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# If the original price of an item in a retail store is marked

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Re: If the original price of an item in a retail store is marked [#permalink]
Bunuel wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

Say the original price is 100.
The price after the mark up = $$100(1+\frac{m}{100}) = 100 + m$$;
The price after the discount = $$(100+m)(1-\frac{d}{100}) = 100-d+m-\frac{md}{100}$$;

The questions asks: is $$100-d+m-\frac{md}{100}>100$$? --> is $$100m-100d-md>0$$

(1) m > d. If $$m=3$$ and $$d=2$$, then the answer is YES nut if but if $$m=60$$ and $$d=40$$, then the answer is NO. Not sufficient.

(2) m = 1.5d. Use the same numbers as above. Not sufficient.

(1)+(2) Use the same numbers. Not sufficient.

Hope it's clear.

Hi Bunuel,
Just to confirm, the formula for 3 variables.
For 3 items
+m , +d, -x
then will it be ...

= 100+m+d-x -(mdx/100)
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Re: If the original price of an item in a retail store is marked [#permalink]
seabhi wrote:
Bunuel wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

Say the original price is 100.
The price after the mark up = $$100(1+\frac{m}{100}) = 100 + m$$;
The price after the discount = $$(100+m)(1-\frac{d}{100}) = 100-d+m-\frac{md}{100}$$;

The questions asks: is $$100-d+m-\frac{md}{100}>100$$? --> is $$100m-100d-md>0$$

(1) m > d. If $$m=3$$ and $$d=2$$, then the answer is YES nut if but if $$m=60$$ and $$d=40$$, then the answer is NO. Not sufficient.

(2) m = 1.5d. Use the same numbers as above. Not sufficient.

(1)+(2) Use the same numbers. Not sufficient.

Hope it's clear.

Hi Bunuel,
Just to confirm, the formula for 3 variables.
For 3 items
+m , +d, -x
then will it be ...

= 100+m+d-x -(mdx/100)

Hello -
If you mean (100+m)(1+d/100)(1-x/100), then obviously it is not equal to 100+m+d-x - mdx/100

Letme know if you meant something else.
---------------------------
Kudos if the post helped
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Re: If the original price of an item in a retail store is marked [#permalink]
Bunuel wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

Say the original price is 100.
The price after the mark up = $$100(1+\frac{m}{100}) = 100 + m$$;
The price after the discount = $$(100+m)(1-\frac{d}{100}) = 100-d+m-\frac{md}{100}$$;

The questions asks: is $$100-d+m-\frac{md}{100}>100$$? --> is $$100m-100d-md>0$$

(1) m > d. If $$m=3$$ and $$d=2$$, then the answer is YES nut if but if $$m=60$$ and $$d=40$$, then the answer is NO. Not sufficient.

(2) m = 1.5d. Use the same numbers as above. Not sufficient.

(1)+(2) Use the same numbers. Not sufficient.

Hope it's clear.

Hi Bunuel

What suppose if the Question does not mention that m & d are integers. In such a case m & d can even be decimals. Still the answer would be E correct?

Thanks
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Re: If the original price of an item in a retail store is marked [#permalink]
buddyisraelgmat wrote:
Bunuel wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

Say the original price is 100.
The price after the mark up = $$100(1+\frac{m}{100}) = 100 + m$$;
The price after the discount = $$(100+m)(1-\frac{d}{100}) = 100-d+m-\frac{md}{100}$$;

The questions asks: is $$100-d+m-\frac{md}{100}>100$$? --> is $$100m-100d-md>0$$

(1) m > d. If $$m=3$$ and $$d=2$$, then the answer is YES nut if but if $$m=60$$ and $$d=40$$, then the answer is NO. Not sufficient.

(2) m = 1.5d. Use the same numbers as above. Not sufficient.

(1)+(2) Use the same numbers. Not sufficient.

Hope it's clear.

Hi Bunuel

What suppose if the Question does not mention that m & d are integers. In such a case m & d can even be decimals. Still the answer would be E correct?

Thanks

Yes, the answer would still be E.
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Re: If the original price of an item in a retail store is marked [#permalink]
singhmaharaj wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

(1) m > d

(2) m = 1.5d

Both the given options were same in which it states that m>d
Final markup/discount is given as m-d-md/100
consider any small number m=2,d=1
then ans will be yes.
consider bigger values m=700,d=600
Ans will be No
both statements not suff....

Ans E
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Re: If the original price of an item in a retail store is marked [#permalink]
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The last thing you want to do is solve for a proof in the actual exam. Think about it in as simple terms as possible. In this case think that the markup can be as high as it wants it to be, but the end price is going to be determined by the discount. For example, lets say the markup of 100 is 150%, the price will now be 250. The discount (d=m/1.5) is now 100% and the price now becomes 0. With small numbers the discount is not as powerful so the total price is higher than 100. Statement 1 is irrelevant since it says the same thing that statement 2 says, thus option E is correct.
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Re: If the original price of an item in a retail store is marked [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If the original price of an item in a retail store is marked [#permalink]
Moderator:
Math Expert
94421 posts
The provided text is a GMAT forum post discussing a problem related to percentage markups and discounts on an item's price. The problem asks whether the final price of an item, after a markup and a discount, is greater than the original price. The discussion includes a detailed solution by a user named Bunuel, who breaks down the problem into a mathematical inequality and evaluates the given statements.

**Content Structure:**
- The post starts with a problem statement and is followed by a solution and discussion.
- The solution involves setting up an inequality to determine if the final price is greater than the original price.
- The discussion includes multiple users contributing with additional questions and clarifications.

**Analysis:**
single_question_with_answer

the text contains a single mathematical question and provides an answer to that question. the solution is detailed and evaluates the sufficiency of the given statements to determine if the final price is greater than the original price.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Last visit was: 20 Jul 2024, 00:46 It is currently 20 Jul 2024, 00:46
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# If the original price of an item in a retail store is marked

SORT BY:
Tags:
Show Tags
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Intern
Joined: 07 Dec 2012
Posts: 2
Own Kudos [?]: 39 [39]
Given Kudos: 7
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642431 [24]
Given Kudos: 86332
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642431 [8]
Given Kudos: 86332
General Discussion
Manager
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Posts: 61
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Schools: ISB '15
Re: If the original price of an item in a retail store is marked [#permalink]
Bunuel wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

Say the original price is 100.
The price after the mark up = $$100(1+\frac{m}{100}) = 100 + m$$;
The price after the discount = $$(100+m)(1-\frac{d}{100}) = 100-d+m-\frac{md}{100}$$;

The questions asks: is $$100-d+m-\frac{md}{100}>100$$? --> is $$100m-100d-md>0$$

(1) m > d. If $$m=3$$ and $$d=2$$, then the answer is YES nut if but if $$m=60$$ and $$d=40$$, then the answer is NO. Not sufficient.

(2) m = 1.5d. Use the same numbers as above. Not sufficient.

(1)+(2) Use the same numbers. Not sufficient.

Hope it's clear.

Hi Bunuel,
Just to confirm, the formula for 3 variables.
For 3 items
+m , +d, -x
then will it be ...

= 100+m+d-x -(mdx/100)
Intern
Joined: 10 Apr 2014
Posts: 23
Own Kudos [?]: 48 [0]
Given Kudos: 3
Re: If the original price of an item in a retail store is marked [#permalink]
seabhi wrote:
Bunuel wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

Say the original price is 100.
The price after the mark up = $$100(1+\frac{m}{100}) = 100 + m$$;
The price after the discount = $$(100+m)(1-\frac{d}{100}) = 100-d+m-\frac{md}{100}$$;

The questions asks: is $$100-d+m-\frac{md}{100}>100$$? --> is $$100m-100d-md>0$$

(1) m > d. If $$m=3$$ and $$d=2$$, then the answer is YES nut if but if $$m=60$$ and $$d=40$$, then the answer is NO. Not sufficient.

(2) m = 1.5d. Use the same numbers as above. Not sufficient.

(1)+(2) Use the same numbers. Not sufficient.

Hope it's clear.

Hi Bunuel,
Just to confirm, the formula for 3 variables.
For 3 items
+m , +d, -x
then will it be ...

= 100+m+d-x -(mdx/100)

Hello -
If you mean (100+m)(1+d/100)(1-x/100), then obviously it is not equal to 100+m+d-x - mdx/100

Letme know if you meant something else.
---------------------------
Kudos if the post helped
Manager
Joined: 14 Jul 2014
Posts: 67
Own Kudos [?]: 95 [0]
Given Kudos: 49
Re: If the original price of an item in a retail store is marked [#permalink]
Bunuel wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

Say the original price is 100.
The price after the mark up = $$100(1+\frac{m}{100}) = 100 + m$$;
The price after the discount = $$(100+m)(1-\frac{d}{100}) = 100-d+m-\frac{md}{100}$$;

The questions asks: is $$100-d+m-\frac{md}{100}>100$$? --> is $$100m-100d-md>0$$

(1) m > d. If $$m=3$$ and $$d=2$$, then the answer is YES nut if but if $$m=60$$ and $$d=40$$, then the answer is NO. Not sufficient.

(2) m = 1.5d. Use the same numbers as above. Not sufficient.

(1)+(2) Use the same numbers. Not sufficient.

Hope it's clear.

Hi Bunuel

What suppose if the Question does not mention that m & d are integers. In such a case m & d can even be decimals. Still the answer would be E correct?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642431 [0]
Given Kudos: 86332
Re: If the original price of an item in a retail store is marked [#permalink]
buddyisraelgmat wrote:
Bunuel wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

Say the original price is 100.
The price after the mark up = $$100(1+\frac{m}{100}) = 100 + m$$;
The price after the discount = $$(100+m)(1-\frac{d}{100}) = 100-d+m-\frac{md}{100}$$;

The questions asks: is $$100-d+m-\frac{md}{100}>100$$? --> is $$100m-100d-md>0$$

(1) m > d. If $$m=3$$ and $$d=2$$, then the answer is YES nut if but if $$m=60$$ and $$d=40$$, then the answer is NO. Not sufficient.

(2) m = 1.5d. Use the same numbers as above. Not sufficient.

(1)+(2) Use the same numbers. Not sufficient.

Hope it's clear.

Hi Bunuel

What suppose if the Question does not mention that m & d are integers. In such a case m & d can even be decimals. Still the answer would be E correct?

Thanks

Yes, the answer would still be E.
Director
Joined: 05 Mar 2015
Posts: 841
Own Kudos [?]: 878 [0]
Given Kudos: 45
Re: If the original price of an item in a retail store is marked [#permalink]
singhmaharaj wrote:
If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?

(1) m > d

(2) m = 1.5d

Both the given options were same in which it states that m>d
Final markup/discount is given as m-d-md/100
consider any small number m=2,d=1
then ans will be yes.
consider bigger values m=700,d=600
Ans will be No
both statements not suff....

Ans E
Intern
Joined: 14 Nov 2017
Posts: 2
Own Kudos [?]: 1 [1]
Given Kudos: 10
Re: If the original price of an item in a retail store is marked [#permalink]
1
Bookmarks
The last thing you want to do is solve for a proof in the actual exam. Think about it in as simple terms as possible. In this case think that the markup can be as high as it wants it to be, but the end price is going to be determined by the discount. For example, lets say the markup of 100 is 150%, the price will now be 250. The discount (d=m/1.5) is now 100% and the price now becomes 0. With small numbers the discount is not as powerful so the total price is higher than 100. Statement 1 is irrelevant since it says the same thing that statement 2 says, thus option E is correct.
Non-Human User
Joined: 09 Sep 2013
Posts: 34041
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If the original price of an item in a retail store is marked [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If the original price of an item in a retail store is marked [#permalink]
Moderator:
Math Expert
94421 posts
user
The provided text is a GMAT forum post discussing a problem related to percentage markups and discounts on an item's price. The problem asks whether the final price of an item, after a markup and a discount, is greater than the original price. The discussion includes a detailed solution by a user named Bunuel, who breaks down the problem into a mathematical inequality and evaluates the given statements.

**Content Structure:**
- The post starts with a problem statement and is followed by a solution and discussion.
- The solution involves setting up an inequality to determine if the final price is greater than the original price.
- The discussion includes multiple users contributing with additional questions and clarifications.

**Analysis:**
TYPE: SINGLE_QUESTION_WITH_ANSWER

The text contains a single mathematical question and provides an answer to that question. The solution is detailed and evaluates the sufficiency of the given statements to determine if the final price is greater than the original price.