A retailer bought a shirt at wholesale and marked it up 80%

Question

A retailer bought a shirt at wholesale and marked it up 80% to its initial price of $45. By how many more dollars does he need to increase the price to achieve a 100% markup?

A. 1
B. 2
C. 3
D. 4
E. 5

Kind of confused here. A 80% markup over $45 would be $81, a 100% markup would be $90, so in order to get a 100% markup he would need to increase the price by $9?! Either there's a mistake in the question or I misunderstood it.

Bunuel · Accepted Answer

The point is that $45 is already a retail price, so a price after 80% mark up on wholesale price.

Say wholesale price x, then 1.8x=45 --> x=25. In order to achieve a 100% markup a retail price should be 2*25=$50, so $5 more.

Answer: E.

surbhi87 · Answer

Got the answer, but not sure if i understand the language of the question ! 
It says "marked it up 80% to initial price OF $45" -> shouldn't this imply that the initial price was $45 ?

Asifpirlo · Answer

For me the typical solution is like below:

Bunuel · Answer

Wholesale price = x.
Initial price = $45.
Mark up = 80%.

1.8x=45 --> x=25.

In order to achieve a 100% markup a retail price should be 2*25=$50, so $5 more.

Hope this helps.

surbhi87 · Answer

Thanks Bunnel. I'm going to need a little more help here !
You said initial price was 45$. Then markup was 80% hence final price would be 45+((80/100)*45) . This would lead to 81.
100% markup from 45 should mean 90. hence 90-81= 9. 
This was my initial approach. When i couldnt find 9 in the options, then i went on to do 1.8x=45
But i still dont get why the language of the question doesnt mean that the initial price was actually 45. 
Per your equation , 1.8x=45 , it seems that 45 was the final price after the markup .

Bunuel · Answer

The point is that $45 is already a retail price (initial price), so a price after 80% mark up on wholesale price. Please check here: a-retailer-bought-a-shirt-at-wholesale-and-marked-it-up-130759.html#p1074292

EMPOWERgmatRichC · Answer

Hi All,

The first sentence in this prompt clearly states the 'order' of events:

1) A retailer bought a shirt at wholesale (let's say X dollars)
2) Marked it up 80%.....1.8X dollars
3) To its initial price of $45

From this, we have an algebra equation:

1.8X = 45

From here, the math can be done in a couple of different ways....

You COULD solve for X then redo the entire calculation to figure out what the increase would need to be for the price to be marked up 100%

OR.....

You COULD set up a ratio....

Since we need a 100% mark-up, we're looking for the value of 2X. This means that we want to increase 1.8X by 0.2X....

1.8X/0.2X = 45/Y where Y is the amount that the price of the item would need to be MARKED-UP to make the markup 100%

1.8X/.2X = 45/Y
9/1 = 45/Y
9Y = 45
Y = 5

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

ScottTargetTestPrep · Answer

We can let x = the increased price and create the following proportion:

1.8/45 = 2/x

1.8x = 90

x = 90/1.8 = 50

Thus, the item needs to be marked up by 5 more dollars.

Answer: E

EgmatQuantExpert · Answer

Solution

Given  
 • A retailer marked up the price of a shirt by 80% to 45.

To find  
 • By how many more dollars does he need to increase the price to achieve a 100% mark-up

Approach and Working out  
 • Price after 80% markup= 45
 o So, 1.8* Cost price = 45
o Cost price = 45/1.8 = 450/18 = 50/2=25 
• So, the price after 100% mark up = 50

Hence, the price of the shirt if increased by $5 will give 100% mark up.

Thus, option E is the correct answer.

Correct Answer: Option E

GMATGuruNY · Answer

An alternate approach is to PLUG IN THE ANSWERS, which represent the dollars needed to increase the markup to 100%.

100% markup = 2 TIMES the wholesale price = probably EVEN
Implication:
When the correct answer is added to $45, the result is probably EVEN.

Since the wholesale price is initially marked up by 80% = 4/5, the wholesale price is almost certain to be a MULTIPLE OF 5.

Only E will yield an even multiple of 5 when added to 45.
Test E.
When the correct answer is plugged in, adding 80% to the wholesale price must yield an initial selling price of $45.

E: 5
New price = 45+5 = 50
Since the new price is twice the wholesale price, the wholesale price = 25.
Adding an 80% markup to the $25 wholesale price, we get:
 25 + \frac{4}{5}*25 = 25+20 = 45 
Success!

E

Gaurisadhwani1 · Answer

why 80% is equal to 1.8

EMPOWERgmatRichC · Answer

Hi Gaurisadhwani1,

In math terms, 80% is equal to 0.8

In this prompt, we are told that the price of a shirt is 'marked UP' 80% to a price of $45. This means that there was an initial price (we can refer to that as 'X'), which was then raised by 80%....

Initial price = X
Raised price = X + .8X = 1.8X

Since this result is equal to $45, we have the equation:

1.8X = 45

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]

greysniper7 · Answer

The wording of this question is really poor from Manhattan

Nightcat · Answer

I am not an English native speaker so when I read the question, my understand is that the wholesale price is $45 (which is wrong). I asked ChatGPT and it was wrong too. Can anyone who is a native speaker let me know if the question seems confusing to you?

egmat · Answer

Hi Nightcat,

This is a language question, not a math one, and your confusion is completely fair. The sentence is packed tightly, so let me slow it down.

Look at the order of events the sentence describes:

1. The retailer  bought  the shirt at wholesale (some unknown price).
2. He  marked it up 80%  - i.e., raised that wholesale price by  80% .
3. The result of that markup was its  initial price of $45 .

The key word is  "to."  "Marked it up  80%to$45 " means the price  ended at  $45  after the markup. So  $45 is the price after the 80% increase , not the wholesale price. This is exactly the point Bunuel and Rich were making in the thread:  $45  is already the marked-up (retail) price, so  1.8 × wholesale = 45 , giving a wholesale of  $25 .

Your reading treated  $45  as the  starting  wholesale price. If that were true, the sentence would instead say something like "bought a shirt for  $45and  marked it up  80% " - with the  $45  coming  before  the markup. Here, the  $45  comes  after  the word "to," so it's the destination of the markup, not the starting point.

A quick parallel to feel the "to":

- "She raised the temperature by  10  degrees  to70° ." -  70°  is the  final  temperature; the start was  60° .
- "He grew the team by  50%to30  people." -  30  is the  final  size; the start was  20 .

Same structure every time:     to     - the number after "to" is where you land, not where you began.

So the math flows naturally: wholesale  $25  -  100%  markup means doubling to  $50  - that's  $5  more than the current  $45 .

Answer: E

A retailer bought a shirt at wholesale and marked it up 80%

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