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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

percentage and interest

by BTGmoderatorRO » Sat Sep 30, 2017 7:47 pm

Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?

(A) Loss of $1,250
(B) Loss of $2,500
(C) Gain of $1,250
(D) Gain of $2,500
(E) Neither a net gain nor a net loss

Is there any detailed and straight forward approach to this question? qa is b

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Source: Beat The GMAT — Problem Solving | Sat Sep 30, 2017 7:47 pm

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by GMATGuruNY » Sun Oct 01, 2017 2:52 am

Roland2rule wrote:Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?

(A) Loss of $1,250
(B) Loss of $2,500
(C) Gain of $1,250
(D) Gain of $2,500
(E) Neither a net gain nor a net loss

Since the selling price of $30,000 is 20% more than the cost price of X, the selling price of $30,000 is equal to 120% of the cost price of X:
30,000 = (120/100)X
30,000 = (6/5)X
(5/6)(30,000) = X
X = 25,000.

Since the selling price of $30,000 is 20% less than the cost price of Y, the selling price of $30,000 is equal to 80% of the cost price of Y:
30,000 = (80/100)Y
30,000 = (4/5)Y
(5/4)(30,000) = Y
Y = 37,500.

Sum of the cost prices = 25,000 + 37,500 = 62,500.
Sum of the selling prices = 30,000 + 30,000 = 60,000.
Net loss = (sum of the cost prices) - (sum of the selling prices) = 62,500 - 60,000 = 2500.

The correct answer is B.

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by EconomistGMATTutor » Fri Oct 13, 2017 9:51 am

Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?

(A) Loss of $1,250
(B) Loss of $2,500
(C) Gain of $1,250
(D) Gain of $2,500
(E) Neither a net gain nor a net loss

Hi Roland2rule,
Lets take a look at your question.

Let the property X has original value of $x, then, it sale price i.e. $30,000 at 20% profit can be represented as:
$$x\ +\ \left(20\%\right)x=30,000$$
$$x\ +\ \left(\frac{20}{100}\right)x=30,000$$
$$x\ +\ \left(0.2\right)x=30,000$$
$$1.2x=30,000$$
$$x=\frac{30,000}{1.2}$$
$$x=25,000$$

Therefore, original price of property X is $25,000 and it was sold at $30,000.
Profit Gained = $30,000 - $25,000 = $5,000

Let the property Y has original value of $y, then, it sale price i.e. $30,000 at 20% loss can be represented as:
$$y\ -\ \left(20\%\right)y=30,000$$
$$y\ -\ \left(\frac{20}{100}\right)y=30,000$$
$$y\ -\ \left(0.2\right)x=30,000$$
$$0.8x=30,000$$
$$x=\frac{30,000}{0.8}$$
$$x=37,500$$

Therefore, original price of property Y is $37,500 and it was sold at $30,000.
Loss = $37,500 - $30,000 = $7,500

There is a gain of $5,000 in property X and loss of $7,500 in property Y.
The loss is greater than the profit, so to find the total loss we will subtract the profit from the loss.

Loss = 7,500 - 5,000 = $2,500

Therefore, Option B is correct.
Hope this helps.

I am available, if you'd like any follow up.

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by Scott@TargetTestPrep » Thu Jan 04, 2018 9:19 am

Roland2rule wrote:Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?

(A) Loss of $1,250
(B) Loss of $2,500
(C) Gain of $1,250
(D) Gain of $2,500
(E) Neither a net gain nor a net loss

We can let x = cost of property X. Thus, the expression (30,000 - x) represents the amount of profit she made on property X.

Since she sold property X for 20% profit, the profit earned from the sale of property X is:

30,000 - x = 0.2x

30,000 = 1.2x

25,000 = x

So, she made a profit of 30,000 - 25,000 = 5,000 dollars on property X.

We can let y = cost of property Y. Thus, the expression (30,000 - y) is negative and represents the loss she experienced from the sale of property Y.

Since she sold property Y at a 20% loss, the loss from the sale of property Y is:

30,000 - y = -0.2y

30,000 = 0.8y

37,500 = y

So, she incurred a loss of 37,500 - 30,000 = 7,500 dollars on property Y.

Since she made 5,000 dollars on property X and lost 7,500 dollars on property Y, she had a net loss of 2,500 dollars.

Answer: B

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