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In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people were diagnosed with high blood pressure. what is the minimum number of people who were having diabetes and high blood pressure
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The correct answer is:
20
$\mathrm{n}(\mathrm{T})=50$
$\mathrm{n}(\mathrm{D})=30$
$\mathrm{n}(\mathrm{H})=40$
$\mathrm{n}(\mathrm{T})=\mathrm{n}(\mathrm{D})+\mathrm{n}(\mathrm{H})-\mathrm{n}(\mathrm{DnH})$
$50=30+40-\mathrm{n}(\mathrm{D} \cap \mathrm{H})$
$\mathrm{n}(\mathrm{D} \cap \mathrm{H})=70-50=20$
Number of people having diabetes and high blood pressure $=20$
$\mathrm{n}(\mathrm{D})=30$
$\mathrm{n}(\mathrm{H})=40$
$\mathrm{n}(\mathrm{T})=\mathrm{n}(\mathrm{D})+\mathrm{n}(\mathrm{H})-\mathrm{n}(\mathrm{DnH})$
$50=30+40-\mathrm{n}(\mathrm{D} \cap \mathrm{H})$
$\mathrm{n}(\mathrm{D} \cap \mathrm{H})=70-50=20$
Number of people having diabetes and high blood pressure $=20$
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