Bunuel wrote:
Of the C condominiums in a certain building complex, 2/3 have at least two bedrooms. If, of those, 1/4 have at least two bathrooms, which of the following expressions represents the number of condominiums in the complex with at least two bedrooms that do not have at least two bathrooms?
(A) C/2
(B) C/3
(C) C/4
(D) C/6
(E) C/12
2 ways to solve this
Method 1:We need the fraction of condominiums that have at least 2 bedrooms and do not have at least 2 bathrooms.
So using the information provided to us,
\(Answer = (1-1/4)(2/3)C = (3/4)(2/3)C = C/2\)
Read it as 3/4th of the condominiums that have at least 2 bedrooms (represented by 2/3rd of the C condominiums) don't have at least 2 bathrooms.
So, the answer is
A.
Method 2:If you're not comfortable with fractions, plug in a value for C that is divisible by both 3 and 4, since we'll need 2/3rd and 3/4th of that number.
Let's take C = 12.
Number of condominiums with at least 2 bedrooms = (2/3)*12 = 8
Number of condominiums with at least 2 bedrooms (the value we got above) that have at least 2 bathrooms = (1/4)*8 = 2
Number of condominiums with at least 2 bedrooms that
do not have at least 2 bathrooms = 8 - 2 = 6
Now, plug in the value of C in the answer choices and see which one gives us a
6.
(A) C/2 - 12/2 =
6(B) C/3 - 12/3 =
4(C) C/4 - 12/4 =
3(D) C/6 - 12/6 =
2(E) C/12 - 12/12 =
1Only choice
A gives us the correct value, hence that is the correct answer.
Note, if by any chance we get multiple choices that give us a 6, we'll need to pick some other value for C, try to intuitively find a number that you feel will make one or more of the remaining choices give a different answer (this will come with practice).
Finally, in short, the correct answer is
A.