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# Decreasing the original price of an item by 25% and then

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Manager
Joined: 28 May 2009
Posts: 155
Followers: 4

Kudos [?]: 89 [1] , given: 89

Decreasing the original price of an item by 25% and then [#permalink]  04 Mar 2013, 07:13
1
KUDOS
00:00

Difficulty:

45% (medium)

Question Stats:

50% (02:35) correct 50% (00:58) wrong based on 100 sessions
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) 0.25(1 + \frac{3z}{100})

(B) 0.25(1 + \frac{z}{100})

(C) 0.25(1 - \frac{3z}{100})

(D) 0.75(1 - \frac{z}{100})

(E) 0.75(1 + \frac{3z}{100})

Source: Gmat Hacks 1800
[Reveal] Spoiler: OA

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Location: India
Concentration: Finance, Marketing
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Kudos [?]: 234 [2] , given: 41

Re: Decreasing the original price of an item by 25% and then [#permalink]  04 Mar 2013, 07:24
2
KUDOS
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) 0.25(1 + \frac{3z}{100})

(B) 0.25(1 + \frac{z}{100})

(C) 0.25(1 - \frac{3z}{100})

(D) 0.75(1 - \frac{z}{100})

(E) 0.75(1 + \frac{3z}{100})

Source: Gmat Hacks 1800

Suppose original Price is X
decreasing by 25%, new price is X (100-25)/100 = 0.75X
Decreasing the new price by z%, new price will be 0.75X * (100-z)/100

= 0.75*(1-(z/100)) * X
original price is decreased by
X - 0.75*(1-(z/100)) * X
= X ( 0.25 + Z*(0.75/100))
= X * 0.25 ( 1 + (3z/100))

hope it helps!
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Joined: 10 Oct 2012
Posts: 627
Followers: 41

Kudos [?]: 561 [1] , given: 135

Re: Decreasing the original price of an item by 25% and then [#permalink]  04 Mar 2013, 07:26
1
KUDOS
Expert's post
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) 0.25(1 + \frac{3z}{100})

(B) 0.25(1 + \frac{z}{100})

(C) 0.25(1 - \frac{3z}{100})

(D) 0.75(1 - \frac{z}{100})

(E) 0.75(1 + \frac{3z}{100})

Let the initial price be 100. Initial drop is by 25%. This gives 75. Assume z=100%. Thus, the final price now will be, a 100% decrease on 75 = 0. This is equivalent to a 100% decrease on the initial price of 100. Put z = 100%, only option A matches.

A.
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Posts: 25207
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Kudos [?]: 25105 [1] , given: 2702

Re: Decreasing the original price of an item by 25% and then [#permalink]  04 Mar 2013, 11:00
1
KUDOS
Expert's post
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) 0.25(1 + \frac{3z}{100})

(B) 0.25(1 + \frac{z}{100})

(C) 0.25(1 - \frac{3z}{100})

(D) 0.75(1 - \frac{z}{100})

(E) 0.75(1 + \frac{3z}{100})

Source: Gmat Hacks 1800

Similar question to practice from OG: increasing-the-original-price-of-an-article-by-15-percent-127086.html

Hope it helps.
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Manager
Joined: 18 Oct 2013
Posts: 81
Location: India
Concentration: Technology, Finance
GMAT 1: 580 Q48 V21
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 27 [0], given: 25

Re: Decreasing the original price of an item by 25% and then [#permalink]  10 Nov 2013, 10:42
Let z=50%

so equivalent change must be 62.5% .So answer is A
Senior Manager
Joined: 17 Dec 2012
Posts: 394
Location: India
Followers: 12

Kudos [?]: 175 [0], given: 9

Re: Decreasing the original price of an item by 25% and then [#permalink]  10 Nov 2013, 16:07
Bunuel wrote:
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) 0.25(1 + \frac{3z}{100})

(B) 0.25(1 + \frac{z}{100})

(C) 0.25(1 - \frac{3z}{100})

(D) 0.75(1 - \frac{z}{100})

(E) 0.75(1 + \frac{3z}{100})

Source: Gmat Hacks 1800

Similar question to practice from OG: increasing-the-original-price-of-an-article-by-15-percent-127086.html

Hope it helps.

An easy approach is to assume a convenient value for z.

1. Let it be 20%
2. The value is first reduced by 25%. So it becomes 75%
3. The above value is then reduced by 20%. So it becomes 60%
4. So the equivalent reduction is 40%

Choice A gives the same equivalent percentage i.e., 0.25(1 + 3*20/100) = 0.25 (1+0.6) = 0.4 = 40%.

If you want to confirm and have the time, you can test for 1 more value of z.
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Re: Decreasing the original price of an item by 25% and then   [#permalink] 10 Nov 2013, 16:07
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