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Re: Decreasing the original price of an item by 25% and then [#permalink]

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04 Mar 2013, 07:24

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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))

So, answer will be A hope it helps!
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Re: Decreasing the original price of an item by 25% and then [#permalink]

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04 Mar 2013, 07:26

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This post was BOOKMARKED

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.

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.
_________________

Re: Decreasing the original price of an item by 25% and then [#permalink]

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17 May 2015, 10:18

Hello from the GMAT Club BumpBot!

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Re: Decreasing the original price of an item by 25% and then [#permalink]

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18 May 2015, 04:13

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For two successive increase/decrease , say a% and b% the total effective increase/decrease will be a+b+ab/100

So here the total decrease will be = -25 -z +25z/100 (for price decrease the sign will be -ve) = -[25 + 75z/100] = -[.25+ .75z/100] % (converting to Percentage decrease) = - .25[1+3z/100] % (-ve sign implies decrease in price)

So the total percentage decrease is .25[1+3z/100] ----- option A

Re: Decreasing the original price of an item by 25% and then [#permalink]

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11 Jul 2016, 05:51

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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