During a one-month period, an online video received 96,000 views (meaning that the video was viewed, in whole or in...

Phase 1: Owning the Dataset

Visual Representation

Since we're dealing with time intervals and ranges, a timeline is the perfect visualization:

Viewing Time Timeline:
0 sec ----[< 10 sec]----| 10 sec ----[10-50 sec]----| 50 sec ----[> 50 sec]---->
         ? views              24,000 views                34,000 views
                                                          
Total: 96,000 views

We know:

• \(\mathrm{Total\ views = 96,000}\)
• Views with TVT between 10-50 seconds (inclusive) = 24,000
• Views with TVT > 50 seconds = 34,000
• Views with TVT < 10 seconds = ?

Phase 2: Understanding the Question

We need to select:

1. Number of views with TVT less than 10 seconds
2. Number of views with TVT 10 seconds or more

Key insight: "TVT 10 seconds or more" includes BOTH the 10-50 second range AND the > 50 second range.

Phase 3: Finding the Answer

Step 1: Calculate views with TVT ≥ 10 seconds
\(\mathrm{Views\ with\ TVT \geq 10\ seconds = Views\ in\ [10-50\ sec] + Views\ in\ [> 50\ sec]}\)
\(\mathrm{= 24,000 + 34,000}\)
\(\mathrm{= 58,000}\)

Step 2: Calculate views with TVT < 10 seconds
Since all views must fall into one of our three categories:
\(\mathrm{Views\ with\ TVT < 10\ seconds = Total\ views - Views\ with\ TVT \geq 10\ seconds}\)
\(\mathrm{= 96,000 - 58,000}\)
\(\mathrm{= 38,000}\)

Let's update our visual:

Viewing Time Timeline:
0 sec ----[< 10 sec]----| 10 sec ----[10-50 sec]----| 50 sec ----[> 50 sec]---->
       38,000 views            24,000 views                34,000 views
                          |←------------ 58,000 views -----------→|

Verification

\(\mathrm{38,000 + 24,000 + 34,000 = 96,000}\) ✓

Phase 4: Solution

Statement 1 (TVT < 10 seconds): 38,000
Statement 2 (TVT ≥ 10 seconds): 58,000

Both values appear in our answer choices and satisfy all the given constraints.