Question

In a market survey, 20% opted for product $A$, 60% for $B$, and the rest were uncertain. If the difference between those who opted for $B$ and those uncertain is $720$, how many individuals were surveyed?

• A. 1440
• B. 1800
• C. 3600
• D. Data inadequate

Hint:

Translate verbal percent gaps into a single net percent and equate it to the given difference to find the total.

Answer 1

The Correct Option is B

Uncertain $=100\%-20\%-60\%=20\%$.
Difference $=60\%-20\%=40\%$ of the total.
So $0.40\times N=720 \Rightarrow N=\dfrac{720}{0.40}= \boxed{1800}$. 

Answer 2

Instead of computing the uncertain percentage first and then equating a percentage difference directly to \(720\), we can use the ratio between the "opted for B" and "uncertain" groups to find their actual numbers first, and check each option.

1. Option A (1440): Since uncertain \(=100\%-20\%-60\%=20\%\), the groups "opted for B" (\(60\%\)) and "uncertain" (\(20\%\)) are in ratio \(3:1\). Their difference of \(2\) parts corresponds to \(720\), so \(1\) part \(=360\). Thus, "opted for B" \(=3\times360=1080\), which is \(60\%\) of the total, giving total \(N=\dfrac{1080}{0.6}=1800\), not \(1440\), so this option is incorrect.
2. Option B (1800): As computed, the total surveyed \(N=1800\), matching this option.
3. Option C (3600): This is exactly twice the computed total of \(1800\), so it is incorrect.
4. Option D (data inadequate): Since the ratio method gives a unique, fully determined value of \(N\), the data is sufficient, ruling out this option.

Using the \(3:1\) ratio between the "B" and "uncertain" groups confirms the total surveyed is \(1800\).

Hence, the correct answer is option B: 1800.