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

Question

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

mau5 · Accepted Answer

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.

BrushMyQuant · Answer

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!

Bunuel · Answer

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

vikrantgulia · Answer

Let z=50%

so equivalent change must be 62.5% .So answer is A

SVaidyaraman · Answer

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.

Moumila · Answer

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)
 = - 
 = -  % (converting to Percentage decrease)
 = - .25  % (-ve sign implies decrease in price)

So the total percentage decrease is .25  ----- option A

HARRY113 · Answer

Simple!

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

use this approach to solve this.

You will end at option A.

Madhavi1990 · Answer

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

stne · Answer

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)

KarishmaB · Answer

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

stne · Answer

Thank you , for clearing this up, Karishma. Without your guidance it would really have been difficult to understand this. Your awesomeness simply dazzles!

JeffTargetTestPrep · Answer

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%

Answer: A

vp1989 · Answer

One simple approach is to use the formula of equivalent percentage.
If one discount is A% and subsequent discount is B%, then equivalent discount is
 Eq. Dis. percent= A+B -\frac{AB}{100} 
So,  Eq. dis. percent= 25+z-\frac{25z}{100} 
   =25+\frac{75z}{100} 
   =25(1+\frac{3z}{100}) 
Since the question is asking final value then,
 Final value =\frac{25}{100}(1+\frac{3z}{100}) 
 Final value =0.25(1+\frac{3z}{100}) ............ hence  (A)

samarpan.g28 · Answer

I believe, that assuming an initial selling price and a value of z will help to find the answer faster. I was thinking of an alternate approach by using the consecutive discount method, and this seems easier. I assumed the selling price as 100 and z as 100, and found a value there. Then put the same in options and (A) was a match. However, if we use the later method then overall discount becomes 25+z -25z/100 = 25(1+3z/100). So overall decrease will be by 25/100 * (1+3z/100) = 0.25(1+3z/100). Option (A) is correct.

Kinshook · Answer

megafan 
 Asked:  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
Let the original price of an item be x.
Decreasing the original price of an item by 25% results in price = .75x
Then decreasing the new price by z% results in price = .75x(1-z/100)

Let the price be decreased by y in total
 .75x(1-\frac{z}{100}) = x(1 - y) 
 1-y = .75(1-\frac{z}{100}) 
 y = 1 - .75(1-\frac{z}{100}) = .25 + \frac{.75z}{100} = .25(1+\frac{3z}{100})

IMO A

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

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