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Increasing the original price of a certain item by 25 percent and then

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Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 23 Mar 2015, 06:43
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Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?

A. 31.25
B. 37.50
C. 50.00
D. 52.50
E. 56.25


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Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post Updated on: 23 Mar 2015, 08:08
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Price * 1.25 * 1.25 = Price \(* \frac{5}{4}*\frac{5}{4}\) = Price * \(\frac{25}{16}\) = Price *(1 \(+ \frac{9}{16}\))

\(\frac{9}{16}\) is 1 sixteenth more than one half; one eighth is .125, so one sixteenth is .0625, so total increase is 56.25%.

Answer:E

Originally posted by eaze on 23 Mar 2015, 07:36.
Last edited by eaze on 23 Mar 2015, 08:08, edited 1 time in total.
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 23 Mar 2015, 07:47
speedilly wrote:
Price * 1.25 * 1.25 = Price \(* \frac{5}{4}*\frac{5}{4}\) = Price * \(\frac{25}{16}\) = Price *(1 \(+ \frac{9}{16}\))

\(\frac{9}{16}\) is 1 sixteenth more than one half; one eighth is .125, so one sixteenth is .0625, so total increase is 56.25%.

Answer:D



i hope you meant to say Answer E.
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 23 Mar 2015, 07:48
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1
Bunuel wrote:
Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?

A. 31.25
B. 37.50
C. 50.00
D. 52.50
E. 56.25



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X*1.25*1.25 = 1.5625 X
so there is a net increase of 56.25% . Answer E.
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 23 Mar 2015, 08:09
Lucky2783 wrote:
speedilly wrote:
Price * 1.25 * 1.25 = Price \(* \frac{5}{4}*\frac{5}{4}\) = Price * \(\frac{25}{16}\) = Price *(1 \(+ \frac{9}{16}\))

\(\frac{9}{16}\) is 1 sixteenth more than one half; one eighth is .125, so one sixteenth is .0625, so total increase is 56.25%.

Answer:D



i hope you meant to say Answer E.


I did! Whoops. Thanks for the correction!
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 24 Mar 2015, 23:00
2
Hi All,

The math behind this prompt can be done in a number of different ways (using fractions, decimals or ratios). The prompt is perfect for TESTing VALUES.

We're told that the original price of an item is increased by 25% and then THAT price is increased by 25%....

IF....
Starting value = $100
+ 25% = 100 + .25(100) = 125

+ 25% = 125 + .25(125) = 125 + 31.25 = 156.25

The question asks how the final price relates to the original price. This is essentially about Percentage Change, which means we should use the Percentage Change Formula:

Percentage Change = (New - Old)/Old = Difference/Original

Doing either calculation will yield the same result:

56.25/100 = 56.25%

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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 25 Mar 2015, 00:50
1
Let Orignal Cost be 100
First Increase = 100 *1.25 = 125
Second Increase = 125 * 1.25 = 156.25

Total Increase = 56.25
Ans : E
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 25 Mar 2015, 01:51
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Answer = E. 56.25

For initial price of 100, twice the hike of 25% means

\((100+25) * \frac{125}{100} = 156.25\)

Hike = 156.25 - 100 = 56.25
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 30 Mar 2015, 03:17
Bunuel wrote:
Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?

A. 31.25
B. 37.50
C. 50.00
D. 52.50
E. 56.25


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
increasefollowedbyincrease_text.PNG
increasefollowedbyincrease_text.PNG [ 19.7 KiB | Viewed 3709 times ]

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 31 Mar 2015, 12:40
Bunuel wrote:
Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?

A. 31.25
B. 37.50
C. 50.00
D. 52.50
E. 56.25


Kudos for a correct solution.


Let original price = 100.
Increase by 25% = 125
Increase by 25% again = 125 * 1.25
= 156.25
This is 56.25 more than original price.

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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 01 Apr 2015, 02:46
Picked an easy number.

100*1,25 = 125
125*1,25 = 156,25
156,25 - 100 = 56,25
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 21 Dec 2016, 22:38
Hi,

Could someone please tell me if we can use the Net change formula a+b+(ab/100)

Thanks!!
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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New post 22 Dec 2016, 14:03
Original = 100
New1 = 100 ( 1.25 ) = 125
New2 = 125(1.25) = 156.25
\(\frac{Change}{Original} = \frac{Percent}{100}\)
E
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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Re: Increasing the original price of a certain item by 25 percent and then   [#permalink] 04 Mar 2018, 04:36
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