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The original price of an article was reduced by 25%.

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The original price of an article was reduced by 25%. [#permalink]

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New post 13 Aug 2017, 20:07
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Question Stats:

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The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price have to be increased in order to restore the price of the article to its original amount?
A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%
[Reveal] Spoiler: OA

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Re: The original price of an article was reduced by 25%. [#permalink]

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New post 13 Aug 2017, 20:18
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HolaMaven wrote:
The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price have to be increased in order to restore the price of the article to its original amount?
A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%
The equation is:
(3/4*9/10)*x=1

Where 3/4 = 25% decrease, 9/10 = the 10% decrease, x the increase we want to find to have the original price 100% or 1.

= (27/40)*x = 1
Cross multiply x = 40/27
x = 1.481 or 48%.
Answer C


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Re: The original price of an article was reduced by 25%. [#permalink]

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New post 13 Aug 2017, 20:23
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HolaMaven wrote:
The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price have to be increased in order to restore the price of the article to its original amount?
A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%


Note the question says "approximately". That tells me an exact solution may be difficult to come by without a calculator.

Plugging in numbers seems to be the easiest way to solve

Let Price = $100
Decrease by 25% = (1-.25) * 100 = 75
Decrease by another 10% = (1 - .10) * 75
Note this is the same as 75 - .1(75) = 75 - 7.5 (since 10% of 75 = 7.5) = 67.5

To get to the original price, we must calculate (100 - 67.5) = 32.5

32.5 / 67.5 is the change to the new price
Note that 32.5 * 2 = 65. Since 65 is just a little smaller than 67.5, this means that 32.5 is just a little bit less than 1/2 of 67.5 (This is where "Approximation" in the question comes in handy)

Looking at the answers, C is the just a little less than 50%
Therefore, the answer is C

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Re: The original price of an article was reduced by 25%. [#permalink]

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New post 13 Aug 2017, 20:32
Even an easier way is eliminating the options.
25%+10% = 35%, too easy and not an answer
(100-35)% = 65%, again too easy
(100-25)% = 75% - 10%*75* = 67.5% Not possible as its only decrease
(100-67.5)%=32.5%, again not possible as this will increase value to 100% but we need to calculate % increase
Thus option C - 48%
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The original price of an article was reduced by 25%. [#permalink]

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New post 13 Aug 2017, 21:02
The best method for such questions is to work with numbers.
When choosing a number, make sure, that the number is easy to work with!

Let the original price of the of the item be 400$,
since there is a decrease of 25%, the price goes down to 300$.
Again, during the special sale(10% decrease) the price goes down to 270$(less by 30$ or 10%)

Since we need to find out by approximately what percentage the price needs to go up,
the percentage increase is \(\frac{130}{270}*100 = \frac{1300}{27} = 48.14 = 48\)% approximately(Option C)
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The original price of an article was reduced by 25%. [#permalink]

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HolaMaven wrote:
The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price have to be increased in order to restore the price of the article to its original amount?
A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%

Expanding a bit on pips883 's good answer, because this method is easier for me than picking numbers with percent change - a rare phenomenon.

Percentage increase and percentage decrease are inversely proportional.

To find percentage by which the changed number must increase or decrease to return to the original

1) Find the fraction for the first change
2) Flip that fraction, and
3) Calculate decimal value. That's the answer.

Here the article was reduced in price twice, by 25 percent and then 10 percent of that.

First decrease = .75 or \(\frac{3}{4}\), and second decrease, taken with the first, = .90 or \(\frac{9}{10}\)

Total decrease: \(\frac{3}{4}\) * \(\frac{9}{10}\) = \(\frac{27}{40}\)

Flip that fraction: \(\frac{40}{27}\)

\(\frac{40}{27}\) = 1.481, approximately 48%

That's the percentage by which the reduced price must increase to return to original.

Answer C

**Or multiply the multipliers --> (.75)(.9) = .625. Change to fraction \(\frac{625}{1000}\) = \(\frac{27}{40}\). Flip and find decimal value.

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Re: The original price of an article was reduced by 25%. [#permalink]

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New post 14 Aug 2017, 14:37
genxer123 wrote:
HolaMaven wrote:
The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price have to be increased in order to restore the price of the article to its original amount?
A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%

Expanding a bit on pips883's good answer, because this method is easier for me than picking numbers with percent change - a rare phenomenon.

Percentage increase and percentage decrease are inversely proportional.

To find percentage by which the changed number must increase or decrease to return to the original

1) Find the fraction for the first change
2) Flip that fraction, and
3) Calculate decimal value. That's the answer.

Here the article was reduced in price twice, by 25 percent and then 10 percent of that.

First decrease = .75 or \(\frac{3}{4}\), and second decrease, taken with the first, = .90 or \(\frac{9}{10}\)

Total decrease: \(\frac{3}{4}\) * \(\frac{9}{10}\) = \(\frac{27}{40}\)

Flip that fraction: \(\frac{40}{27}\)

\(\frac{40}{27}\) = 1.481, approximately 48%

That's the percentage by which the reduced price must [you-tube]increase[/you-tube] to return to original.

Answer C

**Or multiply the multipliers --> (.75)(.9) = .625. Change to fraction \(\frac{625}{1000}\) = \(\frac{27}{40}\). Flip and find decimal value.


Completely agree on that. Actually, my first thought when solving this question was "Come on, pick 10 and do the math". Then I realized that would be much easier if I worked with fractions. So, 99.9% times I pick numbers, but sometimes algebra may be the easiest path.

By the way, thanks for clarifying my solution. It looks much better now.

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Re: The original price of an article was reduced by 25%. [#permalink]

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New post 14 Aug 2017, 14:49
Plugging in numbers should help.
3/4*9/10(1+x/100)=1 Answer C

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Re: The original price of an article was reduced by 25%. [#permalink]

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New post 14 Aug 2017, 22:14
HolaMaven wrote:
The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price have to be increased in order to restore the price of the article to its original amount?
A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%


Let the original price be \(= 100\)

Price was reduced by \(25\)% \(= 75\)% of \(100 = \frac{75}{100} * 100 = 75\)

During special sale price was further decreased by \(10\)% \(= 90\)% of \(75 = \frac{90}{100} * 75 = 67.5\)

Difference of Original price and final price \(= 100 - 67.5 = 32.5\)

Required percent \(=\) (Difference \(/\) Final price )\(*100\)

Required percent \(= (\frac{32.5}{67.5}) * 100 = 48.148\)% \(=\) Approximately \(= 48\)%

Also half or \(50\)% of \(67.5\) or approximately \(68\) is \(= 34\)

Therefore answer should be slightly less than \(50\)%. Percentage required \(= 48\)%

Answer (C)...

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Re: The original price of an article was reduced by 25%. [#permalink]

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New post 15 Aug 2017, 12:39
Yes plugging is a good approach but before plugging in see if you can eliminate answer choice without really doing any calculation. Practice will make you build require confidence to work faster on eliminating answer choice which can help in rectifying casual errors also. Try to reduce your efforts on easy questions so that you can concentrate better on trickier ones.
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Re: The original price of an article was reduced by 25%. [#permalink]

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New post 18 Aug 2017, 09:08
HolaMaven wrote:
The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price have to be increased in order to restore the price of the article to its original amount?
A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%


Let’s let the original price of the article be 100. In the first reduction, it was reduced by 25% and thus becomes 75. In the second reduction, it was reduced by 10% and thus becomes (0.9)(75) = 67.5. We note that the price must increase by 32.5 to be restored to the original price, and 32.5 is very close to, but less than, half of 67.5; therefore, the answer must be very close to, but less than, 50%. Scanning the answer choice, 48% fits our criteria.

Answer: C
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Re: The original price of an article was reduced by 25%.   [#permalink] 18 Aug 2017, 09:08
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