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

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Decreasing the original price of an item by 25% and then [#permalink]  04 Mar 2013, 07:13
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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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Re: Decreasing the original price of an item by 25% and then [#permalink]  04 Mar 2013, 07:24
2
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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))

hope it helps!
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Re: Decreasing the original price of an item by 25% and then [#permalink]  04 Mar 2013, 07:26
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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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Re: Decreasing the original price of an item by 25% and then [#permalink]  04 Mar 2013, 11:00
1
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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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Kudos [?]: 9 [0], given: 29

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
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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]  17 May 2015, 10:18
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Re: Decreasing the original price of an item by 25% and then [#permalink]  18 May 2015, 04:13
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] 18 May 2015, 04:13
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