Sets

[PGMAT]

In a certain building, 1/5 of the offices have both a window and bookshelves. If the rest of the offices in the building have either a window or bookshelves but not both, what is the ratio of the number of offices with a window but not bookshelves to the number of offices with bookshelves but not a window?

(1) The number of offices with a window is 4/5 the number with bookshelves.

(2) 3/10 of the offices with bookshelves also have a window.

Can someone explain how to solve this problem? Thank you.

[dhonu121]

In a certain building, 1/5 of the offices have both a window and bookshelves. If the rest of the offices in the building have either a window or bookshelves but not both, what is the ratio of the number of offices with a window but not bookshelves to the number of offices with bookshelves but not a window?

(1) The number of offices with a window is 4/5 the number with bookshelves.

(2) 3/10 of the offices with bookshelves also have a window.

Can someone explain how to solve this problem? Thank you.

Let us assume that the number of offices in the building is N.
Then number of offices containing both bookshelves and window is N/5.
Also, number of office containing only windows = x and only bookshe.. = y.
Hence x+y+n/5=n
or x+y = 4n/5.

From 1)x= (4/5)y. Using this and original equation both x and y can be obtained in terms of n and x/y will be the answer to the original question.

From 2)(3/10)(y+n/5) = n/5.
Using this and original eq. above we can again solve x and y in terms of n.

hence D is the right answer.

What is the OA ?