IMO B
This problem can be solve using a Venn diagram.
Let's start rephrasing the question
P = number of houses that have a patio
S = number of houses that have a swimming pool
P&S = number of houses that have a swimming pool and a patio
NP&S = number of houses that have neither a swimming pool nor a patio
75 = P + S - P&S + NP&S and we know that P =48 so
75 = 48 + S - P&S + NP&S ---> S = 27 + P&S - NP&S
Now take a look at the statements
1) 38 houses have a patio but no swimming pool
this means that 38 houses only have patio so
P = 38 + P&S ---> 48 = 38 + P&S ---> P&S = 10
can you get the value of S in this equation S = 27 + P&S - NP&S, using that P&S = 10? No insufficient.
2) Number of houses that have a swimming patio and a swimming pool is equal to the number of houses that have neither pool nor patio
P&S = NP&S
S = 27 + P&S - NP&S ---> S = 27 sufficient
Sets
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Source: Beat The GMAT — Data Sufficiency |
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mikeCoolBoy
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Stuart@KaplanGMAT
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Mike's solution is great!Claret wrote:Of 75 houses, 48 have a patio. How many houses have a swimming pool?
a. 38 houses have a patio but no swimming pool
b. Number of houses that have a swimming patio and a swimming pool is equal to the number of houses that have neither pool nor patio
I just wanted to add the general 2-set equation which can be very useful on this type of question:
True # of Objects = (# in group 1) + (# in group 2) + (# in neither group) - (# in both groups)
or
True # = G1 + G2 + neither - both
As Mike applied it to this question:
75 = 48 + pool + neither - both
(1) tells us that "both" = 10 (if 48 have a patio, and 38 have only a patio, then 48-38=10 have both).
So: 75 = 48 + pool + neither - 10
Still 2 variables, can't solve... insufficient.
(2) neither = both, so
75 = 48 + pool + neither - neither
75 = 48 + pool... we can certainly solve for "pool".. sufficient.
(2) is sufficient, (1) isn't... choose (B).
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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ghacker
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Actually without knowing any formula ---- one can answer the question using logic
There are 75 houses , and there are two characteristics -- Patio and swimming pool so what can happen ?
We know from the given that only 48 have a patio what can we derive from this ............ the 48 might or might not have SP , but we don't know how many houses are with out both ........... so lets look at the statements
Statement I :38 houses have a patio but no swimming pool
This doesn't give the with out figure so insufficient
Statement II : Number of houses that have a swimming patio and a swimming pool is equal to the number of houses that have neither pool nor patio
Aha ! this give the neither case so its sufficient so ans = B
There are 75 houses , and there are two characteristics -- Patio and swimming pool so what can happen ?
We know from the given that only 48 have a patio what can we derive from this ............ the 48 might or might not have SP , but we don't know how many houses are with out both ........... so lets look at the statements
Statement I :38 houses have a patio but no swimming pool
This doesn't give the with out figure so insufficient
Statement II : Number of houses that have a swimming patio and a swimming pool is equal to the number of houses that have neither pool nor patio
Aha ! this give the neither case so its sufficient so ans = B
