Study the following information carefully and answer the questions based on it.A salesman visits 274 houses in a town to find out the views…

Solution:

Given information:

Total houses, n(U) = 274

Number of houses which uses all the three only, n(X & Y & Z) = 22

Number of houses which uses X and Z and also Y,

n(X & Z) = no.of houses which uses all the three + no.of houses which uses X and Z but not Y

= 14 + 22

n(X & Z)= 36

Number of houses which uses Y and Z and also X, n(Y & Z) = 39

Number of houses which uses X and Y and also Z,n(X & Y)

=> 157 - ( 14 + 22 + n(X & Y only) ) = 98

157 - ( 36 + n(X & Y only) ) = 98

157 - 36 - n(X & Y only) = 98

157 - 36 - 98 = n(X & Y only)

n(X & Y only) = 157 - 134

n(X & Y only) = 23

n(X & Y) = no.of houses which uses all the three + no.of houses which uses X and Y only

= 23 + 22

n(X & Y)= 45

Number of houses which uses X, n(X) =157

Number of houses which uses Y,

n(Y)= Number of houses which use only Y + houses which use only X and Y + houses which use all the three + houses which use only Y and Z

n(Y) = 48 + 23 + 22 + (39 -22)

n(Y) = 110

n(X or Y or Z)

= n(X) + n(Y) + n(Z) - n(X & Y) - n(Y &Z) - n(X & Z) + n(X & Y & Z)

274 = 157 + 110 + n(Z) - 45 - 39 - 36 + 22

274 = 289 - 120 + n(Z)

n(Z) = 274 - 169

n(Z) = 105

Houses which use only Z = n(Z) - (14 + 22 + 17)

= 105 - 53

= 52

So, the correct option is 3). 52