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Re M1235 [#permalink]
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16 Sep 2014, 00:48



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Re: M1235 [#permalink]
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08 Apr 2015, 05:15
How do you calculate the Change: (20032001)/(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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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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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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Re: M1235 [#permalink]
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11 Oct 2016, 04:13
Bunuel wrote: NilsH wrote: How do you calculate the Change: (20032001)/(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? \(\frac{20032001}{2001}*100=\frac{p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})p}{p}*100=x+y+ \frac{xy}{100}\). Sorry for the basic question but how did the equation for (20032001)/(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? Thanks in advance.



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Re: M1235 [#permalink]
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11 Oct 2016, 06:12
yousefalj wrote: Bunuel wrote: NilsH wrote: How do you calculate the Change: (20032001)/(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? \(\frac{20032001}{2001}*100=\frac{p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})p}{p}*100=x+y+ \frac{xy}{100}\). Sorry for the basic question but how did the equation for (20032001)/(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? Thanks in advance. \(\frac{20032001}{2001}*100=\frac{p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000})p}{p}*100=\) 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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Re: M1235 [#permalink]
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11 Oct 2016, 06:28
Ok i see where i was going wrong now.. thanks a lot, Bunuel.



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Re: M1235 [#permalink]
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31 Dec 2016, 12:43
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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Re: M1235 [#permalink]
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04 May 2017, 19:54
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?



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Re: M1235 [#permalink]
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14 Jan 2018, 08:05



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Re: M1235 [#permalink]
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01 Apr 2018, 12:41
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. BunuelWhere am i going wrong
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Re: M1235 [#permalink]
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01 Apr 2018, 21:14
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. BunuelWhere 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 \(\frac{20032001}{2001}*100=x+y+ \frac{xy}{100}\).
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