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

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A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 08 Jan 2014, 12:58
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A camera lens filter kit containing 5 filters sells for $57.50. If the filters are purchased individually, 2 of them are priced at $10.45 each, 2 at $12.05 each, 1 at $17.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?

A) 7%
B) 8%
C) 8.5%
D) 10%
E) 11%
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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 08 Jan 2014, 13:08
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1
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
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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 08 Jan 2014, 13:16
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.
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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 08 Jan 2014, 20:11
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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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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 08 Jan 2014, 23:37
2
BabySmurf wrote:
A camera lens filter kit containing 5 filters sells for $57.50.
If the filters are purchased individually, 2 of them are priced
at $10.45 each, 2 at $12.05 each, 1 at $17.50. The amount
saved by purchasing the kit is what percent of the total price
of the 5 filters purchased individually?

A) 7%
B) 8%
C) 8.5%
D) 10%
E) 11%



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%
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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 26 Mar 2016, 23:05
What is the easiest / fastest way to figure out 5/62.5? Thanks!
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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 27 Mar 2016, 00:19
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happyface101 wrote:
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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 18 Apr 2017, 14:09
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Top Contributor
happyface101 wrote:
What is the easiest / fastest way to figure out 5/62.5? Thanks!


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
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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 19 Apr 2017, 03:04
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happyface101 wrote:
What is the easiest / fastest way to figure out 5/62.5? Thanks!


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
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Re: A camera lens filter kit containing 5 filters sells for $57 [#permalink]

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New post 30 Jun 2018, 15:47
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Re: A camera lens filter kit containing 5 filters sells for $57   [#permalink] 30 Jun 2018, 15:47
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