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# M12-35

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:48
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55% (hard)

Question Stats:

64% (01:02) correct 36% (01:28) wrong based on 108 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) $$100x + 100y + xy = 1330$$
[Reveal] Spoiler: OA

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Math Expert
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15 Sep 2014, 23:48
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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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08 Apr 2015, 04:15
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?
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08 Apr 2015, 04:55
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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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Location: Switzerland
Concentration: Economics, Finance
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16 Jun 2015, 10:38
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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16 Jun 2015, 10:47
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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17 Jun 2015, 09:49
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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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Joined: 22 Jul 2015
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Concentration: Entrepreneurship, Technology
GMAT 1: 640 Q42 V35
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11 Oct 2016, 03:13
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
Joined: 02 Sep 2009
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11 Oct 2016, 05:12
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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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11 Oct 2016, 05:28
Ok i see where i was going wrong now.. thanks a lot, Bunuel.
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31 Dec 2016, 11:43
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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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04 May 2017, 18:54
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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
Joined: 02 Sep 2009
Posts: 43828

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14 Jan 2018, 07:05
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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# M12-35

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