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

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Math Expert
Joined: 02 Sep 2009
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A merchant sells a certain item for a price that is a whole number of  [#permalink]

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04 Feb 2018, 21:16
00:00

Difficulty:

25% (medium)

Question Stats:

79% (00:43) correct 21% (01:00) wrong based on 32 sessions

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% _________________ BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 3034 Location: India GPA: 3.12 A merchant sells a certain item for a price that is a whole number of [#permalink] ### Show Tags 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) _________________ You've got what it takes, but it will take everything you've got SVP Joined: 26 Mar 2013 Posts: 1777 Re: A merchant sells a certain item for a price that is a whole number of [#permalink] ### Show Tags 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

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 &nbs [#permalink] 05 Feb 2018, 15:32
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