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

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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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New post 20 Dec 2017, 04:10
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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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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New post 21 Dec 2017, 05:35
What does resulting price in cents are positive integer?

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New post 21 Dec 2017, 05:47
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Re: A merchant wants to increase the price of an item so that both the per  [#permalink]

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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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New post 21 Dec 2017, 07:47
Bunuel wrote:
anamika4 wrote:
What does resulting price in cents are positive integer?

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

Thanks

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New post 24 Dec 2018, 04:43
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Re: A merchant wants to increase the price of an item so that both the per   [#permalink] 24 Dec 2018, 04:43
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