Mo2men wrote:
Dear AaronPond,
As you said before, GMAT is reasoning test. However, I tried to do the same in the following GMAT prep question but failed. I hope you help in the following:
https://gmatclub.com/forum/a-camera-len ... s#p2119479Thanks always for you support and explanation
Absolutely! I am very happy to help. As I solve this problem, I will focus on common patterns that the GMAT uses. Pattern recognition is crucial for those of you preparing for the GMAT. This should make a great deal of sense: you will certainly never see this exact problem repeated on the GMAT, so you need to know how to train your brain to strategically attack whole classes of problems.
Now, the setup to this problem is fairly straightforward, once you focus on what it is asking. It asks, "
The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?" This translates to:
\($_{saved}=\frac{\%}{100}($_{total})\)
We want to solve for the "
\(\%\)", so we need to find numerical values for \($_{saved}\) and \($_{total}\). The total amount, \($_{total}\), is easy:
\[
\begin{array}{rr}
20.90 & (2*10.45) \\
24.10 & (2*12.05) \\
+17.50 & \\
\hline
62.50 & \\
\end{array}
\]
The difference between this amount and the discounted amount is also easy: \($_{saved}=62.50-57.50=5\). Plugging our numbers into the initial equation gives us:
\(5=\frac{\%}{100}(62.5)\)
\(\frac{5}{62.5}=\frac{\%}{100}\)
Here is where a common pattern on many GMAT questions rears its head. I call it "
Mathugliness" in my classes. (Get it? It's math. It's ugly. It acts like a thug. But, like most thugs, it's main game is to intimidate.) For those of you studying for the GMAT, it might be useful to know that decimal long division is often a time-killer on the Test. Don't avoid it completely; after all, if you don't see quicker ways of doing the problems, you can always fall back on the division. But manually calculating \(62.5\text{ } \overline{\smash{\big)}\text{ }5\text{ }}\) can be rather time-intensive. Instead, do something that I call "
Stay on Target." Look for ways to simplify what you have, so that the math you have matches the shape and structure of what your answer should look like.
In this case, we know that the left-hand side of the equation will simplify down to a \(\frac{\%}{100}\) format. Use this to your advantage. Try to look for common factors that allow you to manipulate \(\frac{5}{62.5}\) until it starts looking like a percentage. After all, the answer choices show that the math should come out rather pretty. (Incidentally, this is another critical-thinking strategy useful on a wide range of GMAT Quant questions. I call it "
Look Out Below!" If you are not using your answer choices as part of the analysis of the questions, you are missing out on a massive strategic skill!)
In any case, we can easily look for common factors that simplify the math down a great deal. Here is how I would think about it:
\(\frac{5}{62.5}=\frac{50}{625}=\frac{2*25}{25*25}\)
The "25s" in the top and bottom of the fraction cancel each other out, leaving:
\(\frac{\%}{100}=\frac{2}{25}\)
Now, use a strategy I call "
Multiply by 1" to turn your \(\frac{2}{25}\) fraction into the form you want (in other words, a percentage.) We can multiply this fraction by \(\frac{4}{4}\) -- a value equal to "1" -- to get it into the shape we want. By doing so, we avoid doing long division once again.
\(\Big(\frac{2}{25}\Big)*\Big(\frac{4}{4}\Big)=\frac{8}{100}\)
This matches perfectly with answer choice "
B". We have our answer.
Now, for those of you studying for the GMAT, let's take a step back here. This problem, while relatively simple, can actually teach us several patterns seen throughout the GMAT. First, the GMAT tries to bait you into doing math the long way around. But if you use the answer choices as part of the analysis of the problem, look for common factors, and intelligently use math in a strategic (not haphazard) way, you can avoid a lot of "
Mathugliness!"
_________________
Aaron PondVeritas Prep Teacher of the Year / Professionally mentoring GMAT students since 2006 Visit me at https://www.veritasprep.com/gmat/aaron-pond/ if you would like to learn even more "GMAT Jujitsu"!