Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39660

Re: Nice question on percentage [#permalink]
Show Tags
29 Oct 2013, 10:28
AccipiterQ wrote: Bunuel wrote: prashantbacchewar wrote: The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ? (200x)\(100 + 2x) x(2 + x)\(1 + x)^2 2x\1 + 2x x(200 + x)\10,000 100 –( 10,000 \ 100 + x)
I got this question on MGMAT exam and got it wrong during the test. Later during the review I was able to solve this question correctly. I felt I should post this. Let the value of investment at the beginning of January be \(I\). Then the value of the investment at the end of February would be \(I(1+\frac{x}{100})(1\frac{y}{100})\). We are told that these values are equal: \(I=I(1+\frac{x}{100})(1\frac{y}{100})\) > \(100^2=(100+x)(100y)\)Answer: E. This question can also be done by picking some smart numbers for I, x and y (say I=10, x=100 and y=50). how did you get rid of the 100s on the bottom of each fraction and end up with 10000 on the other side? If you took the (1+x/100) portion and multiplied teh whole equation by 100 to get rid of it wouldn't you end up with (100+X)*(100y)=100, since when multiplying by 100 you get rid of the 100 beneath the Y as well? \(1=(1+\frac{x}{100})(1\frac{y}{100})\); \(1=(\frac{100+x}{100})(\frac{100y}{100})\); \(100*100=(100+x)(100y)\). Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 30 Jul 2011
Posts: 11
Location: United States
Concentration: Finance, Economics
GMAT Date: 05312024

Re: The value of an investment increases by x% during January [#permalink]
Show Tags
16 Nov 2013, 12:41
So I have a couple of principles that I think we can apply here to solve the problem quickly. For successive % changes, we must realize the following: 1) if x > y, the change is going to be positive, negative, or zero. For example, 100 is increased by 10% so we get 110. Then 110 is decreased by 2%, the result is ~108. So we have a net positive change. If 110 is decreased by ~9.09%, the result is 100. So we have a net change of 0. If 110 is decreased by ~9.99%, the result is 99, so the net change is negative.
2) If x<y, the net change is always going to be negative. For example, 100 is increased by 10%, which gives us 110 and then 110 is decreased by 11% which gives us ~98.
3) If x=y, the net change is always going to be negative. For example, 100 is increased by 10%, which gives us 110 and then 110 is decreased by 10% which gives us 99. This reminds me of my investment in Apple's stock. One day I'm up 3% and then the next day I'm down 3% and initially, I might think that I'm at a net change of 0, but I actually lost money . If my initial $100 goes up by 3%, I now have 103 (w00t w00t!), but if my $103 goes down by 3% the next day, I have less than my initial 100 because 3% of 103 is more than 3% of 100.
Now, for this problem, we are told that the net change is zero, so using the principles above, we know that x > y and more importantly, we get a net change of zero whenever we increase by 10% and decrease by a little more than 9%. So therefore, all we need to do is plug in 10 for x and the answer choice that gives us ~9 is correct. I think if we remember these very easy principles, it will help us in the long run, because we are able to solve problems such as this one, in under 2 minutes.



Senior Manager
Joined: 15 Aug 2013
Posts: 311

Re: The value of an investment increases by x% during January [#permalink]
Show Tags
03 Aug 2014, 18:34
Bunuel wrote: prashantbacchewar wrote: The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ? (200x)\(100 + 2x) x(2 + x)\(1 + x)^2 2x\1 + 2x x(200 + x)\10,000 100 –( 10,000 \ 100 + x)
I got this question on MGMAT exam and got it wrong during the test. Later during the review I was able to solve this question correctly. I felt I should post this. Let the value of investment at the beginning of January be \(I\). Then the value of the investment at the end of February would be \(I(1+\frac{x}{100})(1\frac{y}{100})\). We are told that these values are equal: \(I=I(1+\frac{x}{100})(1\frac{y}{100})\) > \(100^2=(100+x)(100y)\) > \(100^2=100^2100y+100xxy\) > \(y=\frac{100x}{100+x}\) or which is the same \(y=100\frac{10,000}{100+x}\). Answer: E. This question can also be done by picking some smart numbers for I, x and y (say I=10, x=100 and y=50). Hi Bunuel, How did you make the leap from ? \(y=\frac{100x}{100+x}\) or which is the same \(y=100\frac{10,000}{100+x}\).



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: The value of an investment increases by x% during January [#permalink]
Show Tags
03 Aug 2014, 23:16
russ9 wrote: Bunuel wrote: prashantbacchewar wrote: The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ? (200x)\(100 + 2x) x(2 + x)\(1 + x)^2 2x\1 + 2x x(200 + x)\10,000 100 –( 10,000 \ 100 + x)
I got this question on MGMAT exam and got it wrong during the test. Later during the review I was able to solve this question correctly. I felt I should post this. Let the value of investment at the beginning of January be \(I\). Then the value of the investment at the end of February would be \(I(1+\frac{x}{100})(1\frac{y}{100})\). We are told that these values are equal: \(I=I(1+\frac{x}{100})(1\frac{y}{100})\) > \(100^2=(100+x)(100y)\) > \(100^2=100^2100y+100xxy\) > \(y=\frac{100x}{100+x}\) or which is the same \(y=100\frac{10,000}{100+x}\). Answer: E. This question can also be done by picking some smart numbers for I, x and y (say I=10, x=100 and y=50). Hi Bunuel, How did you make the leap from ? \(y=\frac{100x}{100+x}\) or which is the same \(y=100\frac{10,000}{100+x}\). \(y = 100  \frac{10000}{100+x}\) \(y = \frac{100 * 100 + 100x  100000}{100+x}\) \(y = \frac{100x}{100+x}\)
_________________
Kindly press "+1 Kudos" to appreciate



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: The value of an investment increases by x% during January [#permalink]
Show Tags
03 Aug 2014, 23:37
russ9 wrote: Bunuel wrote: prashantbacchewar wrote: The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ? (200x)\(100 + 2x) x(2 + x)\(1 + x)^2 2x\1 + 2x x(200 + x)\10,000 100 –( 10,000 \ 100 + x)
I got this question on MGMAT exam and got it wrong during the test. Later during the review I was able to solve this question correctly. I felt I should post this. Let the value of investment at the beginning of January be \(I\). Then the value of the investment at the end of February would be \(I(1+\frac{x}{100})(1\frac{y}{100})\). We are told that these values are equal: \(I=I(1+\frac{x}{100})(1\frac{y}{100})\) > \(100^2=(100+x)(100y)\) > \(100^2=100^2100y+100xxy\) > \(y=\frac{100x}{100+x}\) or which is the same \(y=100\frac{10,000}{100+x}\). Answer: E. This question can also be done by picking some smart numbers for I, x and y (say I=10, x=100 and y=50). Hi Bunuel, How did you make the leap from ? \(y=\frac{100x}{100+x}\) or which is the same \(y=100\frac{10,000}{100+x}\). \(y=\frac{100x}{100+x}\) Add / subtract 100 to RHS\(y = 100 + \frac{100x}{100+x}  100\) \(y = 100 + \frac{100x  10000 100x}{100+x}\) \(y = 100  \frac{10000}{100+x}\)
_________________
Kindly press "+1 Kudos" to appreciate



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15949

Re: The value of an investment increases by x% during January [#permalink]
Show Tags
15 Aug 2015, 19:42
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15949

Re: The value of an investment increases by x% during January [#permalink]
Show Tags
31 Oct 2016, 03:19
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 03 Jan 2017
Posts: 201

Re: The value of an investment increases by x% during January [#permalink]
Show Tags
21 Mar 2017, 15:43
I tried to pick smart numbers and then to test the answers
so: 100 * x>(100y)*100*x we need y
let's x=25 125>125*0,8 hence y=20% if we test the cases, E works well



Senior Manager
Joined: 12 Nov 2016
Posts: 365

Re: The value of an investment increases by x% during January [#permalink]
Show Tags
13 Jun 2017, 02:02
Bunuel y= 100 100(10000 + x)  I don't understand why I keep getting this: here are my steps 100[y/100]= 1/ (100 + [x/100]) 100y= 100 /(10000 +x) y= 100 /(10000 +x) 100 y= 100/(10000 +x) + 100 y= 100  100/(10000 +x) Please help




Re: The value of an investment increases by x% during January
[#permalink]
13 Jun 2017, 02:02



Go to page
Previous
1 2
[ 29 posts ]




