Instructions: Answer the questions based on the information given below. The Venn diagram given below shows the estimated readership of 3 daily newspapers (X, Y & Z) in a city. The total readership and advertising cost for each of these papers is as below. The total population of the city is estimated to be 14 million. The common readership (in lakhs) is indicated in the given Venn diagram. The number of people (in lakhs) who read at least one newspaper is
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Add up every separate region of the Venn diagram once each: the three only-regions, the three pairwise overlaps, and the centre.
Instead of finding each only-region first, we can reach the same answer straight from the inclusion-exclusion rule for three sets: at least one $= X + Y + Z - (X\cap Y) - (Y\cap Z) - (X\cap Z) + (X\cap Y\cap Z)$, where $X$, $Y$, $Z$ stand for the total readership of each paper.
From the Venn diagram, the pairwise overlap regions, each one including the centre, work out to: $X\cap Y = 2.5+0.5=3.0$, $Y\cap Z=1.5+0.5=2.0$, $X\cap Z=1.0+0.5=1.5$, and the centre $X\cap Y\cap Z=0.5$.
Plug the totals and overlaps into the formula: $8.7+9.1+5.6-3.0-2.0-1.5+0.5$.
Add the positive terms first: $8.7+9.1+5.6=23.4$, and $23.4+0.5=23.9$. Then subtract the overlaps: $23.9-3.0-2.0-1.5=17.4$.
This matches the region-by-region total exactly, since inclusion-exclusion is just a shortcut for adding every region once instead of working each only-value out separately.
Let's summarize:
At least one newspaper reader count is 17.4 lakh, which is option C.
Either method gets there, the formula route is just quicker once the pairwise overlaps are read carefully off the diagram.
