A camera lens filter kit containing 5 filters sells for $57

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!"

Price of the kit as given: $57.50

Price of the individual filters:
$20.90 (2x 10.45)
+ $24.10 (2x 12.05)
+ $17.50
----------------
$62.50

Amount one would save by buying the kit: $62.50 - $57.50 = $5.00

Savings as percentage of sum of individual prices: $5.00/$62.50

(We know 10% of $62.50 is $6.25. So the answer must be lower than 10%.)
Looking at the answer choices we should then note immediately that the
answer is B without any calculation if we know that the fraction 5/8=0.625.

This showed me how important it is to memorize certain common fractions.
Doing a calculation like 5/62.5 is tedious. But knowing the decimal value of the
fractions by heart helps to solve this problem under a minute.

Important decimal values of fractions of 8 to know are:

1/8 = 0.125
3/8 = 0.375
5/8 = 0.625
7/8 = 0.875

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

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Cost of kit = $57.50
If filters are purchased individually - $10.45*2 + $12.05*2 + $17.50 = $62.50
Amount saved = $62.50 - $57.50 = $5
Required %age = ($5/$62.50)*100 = 8%

So, the correct answer is B.

of course having a grasp of common fraction -> decimal conversion is the best (which I have on my to do list )

here is how I worked it out though

5/62.5 -->

62.5/5 (inverse)

125/10 = 12.5

1/12.5 (inverse) * (8/8)

=8/100
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price of the kit=$57.50
price of 5 filters together when bought individually is $62.50
savings when bought as a kit as percentage of peecentage of price when bought individually is (5/62.5)*100=8%

What is the easiest / fastest way to figure out 5/62.5? Thanks!

Hi,
the easiest and fastest way is to realize what 625 is --- It is 25*25..
si if we multiply 25*25 by 4*4 we will have the answer as 100*100

so\(\frac{5}{62.5}= \frac{5}{62.5} *\frac{( 4*4)}{(4*4)}\)
=>\(\frac{(5*4*4)}{(62.5*4*4)}= \frac{80}{(100*10)}=\frac{8}{100}\)
%= \(\frac{8}{100}*100\) = 8%

Hope it helps
_________________

First, recognize that, one way to convert a fraction into a percent is to multiply the numerator by 100 and evaluate the new fraction.
For example, 1/4 = (100)(1)/4 percent = 100/4 percent = 25 percent
Likewise, 6/5 = (100)(6)/5 percent = 600/5 percent = 120 percent

Second, we need to recognize that there's a nice fraction hiding in 62.5
If we recognize that 0.625 = 5/8 [a useful conversion to know], then 62.5 = 500/8

So we have,
5/62.5 = (100)(5)/62.5 percent
= (100)(5)/(500/8) percent
= 500/(500/8) percent
= (500)(8/500) percent
= 8 percent

Cheers,
Brent
_________________

Another way:

5/62.5 = (5 *10) / 625 = (5 *10) /( 25* 25) ..........It is recommended to memorize the perfect squares of some numbers.

(5 *10) /( 25* 25) = 2/25 = 1/5 * 2/5 = 0.2 * 0.4 =0.08

Most of the discussion revolves around how to easily calculate 5/62.5
Please look up this picture. It contains how easily can we calculate the value without any need to remember any fractions at all.
Hope it helps.

Posted from my mobile device

_________________

My preferred way for decimal conversion here is as follows:

Step 1: You notice that 62.50 is ugly, so let's multiply it by 2 to get rid of the decimal, yielding 125
Step 2: Since you multiplied the denominator, we have to do the same for the numerator: 5 * 2 = 10
Step 3: You now have 10 / 125 which is nicer, but notice that if you lower the denominator by a fifth, it would be 100
Step 4: Again, since we lowered the denominator by a fifth, we need to do the same to the numerator, yielding 8

So, 8/100 = 8%

Thanks a lot AaronPond for your helpful and great response.

Just a typo in the highlighted part. It should be $12.05.

The total cost of the 5 filters when purchased individually is:

2 x 10.45 + 2 x 12.05 + 17.50

20.90 + 24.10 + 17.50

$62.50

Therefore, the amount saved when purchasing them together in a kit is 62.50 - 57.50 = $5, and this is 5/62.5 = 0.08 = 8% of the total cost of the filters when purchased individually.

Answer: B
_________________

Total cost of the 5 filters purchased individually = $10.45 + $10.45 + $12.05 + $12.05 + $17.50 = $62.50
Cost of filter kit = $57.50

The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?
Amount saved = $62.50 - $57.50 = $5.00

Desired percent = (100)($5.00)/$62.50 = 8%

Answer: B

Cheers,
Brent
_________________

\(2 * 10.45 = 20.90\)
\(2 * 12.05 = 24.10\)
\(1 * 17.50 = 17.50\)

\(20.90 + 24.10 + 17.50 = 62.50\)

\(62.50 - 57.50 = $5\)
\(\frac{$5}{62.50} = \frac{10}{125} = = \frac{1}{12.5} = 8%\)

It's good to memorize that 12.5% = 1/8 and 8% = 1/12.5

Answer is B.
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\(( 2*10.45 + 2*12.05 + 17.50 ) - 57.50 = 62.5 - 57.5 = 5\)

So, % saved is \(\frac{5}{62.5}*100 = 8 \)% , Answer is (B)
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