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20 Dec 2017, 03:17
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B
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Difficulty:
55%
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Question Stats:
61% (01:46) correct
39%
(01:59)
wrong
based on 407
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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%
M37-89
A. 2%
B. 4%
C. 10%
D. 33%
E. 100%
M37-89
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06 Dec 2021, 04:05
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Official Solution:
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
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
General Discussion
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?
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?
