pandoraUM wrote:
What is the fastest way to solve this?
\(\frac{(0.513)(0.488)(0.942)}{(0.684)(0.314)(0.183)}\)
a) 4
b) 5
c) 6
d) 7
e) 8
Useful concept: \(\frac{A \times B \times C}{D \times E \times F} = \frac{A}{D} \times \frac{B}{E} \times \frac{C}{F}\)Strategy: As you can imagine, we certainly don't want to actually find the product in the numerator and the product in the denominator and then divide the results. Instead, let's invest a little bit of time identifying any pairs of values that might simplify today " nice" fraction.First off, I recognize that \(0.942\) is exactly \(3 \times 0.314\).
So, let's rewrite our expression as follows: \(\frac{(0.513)(0.488)(0.942)}{(0.684)(0.314)(0.183)} = \frac{0.942}{0.314} \times \frac{(0.513)(0.488)}{(0.684)(0.183)}= 3 \times \frac{(0.513)(0.488)}{(0.684)(0.183)}\)
Next, I know that \(3 \times 0.18 = 0.54\), which means \(\frac{0.54}{0.18} = 3\)
The fraction \(\frac{0.513}{0.183}\) kind of resembles \(\frac{0.54}{0.18} = 3\).
However, since \(0.513\) is a bit smaller than \(0.54\), and since \(0.183\) is a teeny bit bigger than \(0.18\), we know that \(\frac{0.513}{0.183}\) will be a little bit smaller than \(3\).
So, we can rewrite our expression as follows: \(3 \times \frac{(0.513)(0.488)}{(0.684)(0.183)} = 3 \times \frac{0.513}{0.183} \times \frac{0.488}{0.684} = 3 \times little less than3 \times \frac{0.488}{0.684} \)
Finally, we know that \(\frac{4}{6} = \frac{2}{3}\), and \(\frac{440}{660} = \frac{2}{3}\), and \(\frac{460}{690} = \frac{2}{3}\)
Since \(0.488\) is a bit bigger than \(460\), we can conclude that \(\frac{0.488}{0.684}\) is a little bit bigger than \(\frac{2}{3}\).
So, our expression becomes:
\(3 \times little less than3 \times \frac{0.488}{0.684} = 3 \times (little less than3) \times (a little more than \frac{2}{3})\)
The "little more than part" some What cancels out with the " little less than" part to get: \(3 \times 3 \times \frac{2}{3}\), which evaluates to be \(6\)
Answer: C
_________________
Brent Hanneson – Creator of gmatprepnow.com
Before you spend another second preparing for the GMAT, check out my article series, Are you doing it wrong?.
You’ll learn what the GMAT actually tests, and why memorizing a ton of formulas actually makes you less effective.