only}\right)+\left(\text{Hulu and Prime Video only}\right)+\left(\text{Netflix and Prime Video only}\right)+\left(\text{All three}\right)=150$

Substitute all known and variable values:

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

$120+2x=150$

$2x=150-120$

$2x=30$

$x=15$

Thus, the number of students who use only Prime Video is 15.

7. Calculate the number of students who use only one streaming service:

$\text{Students using only one service}=\left(\text{Only Netflix}\right)+\left(\text{Only Hulu}\right)+\left(\text{Only Prime Video}\right)$

$\text{Students using only one service}=15+12+15=42$

Therefore, the total number of students who use only one streaming service is 42.