Of the 90 houses in a certain community, 60 have a garden. How many

Question

Of the 90 houses in a certain community, 60 have a garden. How many houses have a lobby?

1. 50 houses in the community have a garden but do not have a lobby.
2. The number of houses in the community that have both a garden and a lobby is equal to the number of houses that have neither.

Source : Experts Global

chetan2u · Accepted Answer

Hi..

Let's see the statements
1. 50 houses in the community have a garden but do not have a lobby.
60 had garden and 50 have only garden so 10 have both but nothing more.
Insufficient

2. The number of houses in the community that have both a garden and a lobby is equal to the number of houses that have neither.
 L_{only}+G_{only}+both+neither=90 
Let both=x=neither...
We are looking for L_only+x...
So  L_{only}+G_o+B+n=L_o+60+x=90......L_o+x=30 
So Answer 30
Sufficient

B

Bunuel · Answer

This is a copy of the following GMAT Prep question: https://gmatclub.com/forum/of-the-75-ho ... 60352.html

RenB · Answer

Hi  Bunuel   chetan2u   KarishmaB   Kinshook   ScottTargetTestPrep 
I made a 2*2 matrix for this one and got confused and got the qs wrong. But when I solved using the venn diagram, I could correctly answer the qs. Could you please guide me as to when to use a venn and when to use a 2 by 2?

chetan2u · Answer

Hi,

For a 2 by 2 matrix, you should be able to divide the elements in 4 interconnected items. 
For example: Male and Female are two elements of your 2*2 matrix
The next should be two elements that add you to the total in each element : (literate and non-literate) or (sportsman and non sportsman) or (<35yrs and 35&more) and so on.

Here you have houses and we are looking at two characteristics amongst these house. So Venn Diagram

sayan640 · Answer

Hi  RenB  ,  chetan2u

Attached is the 2*2 matrix.  GMATinsight 
USing 1st statement obviously it was not sufficient. 
But using 2nd statement it is sufficient to answer.
Let ,
 The number of houses in the community that have both a garden and a lobby is equal to the number of houses that have neither = x 
The number of  houses that have a lobby = x + 30 - x = 30
The answer will be 30. Hence B

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Of the 90 houses in a certain community, 60 have a garden. How many

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Of the 90 houses in a certain community, 60 have a garden. How many

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