Advertising and Public Relations · TEE · practice

Reach with overlapping media audiences

Optional numerical practice

Extra drills; no claim that these exact questions or allocated marks appeared in TEE

Optional practice question. A campaign reaches 4,000 target members through radio and 3,000 through digital placements. Of these, 1,000 people are reached by both. The target population is 10,000. Find combined unique reach and percentage reach. [3 practice marks]

Answer

Authored illustration: these numbers were chosen to explain a faculty-note concept. No matching supplied-data question was found in the 14 recovered APR papers. Standalone calculation drills are optional practice; their marks are author-set.

Given

Radio reachDigital reachOverlapTarget
4,0003,0001,00010,000

To find

Unduplicated combined reach and its percentage.

Formula and why

|A\cup B|=|A|+|B|-|A\cap B|LaTeX: |A\cup B|=|A|+|B|-|A\cap B|
R_{\%}=\frac{|A\cup B|}{N}\times100LaTeX: R_{\%}=\frac{|A\cup B|}{N}\times100

The shared group appears once in each media count. Subtract it once so every person is counted exactly once.

Step-by-step solution

Step 1. Add the two media counts

4000+3000=7000LaTeX: 4000+3000=7000

Step 2. Remove the duplicate count

7000-1000=6000\text{ unique people}LaTeX: 7000-1000=6000\text{ unique people}

Step 3. Divide by the target population

6000\div10000=0.6LaTeX: 6000\div10000=0.6

Step 4. Express as a percentage

0.6\times100=60\%LaTeX: 0.6\times100=60\%

Final answer: 6,000 unique people; 60% reach.