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

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Manager
Joined: 28 May 2009
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Decreasing the original price of an item by 25% and then  [#permalink]

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04 Mar 2013, 08:13
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95% (hard)

Question Stats:

48% (02:01) correct 52% (01:48) wrong based on 332 sessions

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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

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

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04 Mar 2013, 08:24
2
1
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]

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04 Mar 2013, 08:26
2
1
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]

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04 Mar 2013, 12:00
2
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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Re: Decreasing the original price of an item by 25% and then  [#permalink]

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10 Nov 2013, 11:42
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]

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10 Nov 2013, 17:07
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]

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18 May 2015, 05:13
2
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
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Re: Decreasing the original price of an item by 25% and then  [#permalink]

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11 Jul 2016, 10:22
Simple!

If A is decreased by x% =>
outcome = A (1 - (x/100) ).

use this approach to solve this.

You will end at option A.
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Re: Decreasing the original price of an item by 25% and then  [#permalink]

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10 Dec 2017, 11:10
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+3z/100)

(B) 0.25(1+z/100)

(C) 0.25(1−3z/100)

(D) 0.75(1−z/100)

(E) 0.75(1+3z/100)

Done by POE. So 75 +z/100(75) = 75 [1 + z/100] approx 1/3rd and a little more

So only A fits 0.25 *3z/100 +1 as closest to 1/3rd plus one. Rest do not add up.

Kudos if the answer was useful
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Posts: 581
Re: Decreasing the original price of an item by 25% and then  [#permalink]

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15 Apr 2018, 08:09
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

can anybody help, are we looking for the percentage decrease or are we looking the amount of decrease ?
Let initial amount be 100 after 25% discount we get 75 then z% discount will give $$\frac{(100-z)}{100}*75$$ = $$\frac{100-z}{4}*3$$

So equivalent discount is
100 -$$\frac{300+3z}{4}$$
$$\frac{100+3z}{4}$$

Well as option A after simplification states $$\frac{100+3z}{400}$$

So why this difference ?

( Guaranteed Kudos for anyone who can help with this, thank you)
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- Stne

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Posts: 8373
Location: Pune, India
Re: Decreasing the original price of an item by 25% and then  [#permalink]

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16 Apr 2018, 05:33
1
stne 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

can anybody help, are we looking for the percentage decrease or are we looking the amount of decrease ?
Let initial amount be 100 after 25% discount we get 75 then z% discount will give $$\frac{(100-z)}{100}*75$$ = $$\frac{100-z}{4}*3$$

So equivalent discount is
100 -$$\frac{300+3z}{4}$$
$$\frac{100+3z}{4}$$

Well as option A after simplification states $$\frac{100+3z}{400}$$

So why this difference ?

( Guaranteed Kudos for anyone who can help with this, thank you)

Responding to a pm:

You can easily figure this out by taking numbers instead of variables to understand the concept here:

Say there are 2 discounts - 25% and 20%
Question: What is the overall discount? (it will be in percentage terms only since no actual numbers are provided)

If you assume $100 and then arrive at$75 and then at 80/100 * $75 =$60

Then using the logic used by you above, you say this is $100 -$60 = $40 This 40 is your (100 + 3z)/4 But note that the answer cannot be 40. The overall discount will be in terms of percentage. We say that the discount is 40 per cent i.e. 40/100 i.e. 40%. So it will be (100 + 3z)/400 _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > GMAT self-study has never been more personalized or more fun. Try ORION Free! Director Joined: 27 May 2012 Posts: 581 Re: Decreasing the original price of an item by 25% and then [#permalink] ### Show Tags 16 Apr 2018, 06:20 VeritasPrepKarishma wrote: stne 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 can anybody help, are we looking for the percentage decrease or are we looking the amount of decrease ? Let initial amount be 100 after 25% discount we get 75 then z% discount will give $$\frac{(100-z)}{100}*75$$ = $$\frac{100-z}{4}*3$$ So equivalent discount is 100 -$$\frac{300+3z}{4}$$ $$\frac{100+3z}{4}$$ Well as option A after simplification states $$\frac{100+3z}{400}$$ So why this difference ? ( Guaranteed Kudos for anyone who can help with this, thank you) Responding to a pm: You can easily figure this out by taking numbers instead of variables to understand the concept here: Say there are 2 discounts - 25% and 20% Question: What is the overall discount? (it will be in percentage terms only since no actual numbers are provided) If you assume$100 and then arrive at $75 and then at 80/100 *$75 = $60 Then using the logic used by you above, you say this is$100 - $60 =$40

This 40 is your (100 + 3z)/4

But note that the answer cannot be 40. The overall discount will be in terms of percentage. We say that the discount is 40 per cent i.e. 40/100 i.e. 40%.

So it will be (100 + 3z)/400

Thank you , for clearing this up, Karishma. Without your guidance it would really have been difficult to understand this. Your awesomeness simply dazzles!
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Re: Decreasing the original price of an item by 25% and then  [#permalink]

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17 Apr 2018, 16:10
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) $$0.75(1 + \frac{3z}{100})$$

We can let the original price be 100 and z be 20. Thus the final price is:

100(75/100)(1 - 20/100) = 75(80/100) = 60

We see that the price has reduced by 40%.

Now let’s analyze the answer choices:

A) 0.25(1 + 3z/100)

0.25(1 + 3(20)/100) = 0.25(1.6) = 0.4 = 40%

We see that choice A could be the correct answer. We also see that in choices B, C and E couldn’t possibly be the correct answer. Let’s see if choice D also yield 40% (if it doesn’t, then choice A MUST be the correct answer; if it does, then we have to use another number for z).

D) 0.75(1 - z/100)

0.75(1 - 20/100) = 0.75(0.8) = 0.6 ≠ 40%

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Re: Decreasing the original price of an item by 25% and then &nbs [#permalink] 17 Apr 2018, 16:10
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