A merchant prices a television at 60 percent above . . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

A merchant prices a television at 60 percent above . . . .

by Vincen » Tue Dec 19, 2017 7:29 am

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A merchant prices a television at 60 percent above wholesale. For a Presidents' Day sale, the merchant marks the television down by 25 percent. If he sells the television during the Presidents' Day sale, what percentage over the wholesale price will he have earned?

A. 75
B. 50
C. 35
D. 25
E. 20

The OA is option E.

This is a very real question. I would like to know how to solve it? Experts, may you give me a detailed explanation here? I'd be thankful.

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Source: Beat The GMAT — Problem Solving | Tue Dec 19, 2017 7:29 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

A merchant prices a television at 60 percent above . . . .

by EconomistGMATTutor » Tue Dec 19, 2017 10:34 am

A merchant prices a television at 60 percent above wholesale. For a Presidents' Day sale, the merchant marks the television down by 25 percent. If he sells the television during the Presidents' Day sale, what percentage over the wholesale price will he have earned?

A. 75
B. 50
C. 35
D. 25
E. 20

The OA is option E.

This is a very real question. I would like to know how to solve it? Experts, may you give me a detailed explanation here? I'd be thankful.

Hi Vincen,
Let's take a look at your question.

Let the wholesale price of the television be '$x", then,
$$\text{Price of television with 60% increase}=x+60\%x=x+0.6x=1.6x$$

At Presidents' Day sale, the television is marked down by 20%.
Let's first calculate the discount offered at Presidents' Day sale,
$$Discount=\left(1.6x\right)\left(25\%\right)$$
$$Discount=\left(1.6x\right)\left(0.25\right)$$

New Price after discount will be:
$$\text{New Price after discount} =\ 1.6x-\left(1.6x\right)\left(0.25\right)$$
$$\text{New Price after discount}=\ 1.6x\left(1-0.25\right)$$
$$\text{New Price after discount} =\ 1.6x\left(0.75\right)$$
$$\text{New Price after discount} =\ 1.2x$$
To find the percentage earned over the whole sale price, we will rewrite this expression,
$$\text{New Price after discount} =\ (1+0.2)x$$
$$\text{New Price after discount} =\ (1+\dfrac{20}{100})x$$
$$\dfrac{20}{100} \text{represents 20 percent.}$$

Therefore, the merchant earned 20% profit over the whole sale price.

Hence, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Tue Dec 19, 2017 10:46 am

Vincen wrote:A merchant prices a television at 60 percent above wholesale. For a Presidents' Day sale, the merchant marks the television down by 25 percent. If he sells the television during the Presidents' Day sale, what percentage over the wholesale price will he have earned?

A. 75
B. 50
C. 35
D. 25
E. 20

Let the wholesale price = 100.
After a 60% markup, the regular selling price = 100 + (60% of 100) = 100+60 = 160.
After a 25% discount, the discounted selling price = 160 - (25% of 160) = 160 - 40 = 120.
Profit = (discounted selling price) - (wholesale price) = 120-100 = 20.
Thus:
profit/wholesale = 20/100 = 20%.

The correct answer is E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Sep 13, 2019 3:25 pm

Vincen wrote:A merchant prices a television at 60 percent above wholesale. For a Presidents' Day sale, the merchant marks the television down by 25 percent. If he sells the television during the Presidents' Day sale, what percentage over the wholesale price will he have earned?

A. 75
B. 50
C. 35
D. 25
E. 20

The OA is option E.

This is a very real question. I would like to know how to solve it? Experts, may you give me a detailed explanation here? I'd be thankful.

We can let the wholesale price of the television be $100. Thus the regular retail price of the television is $160, and the discounted price is 160 x 0.75 = $120. We see that $120 is 20% over the wholesale price of $100.

Answer: E

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