ExpertsGlobal5
There are 600 homes in a neighborhood, some of which are government owned. How many of these homes are government owned?
(1) The number of homes that do not have air conditioning is 50 percent more than the number of homes that do.
(2) The number of homes that have air conditioning is four times the number of government owned homes.
Explanation: Let the number of homes that are government owned that do not have air conditioning be G.
Let the number of homes that have air conditioning but are not government owned be A.
Let the number of homes that are both government owned and have air conditioning be B.
Let the number of homes that are neither government owned nor have air conditioning be X.
Since there are 600 homes in a neighborhood: G + A + B + X = 600. (Equation I)
We need to find whether the value of G + B can be determined. Statement (1) G + X = 1.5(A + B) (Equation II)
Substituting Equation II into Equation I does not help determine the value of G + B.
Hence, Statement (1) is insufficient. Statement (2) (A + B) = 4(G + B) (Equation III)
Substituting Equation III into Equation I does not help determine the value of G + B.
Hence, Statement (2) is insufficient. As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements.
Statement (1) and Statement (2) combined Substituting Equation II into Equation I:
G + A + B + X = 600
G + X + A + B = 600
1.5(A + B) + (A + B) = 600
2.5(A + B) = 600
A + B = 240
Substituting the value of (A + B) in Equation III:
(A + B) = 4(G + B)
240 = 4(G + B)
G + B = 240/4
G + B = 60
It is possible to determine the value of G + B.
Hence, Statement (1) and Statement (2) combined are sufficient. C is the correct answer choice.