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# The annual rent collected by a corporation from a certain

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Intern
Joined: 05 Aug 2014
Posts: 30
Re: The annual rent collected by a corporation from a certain [#permalink]

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06 May 2015, 01:06
Hi,
When I evaluated the question,I got reached the inequality in statement 2, hence clearly sufficient. However, in statement 1, I picked values for X and y. X=2 and y=1 and then I substituted them in the inequality xy/100<x−y when it held true, I assumed that the statement is correct. Why was I wrong here? Thanks to anyone who has an answer/insight to share.
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Location: Pune, India
Re: The annual rent collected by a corporation from a certain [#permalink]

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06 May 2015, 02:12
1
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Expert's post
erikvm

So here is the breakdown of this approach:

VeritasPrepKarishma wrote:
This is a question based on successive percentage changes i.e. a number changes by a certain factor, then it changes again by some other factor and so on. Take 100 for example. I first increase it by 10% so it becomes 110. I then decrease 110 by 20% so it becomes 88.
I personally favor multiplying the factor of change together e.g.
$$100 * (1 + \frac{10}{100}) * (1 - \frac{20}{100})$$ = 88

Talks about the concept the question is testing - successive % changes and tells you what the concept is. Uses a random example.

VeritasPrepKarishma wrote:
but a lot of my students like to use the simple formula of two successive percentage changes which is: $$a + b + \frac{ab}{100}$$
(You can derive it very easily. Let me know if you face a problem)

If a number is changed by a% and then by b%, its overall percentage change is as given by the formula.
Using it in the example above, a = 10, b = -20 (since it is a decrease)
$$a + b + \frac{ab}{100}$$ = $$10 - 20 - \frac{10*20}{100}$$ = -12%
So overall change will be of -12%. 100 becomes 88.

Talks about a formula related to this concept. Uses the same example as above.

VeritasPrepKarishma wrote:
In our question above, since we have two successive percentage changes of x% and y% (which is a decrease) so the formula gives us $$x - y - \frac{xy}{100}$$ is the overall change. The question is, whether this change is positive i.e. whether $$x - y - \frac{xy}{100}$$ > 0 or
$$x - y > \frac{xy}{100}$$?
Since statement 2 tells us that $$x - y > \frac{xy}{100}$$, it is sufficient.

And yes, it helps to be clear about exactly what is asked before you move on to the statements.

Here, we come to the given question. Shows you why statement 2 is sufficient. You just use the formula on x and y and you can see that statement 2 is sufficient.
Statement 1 is not sufficient because it tells you that x - y is positive. It doesn't tell you whether x - y - xy/100 is positive.

Pick some numbers to see how statement 1 is not sufficient:

If x = 10 and y = 5,
Rent in 1997 is 100, rent in 1998 is 110 and rent in 1999 is 104.5.
Rent in 1997 < Rent in 1999

But if

If x = 10 and y = 9.99999999 (almost 10 but still x > y)
Rent in 1997 is 100, then rent in 1998 is 110 and rent in 1999 is very slightly more than 99.
Rent in 1997 > Rent in 1999

So the rent in 1997 may be more or less than rent in 1999 if x > y. Hence statement 1 alone is not sufficient.
_________________

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8030 Location: Pune, India Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 06 May 2015, 02:24 1 This post received KUDOS Expert's post naeln wrote: Hi, When I evaluated the question,I got reached the inequality in statement 2, hence clearly sufficient. However, in statement 1, I picked values for X and y. X=2 and y=1 and then I substituted them in the inequality xy/100<x−y when it held true, I assumed that the statement is correct. Why was I wrong here? Thanks to anyone who has an answer/insight to share. Just because the inequality holds true for one set of values such that x > y, it doesn't mean it will hold for all such values. Look at this set of values: x = 10, y = 9.5 x - y = 0.5 xy/100 = 0.95 Here, x - y is not greater than xy/100 though x > y. In your example, you got that x - y is greater than xy/100. So stmnt 1 alone is not sufficient. When you use number picking in DS, be very careful. It is very hard to prove that a statement holds based on some numbers. It is absolutely acceptable to prove that a statement IS NOT SUFFICIENT by assuming numbers because all you need is two set of numbers to do that. For example, to prove that stmnt 1 alone is not sufficient in this question, you just need two examples: one that I gave you and second that you used. We know that stmnt 1 alone is not sufficient. On the other hand, if you are trying to prove that stmnt 1 alone is sufficient, even if you check for 10 values, you cannot be sure that it will hold everytime x > y because there are infinite cases in which x is greater than y. It is possible that you miss one. Hence, to prove that a statement is enough, you will need to rely on logic/pattern recognition etc. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Intern
Joined: 05 Aug 2014
Posts: 30
Re: The annual rent collected by a corporation from a certain [#permalink]

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06 May 2015, 04:44
Thank you Karishma Got it. Do you have any recommendations about how to strategically pick values that could render different results when tested?
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Re: The annual rent collected by a corporation from a certain [#permalink]

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06 May 2015, 20:13
Expert's post
1
This post was
BOOKMARKED
naeln wrote:
Thank you Karishma Got it. Do you have any recommendations about how to strategically pick values that could render different results when tested?

Yes, focus on the transition points i.e. where two sides are equal.
Say you are given x > y. Find what happens at x = y.
For example, in the question above, I took x to be 10 and y to be infinitesimally close to 10 but still less than 10. This would give you the value at the extreme i.e. the lowest value of rent collected in 1999.

Here are a couple of posts on how to choose numbers:

http://www.veritasprep.com/blog/2013/05 ... on-points/
http://www.veritasprep.com/blog/2013/08 ... on-points/
_________________

Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 05 Aug 2014 Posts: 30 Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 10 May 2015, 05:13 VeritasPrepKarishma wrote: naeln wrote: Thank you Karishma Got it. Do you have any recommendations about how to strategically pick values that could render different results when tested? Yes, focus on the transition points i.e. where two sides are equal. Say you are given x > y. Find what happens at x = y. For example, in the question above, I took x to be 10 and y to be infinitesimally close to 10 but still less than 10. This would give you the value at the extreme i.e. the lowest value of rent collected in 1999. Here are a couple of posts on how to choose numbers: http://www.veritasprep.com/blog/2013/05 ... on-points/ http://www.veritasprep.com/blog/2013/08 ... on-points/ Thank you Karishma for sharing the invaluable posts. I truly appreciate it. Retired Moderator Joined: 29 Oct 2013 Posts: 275 Concentration: Finance GPA: 3.7 WE: Corporate Finance (Retail Banking) Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 09 Nov 2015, 14:47 Hi Karishma, Did you manage to make a compilation of all conventional and unconventional formulas? Thanks! _________________ Please contact me for super inexpensive quality private tutoring My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8030 Location: Pune, India Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 09 Nov 2015, 20:23 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED MensaNumber wrote: Hi Karishma, Did you manage to make a compilation of all conventional and unconventional formulas? Thanks! I have discussed all relevant formulas on my blog: http://www.veritasprep.com/blog/categor ... er-wisdom/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Intern
Joined: 16 Dec 2013
Posts: 46
Location: United States
GPA: 3.7
Re: The annual rent collected by a corporation from a certain [#permalink]

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10 Jan 2016, 14:07
I tried the testing cases method. I ended up with D.

Could you give me a couple of cases where I can prove A to be insufficient? I am not able to think of any.
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Posts: 8030
Location: Pune, India
Re: The annual rent collected by a corporation from a certain [#permalink]

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10 Jan 2016, 22:15
1
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Expert's post
Avinashs87 wrote:
I tried the testing cases method. I ended up with D.

Could you give me a couple of cases where I can prove A to be insufficient? I am not able to think of any.

If you are going to test cases to arrive at the answer in DS, you have to be very careful about checking all relevant ranges. In this post above (the-annual-rent-collected-by-a-corporation-from-a-certain-89184-40.html#p1523193), I have given an example of values which show that statement 1 alone is not sufficient. You must find the transition points and then ensure that you test cases around them. Of course, in most cases, it is far better to use logic.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 04 Feb 2014 Posts: 278 Location: India Concentration: General Management, Entrepreneurship GPA: 3 WE: Project Management (Manufacturing) Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 16 Jul 2016, 05:08 Bunuel wrote: thanks wrote: The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997? 1) X is greater than Y 2) xy/100 is less than x-y I'm hoping that someone can elaborate on the number property that gives answer b. PS I'm assuming that there is no way of knowing what level the questions are from the Review books??? Given: Rent in 1997 - $$r$$; Rent in 1998 - $$r*(1+\frac{x}{100})$$; Rent in 1999 - $$r*(1+\frac{x}{100})*(1-\frac{y}{100})$$. Question is $$r<r*(1+\frac{x}{100})*(1-\frac{y}{100})$$ true? --> $$1<1-\frac{y}{100}+\frac{x}{100}-\frac{xy}{10000}$$ --> $$x-y>\frac{xy}{100}$$ true? (1) $$x>y$$, based on this information we can not conclude whether $$x-y>\frac{xy}{100}$$ is true or not. Not sufficient. (2) $$\frac{xy}{100} < x -y$$, directly states that the equation we were testing is true. Sufficient. Answer: B. Hi Bunuel, Though I understand the above given solution, I am still confused why A is wrong. If suppose anything is increased by X and that amount is then decreased by Y when X>Y where we will consider all positive values I can't seem to find a situation where 1997 amount would be less than 1999 amount. e.g X=20% and Y=10% Let the 1997 amount be 100. In 1997=100 In 1998= 120 In 1999= 108 Please explain!! _________________ Kudos if you like my post Math Expert Joined: 02 Sep 2009 Posts: 44636 Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 16 Jul 2016, 08:15 1 This post received KUDOS Expert's post anurag16 wrote: Bunuel wrote: thanks wrote: The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997? 1) X is greater than Y 2) xy/100 is less than x-y I'm hoping that someone can elaborate on the number property that gives answer b. PS I'm assuming that there is no way of knowing what level the questions are from the Review books??? Given: Rent in 1997 - $$r$$; Rent in 1998 - $$r*(1+\frac{x}{100})$$; Rent in 1999 - $$r*(1+\frac{x}{100})*(1-\frac{y}{100})$$. Question is $$r<r*(1+\frac{x}{100})*(1-\frac{y}{100})$$ true? --> $$1<1-\frac{y}{100}+\frac{x}{100}-\frac{xy}{10000}$$ --> $$x-y>\frac{xy}{100}$$ true? (1) $$x>y$$, based on this information we can not conclude whether $$x-y>\frac{xy}{100}$$ is true or not. Not sufficient. (2) $$\frac{xy}{100} < x -y$$, directly states that the equation we were testing is true. Sufficient. Answer: B. Hi Bunuel, Though I understand the above given solution, I am still confused why A is wrong. If suppose anything is increased by X and that amount is then decreased by Y when X>Y where we will consider all positive values I can't seem to find a situation where 1997 amount would be less than 1999 amount. e.g X=20% and Y=10% Let the 1997 amount be 100. In 1997=100 In 1998= 120 In 1999= 108 Please explain!! In your case consider y to be 19%. _________________ Senior Manager Joined: 04 Feb 2014 Posts: 278 Location: India Concentration: General Management, Entrepreneurship GPA: 3 WE: Project Management (Manufacturing) Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 16 Jul 2016, 08:30 Quote: In your case consider y to be 19%. Ohhhh...Got it thanks!! _________________ Kudos if you like my post Manager Joined: 23 Jun 2009 Posts: 197 Location: Brazil GMAT 1: 470 Q30 V20 GMAT 2: 620 Q42 V33 Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 07 Sep 2016, 09:57 1 This post received KUDOS Here is my two cents for those who are struggling odln how to build the comparison with the options. I would NEVER pick numbers since it is extremely time consuming and mistake susceptible. Posted from my mobile device Attachments 20160907_135417.jpg [ 4.75 MiB | Viewed 772 times ] Director Status: Professional GMAT Tutor Affiliations: AB, cum laude, Harvard University (Class of '02) Joined: 10 Jul 2015 Posts: 597 Location: United States (CA) Age: 38 GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: 337 Q168 V169 WE: Education (Education) Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 17 Jan 2017, 19:14 Top Contributor I do not recommend using algebra to evaluate condition #2--it's too complicated for most. Here is a visual that should help, showing you that you can evaluate condition #2 by plugging in to determine the "boundary line" (the value that separates the "Yes" answers from the "No" answers). Attachments Screen Shot 2017-01-17 at 6.13.59 PM.png [ 131.74 KiB | Viewed 459 times ] _________________ Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both in-person (San Diego, CA, USA) and online worldwide, since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong). You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y8zh6qby Date of Birth: 09 December 1979. GMAT Action Plan - McElroy Tutoring Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8030 Location: Pune, India Re: The annual rent collected by a corporation from a certain [#permalink] ### Show Tags 21 Dec 2017, 06:44 thanks wrote: The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997? (1) x > y (2) xy/100 < x-y Check out our detailed video solution of this problem here: https://www.veritasprep.com/gmat-soluti ... ciency_382 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: The annual rent collected by a corporation from a certain   [#permalink] 21 Dec 2017, 06:44

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