Jp27 wrote:
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.
Bunuel - Could you please show me how to solve this problem in 2 set matrix? Many thanks for all your responses so far. Cheers
Lets assume total number of offices is 10x, with window is W, with Bookshelves is B and with both bookshelf and window -D
From question :
1/5*10x = D
or D = 2x
Also we know that: W+B+D = 10x (all offices)
=>
W+B = 8xAnd we need W/B.
Stem 1:
W+D = 4/5 * (B+D)
We know D in terms of x, and we have 2 equations now in terms of W and B. So we can find out Wand B in terms of x and therefore ratio W/X. No need to solve further. Sufficient.
Stem 2:
3/10 (B+D) =D
(Note - B+D represent all offices with bookshelves and D represent offices with bookshelves and windows both)
Again we can find B in terms of x and from equation formed with question stem, we cna find W in terms of x and find ratio.
Sufficient.
Note solving any DS question with double matrix would be more time consuming.
hope it helps.