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Math Expert V
Joined: 02 Sep 2009
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Question Stats: 62% (01:06) correct 38% (01:36) wrong based on 154 sessions

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If the price increased by $$x\%$$ from 2001 to 2002 and by $$y\%$$ from 2002 to 2003, what is the percentage increase from 2001 to 2003?

(1) $$xy = 30$$

(2) $$100x + 100y + xy = 1330$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 55609

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Official Solution:

If the price increased by $$x\%$$ from 2001 to 2002 and by $$y\%$$ from 2002 to 2003, what is the percentage increase from 2001 to 2003?

The price in 2001: $$p$$;

The price in 2002: $$p*(1+\frac{x}{100})$$;

The price in 2003: $$p*(1+\frac{x}{100})(1+\frac{y}{100})=p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})$$;

The percentage increase from 2001 to 2003 is $$\frac{2003-2001}{2001}*100=x+y+ \frac{xy}{100}$$.

(1) $$xy=30$$. Not sufficient.

(2) $$100x+100y+xy=1330$$. Divide both sides by 100: $$x+y+\frac{xy}{100}=13.3$$, directly gives the answer. Sufficient.

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How do you calculate the Change: (2003-2001)/(2001) is obvious, but which values do you put in for the dates?

I can see that you get x/100 + y/100 + xy/10000 in the nominator because you subtract p, but don't you have to divide by "p" then?
Math Expert V
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NilsH wrote:
How do you calculate the Change: (2003-2001)/(2001) is obvious, but which values do you put in for the dates?

I can see that you get x/100 + y/100 + xy/10000 in the nominator because you subtract p, but don't you have to divide by "p" then?

$$\frac{2003-2001}{2001}*100=\frac{p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})-p}{p}*100=x+y+ \frac{xy}{100}$$.
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Bunuel wrote:
If the price increased by $$X\%$$ from 2001 to 2002 and by $$Y\%$$ from 2002 to 2003, what is the percentage increase from 2001 to 2003?

(1) $$XY = 30$$

(2) $$100X + 100Y + XY = 1330$$

Dear Bunuel

Could you explain step by step why 2 is sufficient. I don't see this ... what I know is that the compound increase could be calculated directly like this: (1+x/100)*(1+y/100)-1= Compound Increase

Thanks
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Math Expert V
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reto wrote:
Bunuel wrote:
If the price increased by $$X\%$$ from 2001 to 2002 and by $$Y\%$$ from 2002 to 2003, what is the percentage increase from 2001 to 2003?

(1) $$XY = 30$$

(2) $$100X + 100Y + XY = 1330$$

Dear Bunuel

Could you explain step by step why 2 is sufficient. I don't see this ... what I know is that the compound increase could be calculated directly like this: (1+x/100)*(1+y/100)-1= Compound Increase

Thanks

We need to find the value of $$x+y+ \frac{xy}{100}$$.

(2) says that $$100x+100y+xy=1330$$. Divide both sides by 100: $$x+y+\frac{xy}{100}=13.3$$.
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Bunuel wrote:
reto wrote:
Bunuel wrote:
If the price increased by $$X\%$$ from 2001 to 2002 and by $$Y\%$$ from 2002 to 2003, what is the percentage increase from 2001 to 2003?

(1) $$XY = 30$$

(2) $$100X + 100Y + XY = 1330$$

Dear Bunuel

Could you explain step by step why 2 is sufficient. I don't see this ... what I know is that the compound increase could be calculated directly like this: (1+x/100)*(1+y/100)-1= Compound Increase

Thanks

We need to find the value of $$x+y+ \frac{xy}{100}$$.

(2) says that $$100x+100y+xy=1330$$. Divide both sides by 100: $$x+y+\frac{xy}{100}=13.3$$.

Okay. I am trying to find the logic behind and I would love to verify that the compound increase over 2 years calculated as (1.1*1.1)=21% is the same as this formula above, which I have never seen before. Every day I feel I need to start from the very beginning... _________________
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Bunuel wrote:
NilsH wrote:
How do you calculate the Change: (2003-2001)/(2001) is obvious, but which values do you put in for the dates?

I can see that you get x/100 + y/100 + xy/10000 in the nominator because you subtract p, but don't you have to divide by "p" then?

$$\frac{2003-2001}{2001}*100=\frac{p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})-p}{p}*100=x+y+ \frac{xy}{100}$$.

Sorry for the basic question but how did the equation for (2003-2001)/(2001)x100 become x+y+xy/100 ? I can not seem to foil out to get the result in bold.

Also, is there a link you can recommend for % change problems?

Math Expert V
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yousefalj wrote:
Bunuel wrote:
NilsH wrote:
How do you calculate the Change: (2003-2001)/(2001) is obvious, but which values do you put in for the dates?

I can see that you get x/100 + y/100 + xy/10000 in the nominator because you subtract p, but don't you have to divide by "p" then?

$$\frac{2003-2001}{2001}*100=\frac{p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})-p}{p}*100=x+y+ \frac{xy}{100}$$.

Sorry for the basic question but how did the equation for (2003-2001)/(2001)x100 become x+y+xy/100 ? I can not seem to foil out to get the result in bold.

Also, is there a link you can recommend for % change problems?

$$\frac{2003-2001}{2001}*100=\frac{p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})-p}{p}*100=$$

Reduce by p: $$((1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})-1)*100$$

$$(\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})*100$$

$$=x+y+ \frac{xy}{100}$$
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Ok i see where i was going wrong now.. thanks a lot, Bunuel.
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4
Hey guys, formulas may seem daunting for some people, and definitely true for me.

I plugged in simple numbers to verify my answer.
For example:

From 2001 to 2002 : 10% increase
From 2002 to 2003 : 20% increase

2001 : 100
2002 : 110 (10% increase from 100)
2003 : 132 (20% increase from 110)

From above, the increase is obviously 32%. (100 -> 132)

Statement (1) is obviously NOT Sufficient
Statement (2) on the other hand : x+ y + xy/100 -> 10+20+2 = 32

Statement (2) alone is sufficient. (B)
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I thought that on the Data Sufficiency questions, both statements have to be true (regardless of whether or not they are sufficient)

Now, Statement TWO cannot be true and sufficient, if according to Statement 1, XY = 30, which means that the sum of X + Y should add up to over 10 (such as 5+6 or 3+10). Both statements have to be true, which contradicts statement two where X+Y can't be greater than 8.

Am I missing something here?
Math Expert V
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DanceWithFire wrote:
I thought that on the Data Sufficiency questions, both statements have to be true (regardless of whether or not they are sufficient)

Now, Statement TWO cannot be true and sufficient, if according to Statement 1, XY = 30, which means that the sum of X + Y should add up to over 10 (such as 5+6 or 3+10). Both statements have to be true, which contradicts statement two where X+Y can't be greater than 8.

Am I missing something here?

You are right. Edited the question. Sorry it took so long.
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Bunuel wrote:
Official Solution:

If the price increased by $$x\%$$ from 2001 to 2002 and by $$y\%$$ from 2002 to 2003, what is the percentage increase from 2001 to 2003?

The price in 2001: $$p$$;

The price in 2002: $$p*(1+\frac{x}{100})$$;

The price in 2003: $$p*(1+\frac{x}{100})(1+\frac{y}{100})$$

$$p*(1+\frac{x}{100})(1+\frac{y}{100})$$ = p*(1.01x)(1.01y)

So if we know the value of xy, we can find the percentage inc from 2001 to 2003.
Bunuel
Where am i going wrong
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Math Expert V
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itisSheldon wrote:
Bunuel wrote:
Official Solution:

If the price increased by $$x\%$$ from 2001 to 2002 and by $$y\%$$ from 2002 to 2003, what is the percentage increase from 2001 to 2003?

The price in 2001: $$p$$;

The price in 2002: $$p*(1+\frac{x}{100})$$;

The price in 2003: $$p*(1+\frac{x}{100})(1+\frac{y}{100})$$

$$p*(1+\frac{x}{100})(1+\frac{y}{100})$$ = p*(1.01x)(1.01y)

So if we know the value of xy, we can find the percentage inc from 2001 to 2003.
Bunuel
Where am i going wrong

How did you get the highlighted part?

$$p*(1+\frac{x}{100})(1+\frac{y}{100})=p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})$$ NOT p*(1.01x)(1.01y) and the the percentage increase from 2001 to 2003 is $$\frac{2003-2001}{2001}*100=x+y+ \frac{xy}{100}$$.
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Bunuel KarishmaB niks18 PKN chetan2u gmatbusters

I am at times more comfortable with decimals than fractions since later make me
intimated Can you explain what is incorrect here:
price in 2001: p
price in 2002: (1.0x) * p
price in 2003: (1.0y) * (1.0x) * p

% change = [ (new) - (old) ] / old

Now this is where I faltered: to multiply say 1.01 and 1.03 .
Is the best strategy to use fractions ie % (means to divide by 100)
I found (1+a) (1+b) = 1 + a + b + ab
too prone to mistake in calculations.

Let me know if there is any other approach that I can take?
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Bunuel KarishmaB niks18 PKN chetan2u gmatbusters

I am at times more comfortable with decimals than fractions since later make me
intimated Can you explain what is incorrect here:
price in 2001: p
price in 2002: (1.0x) * p
price in 2003: (1.0y) * (1.0x) * p

% change = [ (new) - (old) ] / old

Now this is where I faltered: to multiply say 1.01 and 1.03 .
Is the best strategy to use fractions ie % (means to divide by 100)
I found (1+a) (1+b) = 1 + a + b + ab
too prone to mistake in calculations.

Let me know if there is any other approach that I can take?

Hey i would like to know what exactly did u mean by this :
price in 2001: p
price in 2002: (1.0x) * p
price in 2003: (1.0y) * (1.0x) * p

i think u consider (X) a single digit .... for example if x= 5%
then price in 2002- 1.05 *p

if (X) is a two digit integer then.... for example if x=20%
the price in 2002- 1.2*p

this is where i guess u did a mistake.... its better like this - (100+x/100)*p
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CPGguyMBA2018 wrote:
Hey guys, formulas may seem daunting for some people, and definitely true for me.

I plugged in simple numbers to verify my answer.
For example:

From 2001 to 2002 : 10% increase
From 2002 to 2003 : 20% increase

2001 : 100
2002 : 110 (10% increase from 100)
2003 : 132 (20% increase from 110)

From above, the increase is obviously 32%. (100 -> 132)

Statement (1) is obviously NOT Sufficient
Statement (2) on the other hand : x+ y + xy/100 -> 10+20+2 = 32

Statement (2) alone is sufficient. (B)

Is this solution ok? Since we are not doing anything on RHS M12-35   [#permalink] 26 Nov 2018, 05:12
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