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A merchant wants to increase the price of an item so that both the per

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Bunuel
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A merchant wants to increase the price of an item so that both the per [#permalink] New post   20 Dec 2017, 03:17
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A merchant wants to increase the price of an item so that both the percent of increase and the resulting price in cents are positive integers. If the price of the item is $2.25, what is the least percent increase the merchant can apply? ($1 = 100 cents)

A. 2%
B. 4%
C. 10%
D. 33%
E. 100%


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Bunuel
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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   06 Dec 2021, 04:05
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A merchant wants to increase the price of an item so that both the percent of increase and the resulting price in cents are positive integers. If the price of the item is \($2.25\), what is the least percent increase the merchant can apply? (\($1 = 100\) cents)

A. \(2\%\)
B. \(4\%\)
C. \(10\%\)
D. \(33\%\)
E. \(100\%\)


Let the percent increase is \(x\%\).

We need to find the least positive integer \(x\) such that \(225*\frac{x}{100}\) is an integer:

\(225*\frac{x}{100}=integer\);

\(x*\frac{9}{4}=integer\)

The least positive integer value of \(x\) is 4.


Answer: B
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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   20 Dec 2017, 04:10
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Starting from the options,
a) 2% = 0.02*225 = 4.5 cents - Not an integer
b) 4% = 0.04*225 = 9 cents - Integer - Right option.


But I have a doubt here: Should 4 in 4% be considered as integer here or as 0.04, which is not an integer?
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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   20 Dec 2017, 10:57
Bunuel wrote:
A merchant wants to increase the price of an item so that both the percent of increase and the resulting price in cents are positive integers. If the price of the item is $2.25, what is the least percent increase the merchant can apply? ($1 = 100 cents)

A. 2%
B. 4%
C. 10%
D. 33%
E. 100%


Find the least % increase that is a positive integer that results in a price in cents that is also a positive integer.

Like ss3617 I am not sure about the part of the question in which "a percent increase is to be a positive integer".

A. 2% * 225 = 4.5
B. 4% * 225 = 9
C. 10% * 225 = 22.5
D. 33% * 225 = 99
E. 100% * 225 = 225

It's either (E) or (B), not sure.
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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   21 Dec 2017, 05:35
What does resulting price in cents are positive integer?

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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   21 Dec 2017, 05:47
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anamika4 wrote:
What does resulting price in cents are positive integer?

Sent from my Pixel 2 using GMAT Club Forum mobile app


It means that the resulting price must be an integer, so it cannot be say 350.4 cents.
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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   21 Dec 2017, 06:18
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Bunuel wrote:
A merchant wants to increase the price of an item so that both the percent of increase and the resulting price in cents are positive integers. If the price of the item is $2.25, what is the least percent increase the merchant can apply? ($1 = 100 cents)

A. 2%
B. 4%
C. 10%
D. 33%
E. 100%


The term "positive integer" does throw off the test taker a bit since price or percentage increase doesn't seem likely to be negative anyway. The important point is that the price should be an integer.

Since we need the smallest percentage increase, we should start from the smallest value. If the price of the item is 225 cents, a 2% increase will not give an integer since 2/100 = 1/50 while 225 is odd. So 225/50 will not give an integer.

4/100 = 1/25
225 is divisible by 25 so this will give us an integer.

Answer (B)
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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   21 Dec 2017, 07:47
Bunuel wrote:
anamika4 wrote:
What does resulting price in cents are positive integer?

Sent from my Pixel 2 using GMAT Club Forum mobile app


It means that the resulting price must be an integer, so it cannot be say 350.4 cents.

Thanks

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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   24 Dec 2018, 04:43
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Bunuel wrote:
A merchant wants to increase the price of an item so that both the percent of increase and the resulting price in cents are positive integers. If the price of the item is $2.25, what is the least percent increase the merchant can apply? ($1 = 100 cents)

A. 2%
B. 4%
C. 10%
D. 33%
E. 100%


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Re: A merchant wants to increase the price of an item so that both the per [#permalink] New post   14 Aug 2022, 22:15
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Bunuel wrote:
anamika4 wrote:
What does resulting price in cents are positive integer?

Sent from my Pixel 2 using GMAT Club Forum mobile app


It means that the resulting price must be an integer, so it cannot be say 350.4 cents.



Hi Bunuel
I'm not sure if it could be the resulting price. I'm assuming the resulting price is the final price after adding the increase, which in this case would be $2.25 + $0.09 = $2.34. However, this is not an integer.

However, if the question mentioned that the resulting increase on the base price should have been an integer then this would have been a valid solution as 9 is an integer.

Until then I believe Option D is better, in which 33% results in 75 cents and the overall final price is $2.25 + $0.75 = $3.00 (integer) and everyone is happy :)

Please let me know if the interpretation is intended differently. Hope I've been able to describe this appropriately.
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A merchant wants to increase the price of an item so that both the per [#permalink] New post   07 Jan 2024, 11:35
sanjitscorps18 wrote:
Bunuel wrote:
anamika4 wrote:
What does resulting price in cents are positive integer?

Sent from my Pixel 2 using GMAT Club Forum mobile app


It means that the resulting price must be an integer, so it cannot be say 350.4 cents.



Hi Bunuel
I'm not sure if it could be the resulting price. I'm assuming the resulting price is the final price after adding the increase, which in this case would be $2.25 + $0.09 = $2.34. However, this is not an integer.

However, if the question mentioned that the resulting increase on the base price should have been an integer then this would have been a valid solution as 9 is an integer.

Until then I believe Option D is better, in which 33% results in 75 cents and the overall final price is $2.25 + $0.75 = $3.00 (integer) and everyone is happy :)

Please let me know if the interpretation is intended differently. Hope I've been able to describe this appropriately.


I agree. Thanks Bunuel for pointing me to this link.
I do think the question could say, the resultant increase (or the amount of increase etc.) in cents is an integer, instead of "resulting price in cents". It could be interpreted as 2.25 + x% of 2.25.
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A merchant wants to increase the price of an item so that both the per [#permalink]
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