The price of a jacket is reduced by 25%. During a special sale the pri

Question

The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 10%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?

A) 32.5
B) 35
C) 48
D) 65
E) 67.5

Kudos for a correct solution.

A) 32.5
B) 35
C) 48
D) 65
E) 67.5

Kudos for a correct  solution .

goldfinchmonster · Answer

1) Let the price of jacket initially be $100.

2) Then it is decreased by 25% , therefore bringing down the price to $75.

3) Again it is further discounted by 10%, therefore bringing down the price to $67.5.

4) Now 67.5 has to be added by  X %  in order to equal the original price.

67.5 + ( X% ) 67.5 = 100.

Solving this eq for X, we get X = 48.1

Ans is C.

dominicraj · Answer

Hi,

Correct answer and approach. +1 C.

Regards,
Dom.

anudeep133 · Answer

Solution:

Let the price be 100. 
Then first reduced price is 100-0.25(100)=75
Second reduced price is 75-0.1(75)=67.5
To increase the price to 100, it should be increased by ((100-67.5)/67.5)*100 = 48.1%

Option C

harishbiyani8888 · Answer

Correct answer is C

In these type of questions it is best to use smart numbers, preferably 100.

Assume the initial price of jacket to be $100.
Price is decreased by 25% , therefore the new price is $75.
The price is further discounted by 10%, therefore the revised price is $67.5.

Now 67.5 has to be added by X % in order to equal the original price.

67.5 + ( X% ) 67.5 = 100.
Therefore, X = 325*10*10/675

Solving this equation for X, we get X = 48.1

BASSLJ · Answer

Assume Jacket costs $100. Reduce by 25% = $75. Reduce by an additional 10% from the discounted price = $75 - $7.5 = $67.5.

Now to get the Jacket to the original price of $100 we must multiply $67.5 by 1 + X where X is a percentage.

So 100 = 67.5X + 67.5
32.5 = 67.5X
32.5/67.5= X
approx 48 = X

Therefore C,

Bunuel · Answer

PRINCETON REVIEW OFFICIAL SOLUTION:

So what’s the answer here? If 35 looks like a good option to you, you’re in good company. It seems that a 25% discount followed by a 10% discount should total a 35% discount. But if the question were really that easy it wouldn’t be on the GMAT. This is where test-taking savvy has to kick in. You aren’t going to spend your time on the GMAT adding together two numbers that appear in the problem and getting the correct answer. That’s way too easy. 35 is a trap answer, and you need to train yourself to spot trap answers. So what’s the real answer if it’s not 35?

Let’s make this more concrete and give the jacket a price. For simplicity, call it a $100 jacket. A 25% discount will be $25, so now we have a $75 jacket. Next, another 10% is taken off. 10% of 75 is 7.5, so the new price is 75 − 7.5 = 67.5. After the two discounts the jacket costs $67.50. (Now you can see why 35% is incorrect. The two discounts can’t simply be added, because the second one is being taken from a different base number (75) than the first one (100) is.) To get back to $100 we have to raise the price $32.50. Now we need to use the percent change formula: Percent change =  \frac{difference}{original}*100 . In a percent increase problem, the “original” number will be the smaller one, so our formula is 32.5/67.5*100. We don’t need to do the full calculation because 32.5/67.5 is a little less than one half, and the only answer that’s in the ballpark is 48% in  Answer C . As you can see, there are a lot of steps to this problem, and anyone who blithely picks 35 and moves on is missing all the important stuff.

Temurkhon · Answer

(3/4)*(9/10)*x=(27/40)*x

so, we need to increase by 13/40 to get x

(13/40:27/40)*100=48%

C

mvictor · Answer

use approximations
say p=1000
drops by 25% = 750
drops by another 10% = 675
we need to increase the price by 325
325/675 => that's almost 1/2, but less than 1/2
A, B, D, E are eliminated just by logically thinking about it.

GMATWhizTeam · Answer

Let the price of the jacket be $1000. After a reduction of 25%, price of jacket = $ 750
This price is reduced further by another 10% during the special sale. 
Therefore, final price of jacket = $ 675, since 10% of 750 = 75.

By what value should this price be increased to restore it to its original value? 675 should be increased by 325 to restore it to 1000.

At this stage, it’s easy to fall for the trap answer option A, if you are not careful. If you compare 325 with 1000, you will say that the price should be increased by 32.5%; however, this is not correct.

You are increasing the number 675 by 325 to get 1000. Therefore, the value 325 should be compared with 675 to find out the required percentage.
Percentage by which price of jacket should be increased to restore it to its original value =  \frac{325 }{ 675}  * 100

Simplifying  \frac{325 }{ 675} , we get  \frac{13 }{27} ;  \frac{13 }{ 26}  =  \frac{1 }{ 2}  = 50%; therefore,  \frac{13 }{ 27}  should be slightly smaller than 50%.

The only number among the options that satisfies this situation is 48. 
675 should be increased by approximately 48% to restore the jacket’s price to its original amount.

The correct answer option is C.

Abhishek009 · Answer

Effective discount is  -25 - 10 + \frac{(-25)(-10)}{100} = -32.5

Thus, % price to be increased is  \frac{32.5}{67.5}*100  ~  48 , Answer must be (C)

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