AAPL wrote:A vinegar and oil salad dressing contains v liters of vinegar and w liters of oil. If there are 5 liters of the dressing in a jar, how much vinegar is in the jar?
(1) (w+2.5)/7.5 = 1/2
(2) If 2.5 liters of oil were added to the jar, 50% of the dressing would be vinegar.
Target question: What is the value of v?
Given: A vinegar and oil salad dressing contains v liters of vinegar and w liters of oil. There are 5 liters of the dressing in a jar.
Since the TOTAL volume is 5, we can write
v + w = 5
Statement 1: (w+2.5)/7.5 = 1/2
We need only recognize that we COULD solve this equation for w.
Once we know the value of w, we can plug it into the given equation
v + w = 5 to find
the value of v
Since we COULD answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: If 2.5 liters of oil were added to the jar, 50% of the dressing would be vinegar.
Let's keep track of volumes in the hypothetical scenario...
If we add 2.5 liters of oil, the NEW volume of oil = w + 2.5 liters
In this scenario, the volume of vinegar = v liters
So, the NEW TOTAL volume =
w + 2.5 + v
We're told that 50% (aka 1/2) of the TOTAL VOLUME is vinegar.
So, we can write: v/(
w + 2.5 + v) = 1/2
Cross multiply to get: 2v = w + 2.5 + v
Simplify: v = w + 2.5
Since this equation is different from the given equation,
v + w = 5, we COULD solve the system of equations and determine the values of v and w (however, actually performing those calculations would be a huge waste of time since we need only determine whether statement 2 provides sufficient information to answer to the
target question)
Since we COULD answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
