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

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Math Expert
Joined: 02 Sep 2009
Posts: 44290
Increasing the original price of a certain item by 25 percent and then [#permalink]

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23 Mar 2015, 06:43
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Question Stats:

81% (01:05) correct 19% (01:05) wrong based on 165 sessions

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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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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

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23 Mar 2015, 07:36
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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%.

Last edited by eaze on 23 Mar 2015, 08:08, edited 1 time in total.
Director
Joined: 07 Aug 2011
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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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%.

i hope you meant to say Answer E.
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Director
Joined: 07 Aug 2011
Posts: 577
GMAT 1: 630 Q49 V27
Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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23 Mar 2015, 07:48
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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.

X*1.25*1.25 = 1.5625 X
so there is a net increase of 56.25% . Answer E.
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Lucky

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Joined: 23 May 2013
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Schools: Stanford '19 (M)
GMAT 1: 760 Q49 V45
GPA: 3.5
Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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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%.

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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24 Mar 2015, 23:00
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Expert's post
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% Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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25 Mar 2015, 00:50
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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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25 Mar 2015, 01:51
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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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Math Expert
Joined: 02 Sep 2009
Posts: 44290
Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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30 Mar 2015, 03:17
Expert's post
1
This post was
BOOKMARKED
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 [ 19.7 KiB | Viewed 2752 times ]

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

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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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Manager
Joined: 18 Dec 2014
Posts: 100
Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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

100*1,25 = 125
125*1,25 = 156,25
156,25 - 100 = 56,25
Intern
Joined: 17 Feb 2016
Posts: 1
Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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21 Dec 2016, 22:38
Hi,

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

Thanks!!
Senior Manager
Joined: 25 Mar 2013
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Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: Increasing the original price of a certain item by 25 percent and then [#permalink]

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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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04 Mar 2018, 04:36
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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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