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Register now and save up to $200 Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code ## OG 13 127 This topic has 3 expert replies and 3 member replies oquiella Master | Next Rank: 500 Posts Joined 12 May 2015 Posted: 164 messages Thanked: 3 times #### OG 13 127 Tue Dec 22, 2015 3:39 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) 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 i 1997? 1. x>y 2. xy/100 Answer: B Please explain reasoning Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### Top Member Marty Murray Legendary Member Joined 03 Feb 2014 Posted: 2050 messages Followed by: 129 members Thanked: 955 times GMAT Score: 800 Tue Dec 22, 2015 10:26 pm Quote: 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 Statement 1: x > y This is a trap answer. One might think that because x > y the rent went up more than it went down, but since the rent was higher in 1998 than in 1997, a smaller percentage decrease from 1998 to 1999 can actually be a greater absolute decrease. Use two extremes. First extreme: x = 100 y = 0 When those numbers are used the 1999 rent will clearly be greater than the 1997 rent. Second extreme: x = 101 y = 100 Using these numbers, the rent collected in 1999 goes to 0. So it can't be greater than that collected in 1997. So we can get two different answers to the question. Insufficient. Statement 2: xy/100 < x - y We know that the rent change from 1998 to 1999 was y percentage of a number affected first by x. So that xy/100 is interesting, and this might be sufficient. Call the 1997 rent R. The 1998 rent is R + xR/100. The 1999 rent is R + xR/100 - (yR/100 + yxR/10,000). So the question becomes the following. Is R < R + xR/100 - (yR/100 + yxR/10,000)? Subtract R from both sides and the question becomes this. Is O < xR/100 - (yR/100 + yxR/10,000)? This is starting to look like Statement 2. Divide both sides by R. Is O < x/100 - (y/100 + yx/10,000)? Is O < x/100 - y/100 - yx/10,000? Is O < x - y - yx/100? Is xy/100 < x - y? We know from Statement 2 that the answer to the question is yes. Sufficient. The correct answer is B. _________________ Marty Murray GMAT Coach m.w.murray@hotmail.com http://infinitemindprep.com/ In Person in the New York Area and Online Worldwide ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13584 messages Followed by: 1796 members Thanked: 13052 times GMAT Score: 790 Wed Dec 23, 2015 4:40 am I posted a solution here: http://www.beatthegmat.com/quick-way-to-solve-t282917.html Another way to evaluate statement 2 is to plug in an easy value for x and solve for y. Statement 2: (xy/100) < x-y Let x=100%. If we plug x=100 into (xy/100) < x-y, we get: (100y)/100 < 100-y 2y < 100 y < 50%. Let the 1997 rent =$100.
Since the 1998 rent increases by x=100%, the 1998 rent = $100 + 100% of 100 =$200.
Since the 1999 rent decreases by y<50%, the 1999 rent = $200 - (less than 50% of 200) = 200 - (less than 100) = MORE THAN$100.
Since the 1997 rent = $100, and the 1999 rent = more than$100, the 1999 rent is greater than the 1997 rent.
SUFFICIENT.

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oquiella Master | Next Rank: 500 Posts
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Thu Dec 24, 2015 4:46 am
Marty Murray wrote:
Quote:
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
Statement 1: x > y

This is a trap answer. One might think that because x > y the rent went up more than it went down, but since the rent was higher in 1998 than in 1997, a smaller percentage decrease from 1998 to 1999 can actually be a greater absolute decrease.

Use two extremes.

First extreme: x = 100 y = 0

When those numbers are used the 1999 rent will clearly be greater than the 1997 rent.

Second extreme: x = 101 y = 100

Using these numbers, the rent collected in 1999 goes to 0. So it can't be greater than that collected in 1997.

So we can get two different answers to the question.

Insufficient.

Statement 2: xy/100 < x - y

We know that the rent change from 1998 to 1999 was y percentage of a number affected first by x. So that xy/100 is interesting, and this might be sufficient.

Call the 1997 rent R. The 1998 rent is R + xR/100. The 1999 rent is R + xR/100 - (yR/100 + yxR/10,000).

So the question becomes the following. Is R < R + xR/100 - (yR/100 + yxR/10,000)?

Subtract R from both sides and the question becomes this. Is O < xR/100 - (yR/100 + yxR/10,000)?

This is starting to look like Statement 2.

Divide both sides by R. Is O < x/100 - (y/100 + yx/10,000)?

Is O < x/100 - y/100 - yx/10,000?

Is O < x - y - yx/100?

Is xy/100 < x - y?

We know from Statement 2 that the answer to the question is yes.

Sufficient.

Can you explain in further detail this part

"Subtract R from both sides and the question becomes this. Is O < xR/100 - (yR/100 + yxR/10,000)?"

### Top Member

Marty Murray Legendary Member
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Thu Dec 24, 2015 5:01 am
oquiella wrote:
Can you explain in further detail this part

"Subtract R from both sides and the question becomes this. Is O < xR/100 - (yR/100 + yxR/10,000)?
Equal amounts can be subtracted from both sides of an inequality.

Here's the inequality. Notice R on both sides.

R < R + xR/100 - (yR/100 + yxR/10,000)?

Now we subtract R from each side of the inequality to get the following.

O < xR/100 - (yR/100 + yxR/10,000)

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### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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Sun Oct 23, 2016 3:43 pm
oquiella 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 i 1997?

1. x>y
2. xy/100
We are given that the rent collected in a building was x percent more in 1998 than it was in 1997 and y percent less in 1999 than it was in was in 1998. Letâ€™s start by defining some variables.

a = the annual rent collected in 1997

b = the annual rent collected in 1998

c = the annual rent collected in 1999

We can now create the following equations, using the "percent greater than" and "percent less than" formulas:

b = [(100+x)/100]a

c = [(100-y)/100]b

We need to determine whether the annual rent collected by the corporation was more in 1999 than in 1997. Thus, we need to determine: Is c > a?

Since b = [(100+x)/100]a and c = [(100-y)/100]b, that means

c = [(100-y)/100][(100+x)/100]a.

Now we can rephrase the question as:

Is [(100-y)/100][(100+x)/100]a > a?

Notice if we divide the entire inequality by a, we have:

Is [(100-y)/100][(100+x)/100] > 1?

Is (100-y)(100+x)/10,000 > 1?

Is (100+x)(100-y) > 10,000 ?

Is 10,000 - 100y + 100x - xy > 10,000 ?

Is -100y + 100x - xy > 0 ?

Is 100 x - 100y > xy ?

Is 100(x - y) > xy ?

Statement One Alone:

x > y

Knowing only that x is greater than y is not enough to determine whether 100(x - y) > xy. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

(xy/100) < (x-y)

Multiplying both sides of the inequality by 100, we have:

xy <100(x - y)

xy < 100(x - y) is exactly the same as saying 100(x - y) > xy. Statement two alone is sufficient to answer the question.

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### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Wed Jan 18, 2017 4:45 am
oquiella 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 i 1997?

1. x>y
2. xy/100

If the price of commodity increases by say 10% = 1/10, then its increased price should decrease by 1/(1+10) = 1/11 = 9.09% to match the initial price.

Or, we can say that if the price of commodity increases by say 1/a, then its price should decrease by 1/(1+a).

In the problem, say x% = 10%, thus to bring the increased price equal to the initial price, we must decrease the increased price by 9.09%.

You may try with these values; you would find that only statement 2 works.

Hope this helps!

-Jay
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