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A merchant sells a certain item for a price that is a whole number of

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A merchant sells a certain item for a price that is a whole number of [#permalink]

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New post 04 Feb 2018, 21:16
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (00:41) correct 23% (01:00) wrong based on 29 sessions

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A merchant sells a certain item for a price that is a whole number of dollars. If the cost of the item to her is $50, then which of the following could be her profit as a percentage of her cost?

(A) 15%

(B) 25%

(C) 33 1/3%

(D) 40%

(E) 75%
[Reveal] Spoiler: OA

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A merchant sells a certain item for a price that is a whole number of [#permalink]

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New post 05 Feb 2018, 03:03
Analyzing the answer options to calculate the total profit

(A) 15% of 50 is 7.5
(B) 25% of 50 is 12.5
(C) 33 1/3% of 50 is 16.67

(D) 40% of 50 is 20
(E) 75% of 50 is 37.5

Since selling price is the sum of the cost price and the profit, only 40%
gives us a whole number for selling price, making it our answer choice.(Option D)
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Re: A merchant sells a certain item for a price that is a whole number of [#permalink]

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New post 05 Feb 2018, 15:32
Bunuel wrote:
A merchant sells a certain item for a price that is a whole number of dollars. If the cost of the item to her is $50, then which of the following could be her profit as a percentage of her cost?

(A) 15%

(B) 25%

(C) 33 1/3%

(D) 40%

(E) 75%


Profit = Price - Cost

\(\frac{Profit}{Cost}\) = \(\frac{Price - Cost}{Cost}\) = \(\frac{Price - 50}{50}\)

Now lets make the denominator = 100...So multiply both numerator and denominator by 2

\(\frac{2Price - 100}{100}\)

Now you can equal each answer choice easily with equation above.......You need answer that creates even number to be divided by 2

Choices A, B, & E makes the number ending with 5 odd............Eliminate

Choice C is very clear ..........................................................Eliminate

Only one answer left.

Answer D

Check it

2Price - 100 = 40.........2Price = 140......P= 70...Bingo :-)
Re: A merchant sells a certain item for a price that is a whole number of   [#permalink] 05 Feb 2018, 15:32
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