In a certain apartment building, residents are allowed to own exactly one dog, exactly one cat, or one dog and one cat…

In a certain apartment building, residents are allowed to own exactly one dog, exactly one cat, or one dog and one cat. No other pets are allowed. There are 22 cats and 17 dogs in the building. If there are 25 apartments that contain only one dog or one cat, how many apartments, in total, contain pets?

(A) 27
(B) 32
(C) 35
(D) 39
(E) 42

Thank you. 🙂

Weekend Challenge – Epic playlist

Thanks to Hurricane Sandy, this has been a rough week for a lot of people. If you’re feeling charitable, please note that I am still giving away Math Guides for donations to the Red Cross. Let me note, before we get into this, that these challenge questions are WAY harder than anything you’d see on (more…)

“Is there a math way?”

When a student asks me how to solve a math problem, my default response is to show, if possible, how to solve it by plugging in, backsolving, or guesstimating. I do this because I figure if the “math way” was obvious, the student wouldn’t be asking me for help in the first place. Besides, problem (more…)

Direct and Inverse Proportionality (Variation)

There are two kinds of proportionality (some call these problems “variation” problems, but I’m sticking with proportionality) problems that you might see on the SAT: direct and inverse. I’m going to cover both here since I’m in the business of preparing you for any eventuality, but you should know that the the former is much (more…)

Parabola Schmarabola

Leonardo da Vinci totally <3’d parabolas. The parabola is actually a hugely important mathematical concept with tons of forms, properties, and even its own history. It can open up, down, left, right, or any other direction. It can be used to graph the trajectory of my last AT&T cell phone that I threw in a (more…)