The price of a consumer good increased by p%. . .

Question

The price of a consumer good increased by $p$% during $2012$ and decreased by $12$% during $2013$. If no other change took place in the price of the good and the price of the good at the end of $2013$ was $10$% higher than the price at the beginning of $2012$, what was the value of $p$?

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Official Answer

D

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BrentGMATPrepNow · Accepted Answer

Let  $100  be the original price

The price of a consumer good increased by p% during 2012  
p% = p/100, so a p% INCREASE is the same a multiplying the original price by 1 + p/100
So, the new price = ( $100 )(1 + p/100)

The price then decreased by 12% during 2013  
A 12% DECREASE is the same a multiplying the price by 0.88
So, the new price = ( $100 )(1 + p/100)(0.88)

The price of the good at the end of 2013 was 10% higher than the price at the beginning of 2012  
If the original price was  $100 , then the price at the end of 2013 was  $110 
So, we can write:  $110  = ( $100 )(1 + p/100)(0.88)
Simplify:  $110  = (100 + p)(0.88)
Simplify more:  $110  = 88 + 0.88p
Subtract 88 from both sides: 22 = 0.88p
So, p = 22/0.88 = 25
Answer:  D

Abhishek009 · Answer

Price's corresponding to year -

2011 =  100 
2012 =  100 + p 
2013 =  \frac{88}{100}(100 + p)

Further ,  \frac{88}{100}(100 + p)  =  110

Or,  \frac{8}{100}(100 + p)  =  10

Or, 800 + 8p = 1000

Or, 8p = 200

So, p = 25%
 
Hence, answer will be (D) 25%

Joc456 · Answer

Lets start with a number for the original value. 100 is the easiest.

So we're looking for a value of 110 at the end of 2013.

Just by looking at the values we can get an idea of what to start testing. If we're increasing 100 by p% then decreasing it by 12% and the original value is still 10% higher we need a value much higher than 12. 25% is the easiest value to start with.

100+25%=125

125-12%=110

D

stonecold · Answer

For all the algebra loving people out there=>
Let price at the beginning of 2012 be $x
so after the end of 2012=> x 
And finally at the end of 2013 => x

As per question=> Price was simple 10 percent greater
Hence x  must be the final price.
Equating the two we get
=> x =x  
=> 44p+4400=5500
=> 44p=1100
=> p=1100/44=> 100/4=> 25.
So p must be 25

falakdoshi · Answer

Let Price = 100

Increased by P% = 100(1+P/100)

Treat it like successive percents;

So a 12% decrease would mean 88% of (1+P/100) of 100

The key words are no other change took place. So there are no further successive percents, and the final price = 110

Therefore:

88/100 * (1+P/100) * 100 = 110

=> 8800 + 88P = 11,000
=> 88P = 2200 
=> P = 2200/88
=> P = 25%

EgmatQuantExpert · Answer

Hey,

The given question can be solved in a number of ways. Let's look at two most common ways to solve this question. We will share two more ways of solving this question tomorrow.

Method 1 :

o Therefore, the price at the end of 2013 = $100 + (10$ % of $100) = 110$

Therefore, the price at the beginning of 2013 is 125 and we got this value after p% increase over the initial value.
Thus, we can write –

Method 2 :

Conventional method –

o Price at the beginning of 2013 $= 100 + (p$ % of $100) = 100 + p$

o Value at the beginning of 2013 $* (1 – \frac{12}{100}) = (100 + p) * \frac {22}{25}$……………..(i)

Therefore, $p = 25$%

There are more innovative ways to solve this question. A few of them have not been discussed here. Can you all think of any other way to solve it? Would love to see a few other methods!

I will post two more ways to solve this question tomorrow. In the mean time, expecting some more responses with other ways to solve this question

Thanks,
Saquib
e-GMAT
Quant Expert

I will post two more ways to solve this question tomorrow. In the mean time, expecting some more responses with other ways to solve this question

Thanks, Saquib e-GMAT Quant Expert

EgmatQuantExpert · Answer

Hi,

Thanks for posting a different way of approaching this problem. In fact, the approach followed by you is very close to one of the innovative ways that we talked about in our official solution. The only difference being in your approach you have concluded that p should be much larger than 12. Going a step further,   you can also conclude that p should be larger than 22% (12%+10%).   Once you do so, you don't even need to pick any number. The only option which will satisfy it is D. 25%.

When we post our detailed solution using the two innovative methods tomorrow, we will explain how we can conclude that p should be greater than 22%   .

Regards,
Saquib

EgmatQuantExpert · Answer

As discussed, let's look at one of the innovative ways of solving the above question.    It is one of the quickest ways to solve a question that involves successive percentage increase/decrease on the same value.    Please take a note of this approach and apply it on some GMAT questions to master it.

So, let's quickly look at this    smart approach.

When a number is    increased successively    by two percentage, let's assume,  a % and  b %, the net increase in the value of the number can be expressed by the formula,

Net increase  =a+b+\frac {ab}{100}

Le's take a simple example to understand. If we increase a number, let's say, X successively by 10% and 20% respectively, the net increase according to the above formula should be,

Net increase  =10+20+\frac {10*20}{100}=10+20+\frac {200}{100} = 10+20+2 = 32 %

Isn't that quick!! A nice method to keep in your arsenal to solve Percent question involving successive increase quickly.

One good thing about the above formula is that you can use it to calculate the net decrease in case of successive decrease too.    All you need to do is in case of decrease represent the percent as negative. Easy isn't it   . Let's see an application quickly.

If we decrease a number, let's say, X successively by 10% and 20% respectively, the net increase according to the above formula should be,

Net increase  =(-10)+(-20)+\frac {(-10)*(-20)}{100}=-10-20+\frac {200}{100} = -10-20+2 = (-28) %

Notice carefully, the sign of the net increase is negative, clearly indicating the after the successive decrease the value of the original number, decreased instead of increasing. And what was the magnitude??? Right 28%. The net decrease is 28%.

So, before we use this approach to give you an official answer for the above question, would you like to have a quick stab at it. Remember, you need to be careful about the sign of the change. Increase is represented by positive and decrease is represented by negative. All the best.

We will post the detailed solution tomorrow and then we will show another innovative method of solving this question.

Regards,
Saquib

EgmatQuantExpert · Answer

Alright, so let's look at the official solution to the above questions using the innovative formula on Net increase discussed in the last post.

We know that the price of the consumer good increased by  p % and then decreased by  12 %. Hence, using the formula for net increase we can say,

Net increase  =p+(-12)+\frac {p*(-12)}{100}=p-12-\frac {3p}{25} = (\frac {22p}{25} - 12) %

It is given in the question that the net increase finally is  10 %. Hence, we can equate the two values.

(\frac {22p}{25} - 12) % =  10 %    
or,      \frac {22p}{25} = 10+12 = 22 %    
or,      p = 25 %

Hence, the answer is 25%.

Now, with this understanding try to solve this question in an even better way. Give it a try and we will post the official solution in another innovative way soon.

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Quant-workshop_Webinar-e1533628475738.jpg

Abhishek009 · Answer

p - 12 - \frac{12p}{100} = 10

100p - 1200 -12p = 1000

88p = 2200 
 p = 25 
  
Hence, the correct answer must be (D) 25

ScottTargetTestPrep · Answer

We let the 2012 price = n and thus, the price at the end of 2013 will be:

(1 + p/100)(0.88)(n)

Since the price at the end of 2013 was 10% higher than at the beginning of 2012, we can create the equation:

1.1n = (1 + p/100)(0.88)(n)

1 = (1 + p/100)(0.8)

1 = 0.8 + 0.8p/100

Multiplying by 100, we have:

100 = 80 + 0.8p

20 = 0.8p

25 = p

Alternate Solution:

Let’s let the price at the beginning of 2012 be 100. Since the price at the end of 2013 was 10% higher, the price at the end of 2013 is 1.1 x 100 = 110. We know the price decreased by 12% and became 110; therefore, before decreasing by 12%, the price was 110/0.88 = 125. Now, the price of 100 increases by p percent and becomes 125; therefore the value of p is   x 100 = 25.

Answer: D

KanishkM · Answer

10 % will be a successive percentage change, which is calculated by

a + b + ab/100 = Percentage change

p - 12 - 12p/100 = 10

100p -1200 - 12p = 1000
p = 2200/88

p = 25 %

D

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The price of a consumer good increased by p%. . .

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