# Thread: help - venn diagrams - logic

1. ## help - venn diagrams - logic

Of 75 houses 48 have a patio. How many have a swimming pool?

1) 38 houses have a patio but not a swimming pool

2) houses with both patio and swimming pool = houses without them both

A) Statement 1) alone is sufficient
B) Statement 2) alone is sufficient

C) Statements 1) and 2) together are sufficient
D) Each statement alone is sufficient
E) Statement 1) and 2) together are not sufficient

2. Originally Posted by simone
Of 75 houses 48 have a patio. How many have a swimming pool?

1) 38 houses have a patio but not a swimming pool

2) houses with both patio and swimming pool = houses without them both

A) Statement 1) alone is sufficient
B) Statement 2) alone is sufficient

C) Statements 1) and 2) together are sufficient
D) Each statement alone is sufficient
E) Statement 1) and 2) together are not sufficient
C, the statements are sufficient together.

by statement (1), we know that 38 people of the 48 who have patios do not have swimming pools, it means that 10 have both. by statement (2), we know that the number of people who have neither is 10 also. this, we have accounted for everyone except those with only a swimming pool. this can just be the leftover people then. we know about 58 people so far, so it must be that 78 - 58 = 20 have pools but no patio. then we can see that the people with swimming pools are the sum of people with swimming pools only and the people who have both swimming pools and patios, which is 30

3. ## different correct answer quoted by book

that's what I've also come up with, same reasoning (except the total is 75, not 78, so the houses with only swimming pools would be 17), but the book I'm practicing on posts B) as the correct answer. Any clues please Jhevon?

4. Originally Posted by simone
that's what I've also come up with, same reasoning (except the total is 75, not 78, so the houses with only swimming pools would be 17), but the book I'm practicing on posts B) as the correct answer. Any clues please Jhevon?
ah, yes, indeed!

draw the Venn Diagram like this:

Forget statement (1), we only consider (2). (statement (1) by it self is not sufficient by the way).

draw the circles as i did before. now in the intersection write x (since we don't know how many are in there.

so in the section for P alone, we will have 48 - x and outside both circles we have x people with none (just like those with both).

since there are 75 people in all, the number of people who have swimming pools but not patios are 75 - (48 - x) - x - x = 27 - x

now all the people with swimming pools are those with both and those with swimming pools but not patios, and that is (27 - x) + x = 27

so statement (2) alone is sufficient after all

...sorry for misleading you, i always jump the gun with questions like these. if i realize (1) doesn't work, then i consider (1) AND (2). that is not the right strategy here. consider (1) alone, then consider (2) alone, then consider both

5. you're unfathomably good.