Question

In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive

Answer 1

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Total number of households in the city = 150,000

Percentage of households have cable television = 80%

Percentage of households have video cassette = 20%

So, by the rule of sets:

$n(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\100=80+60-n(A\cap B)\\\\100-140=-n(A\cap B)\\\\-40=-n(A\cap B)\\\\n(A\cap B)=40\%$

So, Number of households that have both is given by

$\dfrac{40}{100}\times 150000\\\\=60000$

It can be of maximum 90,000 because if it is 120000,

Then remaining(=30000) will be split into 80:60 i.e. 4:3 .

it can't be less like 30000.

Hence, Option 'C' is correct.