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