data suff...

[rohitjjw]

of 75 houses, 48 have a patio. how many houses have swimming pool.

1. 38 have patio but not swimming pool

2. no. of houses have patio and swimming pool is equal to no. of houses that have neither swimming pool nor patio.

now ans the quest in A, B, C, D, E pattern as usual.......

[niksworth]

75 H => 48 P

Q) SP?

Statement 1
38 P, but no SP
=> 10 P and SP

But what about rest 27 H without P? Do they have SP?

Insufficient.

Statement 2
No. of houses have P and SP = unknown
No. of houses having neither P nor SP = unknown

Insufficient.

Together
No. of houses have P and SP = 10
=> No. of houses having neither P nor SP = 10
No. of houses without P = 27
No. of houses without P and SP = 10
=> No. of houses without P but with SP = 17.

So, total no. of houses with SP = 17+ 10 = 27

Sufficient.

Answer C

[rohitjjw]

hi niksworth,

first of all thanks for your reply.
even i marked the same ans in the gmat prep software test but acc. to them the right ans is option B, i.e. , only statement 2 is enough. so got screwed up.....

[niksworth]

Ah! Major Major goof up. My sincere apologies. This is what happens when you jump the gun.

Statement 2 is sufficient. I'll explain how.

There are 75 houses
This can be divided into 48 Patio houses and 27 Non Patio houses. (given in question stem).

We need to find total houses with swimming pool.

48 Patio houses can be divided into two groups - Patio with Swimming Pool and Patio with no Swimming Pool.
Let Patio with Swimming Pool = x
Then Patio with no swimming Pool = 48-x

Similarly 27 Non Patio houses can be divided into - Non Patio with Swimming Pool and Non Patio with no Swimming Pool.
Let Non Patio with Swimming Pool = y
Then Non Patio with no Swimming Pool = 27-y.

According to Statement 2,
Patio with Swimming Pool = Non Patio with no Swimming Pool
=> x = 27-y
=> x+y = 27

But x + y is also equal to Patio with Swimming Pool + Non Patio with Swimming Pool = Total houses with Swimming Pool.
Thus Total houses with Swimming Pool = x + y = 27.

Hence, 2 is sufficient.

Hope this clarifies your doubt.