Of the guests at a charity fundraiser

[selfmade]

Of the guests at a charity fundraiser, 180 own both a house in the Hamptons and a house in Palm Beach. If not every guest at the fundraiser owns a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests own a house in Palm Beach.

(2) Two-thirds of the guests own a house in the Hamptons.

[selango]

P(HnB)=180

Total guests=x

stmt1,

P(B)-P(HnB)=X/2

P(B)-180=x/2

P(B)=180+x/2

No info abt Hamptons

Insuff

stmt2,

P(H)-P(HnB)=2x/3

P(H)-180=2x/3

P(H)=180+2x/3

No info abt palm beach

Insuff

Combining 1 and 2

P(B)/P(H)=(180+x/2)/(180+2x/3)

=(360+x)/2/(540+2x)/3

We dont know value of X

Insuff

Pick E

[goyalsau]

Should be E,

from Ist statement if
X is the total no. of guest , p is people who only own P house.

x/2=180+p

from IInd statement if
X is the total no. of guest , h is people who only own h house.
2x/3=180+h

can't solve even with the statements together.

By the way
What is the official Answer?

[selfmade]

OA is E

[goyalsau]

What is the Source of the Question.
Seems to be a very intimidating..

[sumit.sinha]

Of the guests at a charity fundraiser, 180 own both a house in the Hamptons and a house in Palm Beach. If not every guest at the fundraiser owns a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests own a house in Palm Beach.

(2) Two-thirds of the guests own a house in the Hamptons.

_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________x_______________180+x
Not Palm Beach___y_________________z_______________y+z
Total__________180+y_____________x+z_______________T

We need to find x/y?

(1)
180+x = T/2
i.e. x = (T/2) - 180 --------------------------1
also y+z = T/2
i.e y = (T/2) - z
Or z = (T/2) - y ------------------------------2
INSUFFICIENT

(2)
180 + y = 2T/3
i.e. y = (2T/3) - 180 -----------------------3
also x+z = T/3
i.e. x = (T/3) - z
OR z = (T/3) -x ------------------------------4
INSUFFICIENT

(1) and (2) together
using equations 2 and 4: i.e. equating value of z
we get T = 6(x + y) ------------------------5

Now using equations 1 and 5
we get the equation 2x + 3y = 180 -------6

Now using equation 3 and 5
we get the equation 4x + 3y= 180 --------7

Solving equation 6 and 7 we get
x =0
and y=60

Optionally, we can even complete the matrix as:
_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________0_______________180
Not Palm Beach___60_______________120______________180
Total___________240______________120_______________360

Therefore, Ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach = 0

CORRECT ANSWER (C)

How about this? LOL

[goyalsau]

Of the guests at a charity fundraiser, 180 own both a house in the Hamptons and a house in Palm Beach. If not every guest at the fundraiser owns a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests own a house in Palm Beach.

(2) Two-thirds of the guests own a house in the Hamptons.

_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________x_______________180+x
Not Palm Beach___y_________________z_______________y+z
Total__________180+y_____________x+z_______________T

We need to find x/y?

(1)
180+x = T/2
i.e. x = (T/2) - 180 --------------------------1
also y+z = T/2
i.e y = (T/2) - z
Or z = (T/2) - y ------------------------------2
INSUFFICIENT

(2)
180 + y = 2T/3
i.e. y = (2T/3) - 180 -----------------------3
also x+z = T/3
i.e. x = (T/3) - z
OR z = (T/3) -x ------------------------------4
INSUFFICIENT

(1) and (2) together
using equations 2 and 4: i.e. equating value of z
we get T = 6(x + y) ------------------------5

Now using equations 1 and 5
we get the equation 2x + 3y = 180 -------6

Now using equation 3 and 5
we get the equation 4x + 3y= 180 --------7

Solving equation 6 and 7 we get
x =0
and y=60

Optionally, we can even complete the matrix as:
_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________0_______________180
Not Palm Beach___60_______________120______________180
Total___________240______________120_______________360

Therefore, Ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach = 0

CORRECT ANSWER (C)

How about this? LOL

Its very good that you solved it but can you please explain the reasoning behind the 2 equations that i marked in red above. What is the Base of those 2 questions. As per my knowledge no where in the statement any thing is given of that sort.
I will very pleased if you share your reasoning behind and next time whenever i put to answer E for any question I will be more care full that's for sure.

[sumit.sinha]

Of the guests at a charity fundraiser, 180 own both a house in the Hamptons and a house in Palm Beach. If not every guest at the fundraiser owns a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests own a house in Palm Beach.

(2) Two-thirds of the guests own a house in the Hamptons.

_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________x_______________180+x
Not Palm Beach___y_________________z_______________y+z
Total__________180+y_____________x+z_______________T

We need to find x/y?

(1)
180+x = T/2
i.e. x = (T/2) - 180 --------------------------1
also y+z = T/2
i.e y = (T/2) - z
Or z = (T/2) - y ------------------------------2
INSUFFICIENT

(2)
180 + y = 2T/3
i.e. y = (2T/3) - 180 -----------------------3
also x+z = T/3
i.e. x = (T/3) - z
OR z = (T/3) -x ------------------------------4
INSUFFICIENT

(1) and (2) together
using equations 2 and 4: i.e. equating value of z
we get T = 6(x + y) ------------------------5

Now using equations 1 and 5
we get the equation 2x + 3y = 180 -------6

Now using equation 3 and 5
we get the equation 4x + 3y= 180 --------7

Solving equation 6 and 7 we get
x =0
and y=60

Optionally, we can even complete the matrix as:
_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________0_______________180
Not Palm Beach___60_______________120______________180
Total___________240______________120_______________360

Therefore, Ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach = 0

CORRECT ANSWER (C)

How about this? LOL

Its very good that you solved it but can you please explain the reasoning behind the 2 equations that i marked in red above. What is the Base of those 2 questions. As per my knowledge no where in the statement any thing is given of that sort.
I will very pleased if you share your reasoning behind and next time whenever i put to answer E for any question I will be more care full that's for sure.

"also y+z = T/2" - It means as One-half of the guests own a house in Palm Beach, so the remaining one-half of the guests do not own a house in Palm Beach.

Similarly,
"also x+z = T/3" - It means as Two-thirds of the guests own a house in the Hamptons, so the remaining one-third of the guests do not own a house in the Hamptons.

[kvcpk]

(1) and (2) together
using equations 2 and 4: i.e. equating value of z
we get T = 6(x + y) ------------------------5

You were right till this point.

Using eqtns 2 and 4,
T/2 -y = T/3 -x
T/2 - T/3 = y-x
T = 6(y-x) ....................6

Using, eqtns 1 and 5,
x = 3(y-x) -180
3y-4x=180

Using eqtns 3 and 5,
y = 4(y-x) - 180
3y-4x = 180

This is same as the above equation.

So its not solvable.

Hope this helps!!

[sumit.sinha]

(1) and (2) together
using equations 2 and 4: i.e. equating value of z
we get T = 6(x + y) ------------------------5

You were right till this point.

Using eqtns 2 and 4,
T/2 -y = T/3 -x
T/2 - T/3 = y-x
T = 6(y-x) ....................6

Using, eqtns 1 and 5,
x = 3(y-x) -180
3y-4x=180

Using eqtns 3 and 5,
y = 4(y-x) - 180
3y-4x = 180

This is same as the above equation.

So its not solvable.

Hope this helps!!

Great Catch!!!

Thanked you

[goyalsau]

Of the guests at a charity fundraiser, 180 own both a house in the Hamptons and a house in Palm Beach. If not every guest at the fundraiser owns a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests own a house in Palm Beach.

(2) Two-thirds of the guests own a house in the Hamptons.

_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________x_______________180+x
Not Palm Beach___y_________________z_______________y+z
Total__________180+y_____________x+z_______________T

We need to find x/y?

(1)
180+x = T/2
i.e. x = (T/2) - 180 --------------------------1
also y+z = T/2
i.e y = (T/2) - z
Or z = (T/2) - y ------------------------------2
INSUFFICIENT

(2)
180 + y = 2T/3
i.e. y = (2T/3) - 180 -----------------------3
also x+z = T/3
i.e. x = (T/3) - z
OR z = (T/3) -x ------------------------------4
INSUFFICIENT

(1) and (2) together
using equations 2 and 4: i.e. equating value of z
we get T = 6(x + y) ------------------------5

Now using equations 1 and 5
we get the equation 2x + 3y = 180 -------6

Now using equation 3 and 5
we get the equation 4x + 3y= 180 --------7

Solving equation 6 and 7 we get
x =0
and y=60

Optionally, we can even complete the matrix as:
_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________0_______________180
Not Palm Beach___60_______________120______________180
Total___________240______________120_______________360

Therefore, Ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach = 0

CORRECT ANSWER (C)

How about this? LOL

Its very good that you solved it but can you please explain the reasoning behind the 2 equations that i marked in red above. What is the Base of those 2 questions. As per my knowledge no where in the statement any thing is given of that sort.
I will very pleased if you share your reasoning behind and next time whenever i put to answer E for any question I will be more care full that's for sure.

"also y+z = T/2" - It means as One-half of the guests own a house in Palm Beach, so the remaining one-half of the guests do not own a house in Palm Beach.

Similarly,
"also x+z = T/3" - It means as Two-thirds of the guests own a house in the Hamptons, so the remaining one-third of the guests do not own a house in the Hamptons.

Thanks for your comment Can you please explain the equation 5
How to get that.

[selfmade]

This question is from Manhattan Practice Test

[goyalsau]

Of the guests at a charity fundraiser, 180 own both a house in the Hamptons and a house in Palm Beach. If not every guest at the fundraiser owns a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests own a house in Palm Beach.

(2) Two-thirds of the guests own a house in the Hamptons.

_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________x_______________180+x
Not Palm Beach___y_________________z_______________y+z
Total__________180+y_____________x+z_______________T

We need to find x/y?

(1)
180+x = T/2
i.e. x = (T/2) - 180 --------------------------1
also y+z = T/2
i.e y = (T/2) - z
Or z = (T/2) - y ------------------------------2
INSUFFICIENT

(2)
180 + y = 2T/3
i.e. y = (2T/3) - 180 -----------------------3
also x+z = T/3
i.e. x = (T/3) - z
OR z = (T/3) -x ------------------------------4
INSUFFICIENT

(1) and (2) together
using equations 2 and 4: i.e. equating value of z
we get T = 6(x + y) ------------------------5

Now using equations 1 and 5
we get the equation 2x + 3y = 180 -------6

Now using equation 3 and 5
we get the equation 4x + 3y= 180 --------7

Solving equation 6 and 7 we get
x =0
and y=60

Optionally, we can even complete the matrix as:
_____________Hamptons_________Not Hamptons________Total
Palm Beach_____180________________0_______________180
Not Palm Beach___60_______________120______________180
Total___________240______________120_______________360

Therefore, Ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach = 0

CORRECT ANSWER (C)

How about this? LOL

Its very good that you solved it but can you please explain the reasoning behind the 2 equations that i marked in red above. What is the Base of those 2 questions. As per my knowledge no where in the statement any thing is given of that sort.
I will very pleased if you share your reasoning behind and next time whenever i put to answer E for any question I will be more care full that's for sure.

"also y+z = T/2" - It means as One-half of the guests own a house in Palm Beach, so the remaining one-half of the guests do not own a house in Palm Beach.

Similarly,
"also x+z = T/3" - It means as Two-thirds of the guests own a house in the Hamptons, so the remaining one-third of the guests do not own a house in the Hamptons.

Thanks for your comment Can you please explain the equation 5

Waiting for your reply????????????
How to get that.

[kvcpk]

Thanks for your comment Can you please explain the equation 5

Waiting for your reply????????????
How to get that.

Hey, See my post above.
Eqtn5 is wrong. I wrote the right eqtn.

[Sam_GMAT]

P(HnB)=180

Total guests=x

stmt1,

P(B)-P(HnB)=X/2

P(B)-180=x/2

P(B)=180+x/2

No info abt Hamptons

Insuff

stmt2,

P(H)-P(HnB)=2x/3

P(H)-180=2x/3

P(H)=180+2x/3

No info abt palm beach

Insuff

Combining 1 and 2

P(B)/P(H)=(180+x/2)/(180+2x/3)

=(360+x)/2/(540+2x)/3

We dont know value of X

Insuff

Pick E

Statement 1. Your equation P(B)=180+x/2, seems to assume that statement 1 talks abt people who ONLY own house in Palm Beach. Correct me if I am wrong?