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

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Intern
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If the original price of an item in a retail store is marked [#permalink]

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26 Nov 2013, 07:10
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95% (hard)

Question Stats:

36% (02:04) correct 64% (01:37) wrong based on 362 sessions

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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

[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Nov 2013, 07:12, edited 1 time in total.

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Re: If the original price of an item in a retail store is marked [#permalink]

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26 Nov 2013, 07:41
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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.
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Re: If the original price of an item in a retail store is marked [#permalink]

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26 Nov 2013, 07:59
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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.

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Hope this helps.
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Re: If the original price of an item in a retail store is marked [#permalink]

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12 Apr 2014, 11:17
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]

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12 Apr 2014, 12:53
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.
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Re: If the original price of an item in a retail store is marked [#permalink]

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19 Jan 2015, 00:20
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]

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19 Jan 2015, 01:52
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]

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25 Apr 2016, 07:27
Hello from the GMAT Club BumpBot!

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Re: If the original price of an item in a retail store is marked [#permalink]

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10 Jun 2016, 10:55
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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06 Aug 2017, 12:22
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] 06 Aug 2017, 12:22
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