draw a diagram?

[robbie523]

Of the 75 houses in a certain community, 48have a patio. How many of the houses inthe community have a swimming pool?

(1) 38 of the houses in the community have apatio but do not have a swimming pool.

(2) The number of houses in the communitythat have a patio and a swimming pool is equal to the number of houses in thecommunity that have neither a swimming pool nor a patio.


I'm confused of this quesiton is because, the question is asking how many of the houses in the community have a swimming pool, not how many houses only have a swimming pool, but the OA seems to mislead me more

[ashis979]

Tried my best to recreate a table, apologies if it's pretty messed up. Stuff in bold are the items you can solve for based on what is provided.

This is what the question is telling you:

________Patio_____No Patio_____Total
Pool____ ___ _____ ______ _____ [?]
No Pool
Total___ 48 ______ 27 _________ 75

From the question you can only determine that the # of houses that DO NOT have a patio = 27.

STMT 1:
________Patio_____No Patio_____Total
Pool____ 10______ X ______ ___ [?] or X+10
No Pool_ 38 ______ ______ ______
Total___ 48 ______ 27 _________ 75

From Stmt 1, you can only solve for the # of houses that have BOTH a patio and a pool. You are trying to solve for the top right box...NOT SUFFICIENT.

STMT 2:
________Patio_____No Patio_____Total
Pool____ X__ _____ 27-X _____ 27
No Pool 48-X ______ X ___ _____ 48
Total___ 48 ______ 27 _________ 75

From Stmt 2, you can assume that # of houses with patio & pool = # of houses without patio & pool = X. So, when you solve across for the # of houses that DO NOT have a pool (Row 2, not counting header) you get 48-X+X=48. Therefore, # of houses without a pool=48 and the # of houses WITH a pool=75-48=27. Alternatively, just solve across for the # of houses that HAVE a pool (Row 1, not counting header), you get X+27-X=27. So Stmt 2 is SUFFICIENT. So the answer is B.

[robbie523]

I still have one question in mind!


we do know the totall number of house that DO NOT have pool,


first, the total number of people who has pool should not be 27, nothing in the question is saying that, 48 house hv patio only

the total number of people who has no pool can not be 48, since the question only say 48 is the total number of patio

48 is the number given to regard the patio and no patio! how can it be used for pool and no pool？ can you explain

27 is the number that has pool only and has no patio! this number doesn't need to be minus X again! X is the part that has both, which 27 is already a number that hasn't include both

75 - X + X = 75 which this number has cancelled out the intersection and included the the part that has neither.

well, thanks for your graph thou, great help. my I'm just stuck here with confusion

[ashis979]

Ok, here is a more detailed explanation:

-----
1. "we do know the totall number of house that DO NOT have pool"
Yes, we do not. If we did, then we'd have the answer immediately. It would just be the total number of houses in the community less that number.

2. "first, the total number of people who has pool should not be 27
It's not a question of what the total number of houses that have pools should or should not be. That is what the question is asking you to find, and it just so happens to be that 27 houses in the community have a pool (be it houses that just have a pool only or houses that have both a pool and a patio).

3. "nothing in the question is saying that, 48 house hv patio only"
No, but the question does say that 48 of the 75 houses in the community have a patio (be is houses that just have a patio or houses that have both a patio and a pool).

4. "the total number of people who has no pool can not be 48, since the question only say 48 is the total number of patio"
Again, I'm not sure why you are going about what the number of houses that do not have a pool can or cannot be. The number of houses that do not have a pool has unlimited possibilities from 0-75. But as we know from the stem- the number of houses that have a patio is 48, it means:
# of houses with patio only+# of houses with patio and pool=48...(i)

We also know:
# of houses with no pool=# of houses with patio only+# of houses with neither...(ii)

From statement 2 we know that # of houses with both=# of houses with neither...(iii)

So, let's say that the number of houses with both=X
Equation (iii) is now,
# of houses with both=# of houses with neither=X. Plug this into equation (i),

# of houses with patio only+X=48
=> # of houses with patio only=48-X...(iv). Plug into equation (ii),

# of houses with no pool=48-X+# of houses with neither
=> From equation (iii) we already know that # of houses with neither=X.
So, # of houses with no pool=48-X+X=48
Therefore, # of houses with a pool=75-48=27...THE ANSWER.

5. "48 is the number given to regard the patio and no patio! how can it be used for pool and no pool？ can you explain"
48 is not the number with regards to patio and no patio, it is the number with regards to the houses having a patio...read the question again. See equation (i) above to see what its components are.

6. "27 is the number that has pool only and has no patio! this number doesn't need to be minus X again! X is the part that has both, which 27 is already a number that hasn't include both"
27 is NOT the number that has pool only. The number of houses that have pool only is 27-X (the total # of houses that have a pool MINUS the # of houses that have a pool and a patio, and from equation (iii) above that number is X).
-----

Given that the intersection of having both and the intersection of having neither are the same number, it is essentially: # of houses with a patio=# of houses without a pool.

Hope that helps.

[tohellandback]

Please check the image attached.

we need to know how many people have neither, to answer the question.
1) we don't know how many people have neither. NOT SUFF

2) from this statement , we know that no of houses which have neither is 10. check the image.

so , S+48+10=75
you can find S
SUFF

so B

[robbie523]

thank you thank you thank you, you finally solved my douts.


the house that has pool, minus the house have both, and plus the house of neither, = the house that don't have patio

the house that has patios, minus the house have both, plus the house that have neighter = the house that don't have pool!

I was thinking in the wrong direction, I always tried combined two number of 48 and 27 together, which had great mis understanding

[ashis979]

Yes, you have it down now.