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Senior SC Moderator V
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In order to give his customers a 25-percent discount on the price and  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 62% (01:54) correct 38% (01:59) wrong based on 144 sessions

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In order to give his customers a $$25-percent$$ discount on the price and still net a $$25-percent$$ profit on the cost of an item, at what price should a merchant mark an item if it cost him $$16.80$$?

(A) $$21.00$$
(B) $$21.90$$
(C) $$25.20$$
(D) $$26.25$$
(E) $$28.00$$

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In order to give his customers a 25-percent discount on the price and  [#permalink]

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Let's talk strategy here. It looks like many of the approaches in this forum focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to use strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The "GMAT Jujitsu" I will show you here will be useful for numerous questions, not just this one. My solution here is going to walk through not just what the answer is, but how to strategically think about it.

Let's start with breaking down the original question. We know that the the cost of the item is $$16.80$$. We also know that $$Profit = Revenue - Cost$$. If the merchant wants to have a profit of 25% of the cost, that means that the revenue (the price he actually charged for the item) must be $$1.25*Cost$$. After all, $$Profit = 1.25*Cost - Cost = .25*Cost$$. Note that this part of the problem is not a percentage change issue, but it looks a little like one, because in the end you are looking for Revenue. In order for Profit to be 25% of Cost, then the Revenue must be 125% "of" cost. Our leverage from here on out, however, is the revenue ($$16.80*1.25$$), since this is the amount of money the merchant receives.

Here is where the first strategic approach comes in. I call it in my classes "Fractions Are Your Friends." Many math questions are made easier if you can think of decimals in terms of their corresponding fractional equivalents. Decimal multiplication and division -- while useful -- are often the long way around when it comes to math. It should be easy to see that $$1.25 = \frac{5}{4}$$. Thus,

$$Price_{(Actual)}=16.80*1.25=16.80(\frac{5}{4}$$)

You should be able to see how quickly we can divide $$16.80$$ by $$4$$, and then multiply by $$5$$. If you use the fractions and break up math into easier-to-digest parts, the math is doable in your head. This is not accidental. The GMAT often designs problems so that the math is easy for those that know how to think about the problems. For purposes of visualization, here is what it looks like:

$$16.80*\frac{5}{4}=(\frac{(16+.80)}{4})*5=(4+.2)*5=20+1=21$$

The actual price is $$21$$.

Now, this price is the what the merchant is actually charging his customers. This, however, is the already-discounted price. The target of this question is the price at which the original item was marked. A discount is a percentage change, so we can use the formula $$V_{(final)}=V_{(initial)}*(1\pm(\frac{\%}{100}))$$. In the case of this question, our actual price is the final value, $$V_{(final)}$$. Our initial value, $$V_{(initial)}$$, is what the merchant originally wanted to charge. Using "Fractions Are Your Friends" again, we get:

$$V_{(final)}=V_{(initial)}*(1\pm(\frac{\%}{100}))$$
$$21=\text{Price}_{(initial)}*(1-(\frac{25}{100}))$$
$$21=\text{Price}_{(initial)}*(1-\frac{1}{4})$$
$$21=\text{Price}_{(initial)}*(\frac{3}{4})$$
$$\text{Price}_{(initial)}=21*(\frac{4}{3})=28$$

Again, notice how easy it is if you keep the numbers in fractions. $$21*1.3333$$ is messy. But cancelling out the factor of $$3$$ from $$21$$ (leaving $$7*4$$ in the numerator) is a piece of proverbial cake.

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Originally posted by AaronPond on 04 Jul 2018, 10:23.
Last edited by AaronPond on 20 Feb 2019, 15:40, edited 1 time in total.
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Director  D
Joined: 05 Mar 2015
Posts: 993
Re: In order to give his customers a 25-percent discount on the price and  [#permalink]

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ziyuenlau wrote:
In order to give his customers a $$25-percent$$ discount on the price and still net a $$25-percent$$ profit on the cost of an item, at what price should a merchant mark an item if it cost him $$16.80$$?

(A) $$21.00$$
(B) $$21.90$$
(C) $$25.20$$
(D) $$26.25$$
(E) $$28.00$$

so finally he should have 25% profit over $16.8 which is 16.8(1+25/100)=$21
but this $21 is discounted price of SP say x at 25% again x(1-25/100) = 21 thus x=$28

Ans E
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Re: In order to give his customers a 25-percent discount on the price and  [#permalink]

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ziyuenlau wrote:
In order to give his customers a $$25-percent$$ discount on the price and still net a $$25-percent$$ profit on the cost of an item, at what price should a merchant mark an item if it cost him $$16.80$$?

(A) $$21.00$$
(B) $$21.90$$
(C) $$25.20$$
(D) $$26.25$$
(E) $$28.00$$

Cost Price + Profit = Selling Price = Marked Price - Discount

Now, here Selling Price will be 16.80*125/100 = 21

Now, at this point we have here , Selling Price which is 75% of Marked Price...

So, Marked Price = 21/0.75

Or, Marked Price = 28.00

Hence Correct answer must be (E) 28

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In order to give his customers a 25-percent discount on the price and  [#permalink]

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In order to give his customers a 25−percent25−percent discount on the price and still net a 25−percent25−percent profit on the cost of an item, at what price should a merchant mark an item if it cost him $16.80? (A)$21.00
(B) $21.90 (C)$25.20
(D) $26.25 (E)$28.00

Do it in steps:

Given: Cost price : $16.80 Final result to achieve is "to gain 25%" of cost price so keeping end result in mind find the 25% of Cost price =$16.80*(25/100) =$16.80 *(1/4) =$4.20

Now add the profit in the cost price=$16.80+$4.20= $21.00 Now you should use the options that is when you apply discount of 25% on any of the option and if it gives you$21.00 as a result then it is your answer:

if you give the discount of 25 % on $28.00=$28.00 - $28.00 (25/100) =$28.00 -$7.00 =$21.00

Intern  B
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Concentration: Finance, Technology
Re: In order to give his customers a 25-percent discount on the price and  [#permalink]

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According to the question:
$$(1-0.25)P = (1+0.25) * 16.8$$

$$\therefore P = 28.00$$
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SVP  V
Joined: 26 Mar 2013
Posts: 2230
Re: In order to give his customers a 25-percent discount on the price and  [#permalink]

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AaronPond wrote:
Let's talk strategy here. It looks like many of the approaches in this forum focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to use strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The "GMAT Jujitsu" I will show you here will be useful for numerous questions, not just this one. My solution here is going to walk through not just what the answer is, but how to strategically think about it.

Hi AaronPond

Thanks for your great explanation Can you please shed light about the meaning of mark price, mark up and mark down? What kind of relationship with revenue or price?

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Location: India
Concentration: Finance, Marketing
GPA: 4
Re: In order to give his customers a 25-percent discount on the price and  [#permalink]

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Mo2men wrote:
AaronPond wrote:
Let's talk strategy here. It looks like many of the approaches in this forum focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to use strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The "GMAT Jujitsu" I will show you here will be useful for numerous questions, not just this one. My solution here is going to walk through not just what the answer is, but how to strategically think about it.

Hi AaronPond

Thanks for your great explanation Can you please shed light about the meaning of mark price, mark up and mark down? What kind of relationship with revenue or price?

So basically we have a cost price first to which a % of margin is added to reach the marked price. This margin is added so as to leave some room for discount and still earn profit.
After the Marked price , some discount is given and the product is sold at selling price or marked down price. When we subtract cost price from this selling price we get Profit.

so if CP is 100 Rs
MP is 130 Rs (30% up the CP)

a discount of 10% on MP is given i.e Rs 13
so SP - 117
Profit - Rs 17 or 17%

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Re: In order to give his customers a 25-percent discount on the price and  [#permalink]

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hazelnut wrote:
In order to give his customers a $$25-percent$$ discount on the price and still net a $$25-percent$$ profit on the cost of an item, at what price should a merchant mark an item if it cost him $$16.80$$?

(A) $$21.00$$
(B) $$21.90$$
(C) $$25.20$$
(D) $$26.25$$
(E) $$28.00$$

We need to apply a profit of 25%:

Intermediate Price = 125% of 16.8 = (5/4) * 16.8

Also give a 25% discount on the selling price:

75% of selling price = intermediate price

(3/4) * SP = (5/4)*16.8

=> SP = (16.8 * 5)/3 = 84/3 = 28

Hence E is the correct answer
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Re: In order to give his customers a 25-percent discount on the price and  [#permalink]

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cost(1+p/100)=Marked Price (1-d/100)

16.80(1+25/100)=M(1-25/100)

16.80(1.25)=.75M

[16.80(1.25)]/.75=M

28=m Re: In order to give his customers a 25-percent discount on the price and   [#permalink] 03 Feb 2019, 08:13
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