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 ratio of the number of students who use exactly two streaming services to the number of students who use only Hulu.

The correct option is 29:4.

Step 1: Define the regions of the Venn diagram
Let the total number of college students surveyed be 150.
We can divide the students into seven mutually exclusive categories based on their usage of Netflix, Hulu, and Prime Video:

• Only Netflix = $n_{\text{N}}$

• Only Hulu = $n_{\text{H}}$

• Only Prime Video = $n_{\text{P}}$

• Only Netflix and Hulu = $n_{\text{N and H}}$

• Only Hulu and Prime Video = $n_{\text{H and P}}$

• Only Netflix and Prime Video = $n_{\text{N and P}}$

• All three services = $n_{\text{All}}$

Step 2: Calculate known values from the given statements

1. 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.

$n_{\text{H and P}}=30$

$30=2\times n_{\text{N}}$

$n_{\text{N}}=\frac{30}{2}=15$

2. The ratio of students who use only Netflix to those who use only Hulu is 5:4.

$\frac{n_{\text{N}}}{n_{\text{H}}}=\frac{5}{4}$

$\frac{15}{n_{\text{H}}}=\frac{5}{4}$

$n_{\text{H}}=\frac{15\times 4}{5}=12$

3. 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.

$n_{\text{N and P}}=30+(40\%\text{of}30)$

$n_{\text{N and P}}=30+12=42$

4. The number of students who use all three streaming services is 21.

$n_{\text{All}}=21$

5. The number of students who use only Prime Video is equal to the number of students who use both Netflix and Hulu only.

$n_{\text{P}}=n_{\text{N and H}}$

Step 3: Solve for remaining values using total surveyed students

The total number of students is 150. Summing all seven categories:

$n_{\text{N}}+n_{\text{H}}+n_{\text{P}}+n_{\text{N and H}}+n_{\text{H and P}}+n_{\text{N and P}}+n_{\text{All}}=150$

Substitute the values calculated above:

$15+12+n_{\text{P}}+n_{\text{N and H}}+30+42+21=150$

$120+n_{\text{P}}+n_{\text{N and H}}=150$

$n_{\text{P}}+n_{\text{N and H}}=30$

Since $n_{\text{P}}=n_{\text{N and H}}$:

$2\times n_{\text{N and H}}=30$

$n_{\text{N and H}}=15$

$n_{\text{P}}=15$

Step 4: Determine the required ratio

The total number of students who use exactly two streaming services is:

$\text{Students using exactly two services}=n_{\text{N and H}}+n_{\text{H and P}}+n_{\text{N and P}}$

$\text{Students using exactly two services}=15+30+42=87$

The number of students who use only Hulu is:

$n_{\text{H}}=12$

Calculating the ratio of students using exactly two services to students using only Hulu:

$\text{Ratio}=\frac{87}{12}$

Dividing both the numerator and the denominator by 3 gives:

$\text{Ratio}=\frac{29}{4}=29:4$

Hence, the final ratio is 29:4.