Data Sufficiency

50% of the people in a certain city have a Personal Computer and an Air-conditioner . What percent of people in the city have a personal computer but not an Air-conditioner.

(1) 60% of the people in the city have a Personal Computer.

(2) 70% of the people in the city have an Air-conditioner.

A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Given:
N(Pc & Ac ) 50%

Asked:
NPc & ~Ac = ?

1. NPc = 60%
N (Pc & ~Ac) = Npc - N(Pc & Ac)
=60% - 50%
=10%
Ans:A or D

2. NAc = 70%
Here we dont know,N(Pc U Ac ) = 100% , i.e is not mentioned.
Hence we can't assume ( There could be possible this survery has TV also then Ac +Pc+Tv = 100%, even then with condition-1, we can identiy N (Pc & ~Ac)% )
N(Pc U Ac) = 100%, it could be 80% or 90%,Hence we can't apply:
N(Pc U Ac) = N(Pc) + N (Ac) - N (Pc & Ac).

Hence. Ans : A

We dont know how many people do not have neither PC nor AC