What is answer .. why statement 2 can't give answer?

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vr4indian: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sat Jun 07, 2008 5:48 am

by vr4indian » Tue Sep 16, 2008 5:47 am

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.

Source: Beat The GMAT — Data Sufficiency | Tue Sep 16, 2008 5:47 am

krishnamurthyu: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Fri May 04, 2007 3:51 am

by krishnamurthyu » Tue Sep 16, 2008 7:56 am

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

4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Tue Sep 16, 2008 9:31 am

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

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