Ms. Adams sold two properties, X and Y, for $30,000 each. She sold pro

Question

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

(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

GMATinsight · Accepted Answer

There is a property to solve such questions with  Common Selling Price  and  Common %gain and loss . such cases always result in a loss and...

Total %Loss = (Common Gain% or Loss%/10)^2

Hence Here Loss% = (20/10)^2 = 4%

which means he recovered only 96% of his investment which amount to a total revenue = 30000 + 30000 = 60000

i.e. 96% of cost = 60000
therefore, 4% of cost ( Loss ) = $2500

Answer: Option  B

KarishmaB · Answer

Check out this post: https://anaprep.com/arithmetic-profit-o ... e-formula/ It discusses how and why we get this formula: When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is an overall loss. The loss% = (x^2/100)% So the loss % here is (20^2/100)% = 4% Now just approximate. The Cost price will be higher than the selling price and overall selling price is 2*30,000 = $60,000 4% of selling price (60,000) is 2400 so 4% of cost price will be slightly higher. Answer must be (B)

GMATinsight · Answer

ALTERNATE

COST PRICE = SELLING PRICE - PROFIT

i.e. COST PRICE of X = 30,000 - (20/100)* COST
i.e. 1.2 Cost of X = 30000
i.e. Cost of X = 30000/1.2 = 25000

Similarly,
COST PRICE = SELLING PRICE + LOSS

i.e. Cost of Y = 30,000 + (20/100)* COST
i.e. 0.8 Cost of Y = 30000
i.e. Cost of Y = 30000/0.8 = 37500

Total Cost of X and Y = 25000 + 37500 = 62500
Total Revenue = 62500 - 60000 = 2500

Answer: Option  B

CharmiShah · Answer

COST PRICE = SELLING PRICE - PROFIT

i.e. COST PRICE of X = 30,000 - (20/100)* COST
i.e.  1.2 Cost of X = 30000  -------> I got that because of 20% you did 1.2 but why 1.2 Cost of X = 30000 ..?
i.e. Cost of X =   30000/1.2   = 25000 -------> why division ?

Similarly,
COST PRICE = SELLING PRICE + LOSS

i.e. Cost of Y = 30,000 + (20/100)* COST
i.e.  0.8 Cost of Y = 30000  ------> Same as above query that 20% loss is 0.80 but what it has to do with X that I didnt get.
i.e. Cost of Y =  30000/0.8 = 37500-------> why division ?

Total Cost of X and Y = 25000 + 37500 = 62500
Total Revenue = 62500 - 60000 = 2500

I could not get this solution. Could you please explain .

GMATinsight · Answer

These are simple arithmatic calculations

COST of X = 30,000 - (20/100)* COST of X
i.e. COST of X = 30,000 - 0.2* COST of X
i.e. COST of X+ 0.2* COST of X = 30,000 
i.e. 1.2* COST of X = 30,000 
i.e. COST of X = 30,000 / 1.2 = 25000

Similarly,
COST of X = 30,000 + (20/100)* COST of X
i.e. COST of X = 30,000 + 0.2* COST of X
i.e. COST of X- 0.2* COST of X = 30,000 
i.e. 0.8* COST of X = 30,000 
i.e. COST of X = 30,000 / 0.8 = 37500

I hope it helps!

CharmiShah · Answer

yes now I got it. 
many thanks.

GMATinsight · Answer

Tradition of extending " Thanks " on GMAT CLUB is by pressing the button of +1KUDOS

muzdamahbub · Answer

The underlying concept here is percent change.

The problem give us the selling price, so we need to find the original price of each property before their respective increase and decrease in price.

Step 1-The selling price of the first property is $30,000. this is the price AFTER an increase of 20%, so the original price is x times 1.20 since the price INCREASED 20%. That leaves us with x*1.20=30,000------->x=25,000. Thus, the price increased $5,000

Step 2-The selling price of the Property y is 30,000. This is the price AFTER a decrease of 20%, so the original price is y times .80 since 1.00-.20=.80. That leaves us with y*.80=30,000-------y=37,500. Thus the price decreased 75,00

Finally, we need to find out whether or not Ms. Adams made money. So we vet the two prices. 5000-7500=-2500. So overall, 
she lost 2500.

This problem is a lot easier to manage if you make a table using the formula for percent change...

ScottTargetTestPrep · Answer

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

kelly_jacques · Answer

KarishmaB Thank you once again for your excellent answers on GMATClub. Do you have a suggestion for more accurately using your method? It saves so much time, but I have run into other problems where there is more than one possible answer. In this case, the other loss option was below 2400, so we knew it was incorrect and there was only one answer. However, if we take a similar example like this one https://gmatclub.com/forum/a-lady-sold- ... fl=similar, when you solve it in your way (i.e. (20/10)^2 and multiply it by the selling price, there are two possible loss answers that could be feasible. How am I supposed to know which one is correct without doing the long method?

KarishmaB · Answer

The formula gives you the overall loss %. You can use it to get cost price and then get the overall loss. I have shown how to do it here: https://gmatclub.com/forum/a-lady-sold- ... l#p3220223 You don't need to use the long method then.

Abhishek009 · Answer

CP of item X is  \frac{30000}{120}*100 = 25000 
CP of item Y is  \frac{30000}{80}*100 = 37500

Total CP of X & Y is 62500
Total SP X & Y is 60000

So, Loss is 2500, Answer must be (B)

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