nidhis.1408 wrote:In a certain apartment complex, 1/4 of the apartments have terraces. If 1/8 of the apartments, including 1/5 of those that have terraces, have skylights, what fraction of the apartments have neither terraces nor skylights?
a. 17/20
b. 27/40
c. 13/40
d. 5/17
e. 1/8
Hi nidhis.1408!
As soon as I see the word "neither" in a problem where we have 2 different descriptions of something (w/ terrace, vs w/skylights), I know I'm in an overlapping sets problem, so it is time to build my matrix. To start, I build a 3x3 grid and look for descriptions that can be BOTH. I will use one of these to label my top left box. So it sounds like apartments can have BOTH terraces AND skylights, so those will start my labeling...
Now, to get the other labels, I just think of the exact opposite things... what is the opposite of "Terrace"? - ah "NO Terrace"! Then finish off with totals...
Okay, since there are no real numbers given, just fractions I"m going to pick a smart number for my total. If these had been percents I would pick 100, but with fractions I choose a number divisible by all of those denominators, so what about 80 just to be safe?
So, 80 is my total, then:
1/4(80)=20 have terraces,
1/8(80)=10 have skylights,
and
1/5(terraces) ALSO have skylights, so 1/5(20)=4.
Let's plug in, circle the box we want and fill in the other values by adding and subtracting across rows or down the columns...
Now, the box we want is 54...but that isn't the fraction we're looking for. We need to take that number and divide it by the total (80).
54/80 = 27/40.
Our answer is B.
Hope this helps!
Whit
