Berbatov wrote:
Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can point 1/4 of the same house in b hours. Working together, Alan and Bob can paint 1/3 of the house in c hours. What is the value of b in terms of a and c?
a) (3ac)/(a+c)
b) (4a-12c)/(3ac)
c) (3ac)/(4a-12c)
d) (ac)/(a+2c)
e) (ac)/(a+c)
Plugging In AND Hidden Plug In all in one question!
Plugging In: Any time I see variables that are repeated in the answer choices, I'm going to lean toward plugging in. Let's just make up values for a and b.
Hidden Plug In: On work/rate questions, we can often make our lives easier by changing the definition of the job. Instead of painting a house, let's make the job solving 24 GMAT questions.
Alan can solve the 24 questions in a hours. Let's make a=6. So Alan can solve 4 questions per hour.
Bob can solve 1/4 the number of GMAT questions (so 6 questions) in b hours. Let's make b=3. So Bob can solve 2 questions per hour.
Together they can solve 4+2=6 questions per hour.
Together they can solve 1/3 the number of GMAT questions (so 8 questions) in c hours. How long does it take them to solve 8 questions at a rate of 6 questions per hour? 1.333. So c=1.333.
What is the value of b in terms of a and c? We have b=3. Let's go find that in the answer choices using a=6 and c=1.333.
(A) 24/7.333 Wrong.
(B) (24-16)/24 = 8/24 Wrong.
(C) 24/(24-16) = 24/8 = 3 Keep it.
(D) 8/8.667 Wrong.
(E) 8/7.333 Wrong.
Answer choice C.
ThatDudeKnowsPluggingIn
ThatDudeKnowsHiddenPlugIn