GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Aug 2019, 14:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The annual rent collected by a corporation from a certain

Author Message
TAGS:

### Hide Tags

Manager
Joined: 22 Jul 2008
Posts: 76
Location: Bangalore,Karnataka
The annual rent collected by a corporation from a certain  [#permalink]

### Show Tags

29 Dec 2009, 05:55
16
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:22) correct 42% (02:46) wrong based on 190 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 57025

### Show Tags

29 Dec 2009, 13:14
3
4
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.

_________________
##### General Discussion
Senior Manager
Joined: 30 Aug 2009
Posts: 255
Location: India
Concentration: General Management

### Show Tags

29 Dec 2009, 09:03
kirankp 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

will go with B

let annual rent collected be 20000 in 1997

stmnt1 - x>y. let x = 25% and y = 10% then amount collected in 1998 will be 25000 and amount collected in 1999 will be 22500. so annual rent collected in 1999 is more than 1997
let x=25% and y=20% then amount collected in 1998 will be 25000 and amount collected in 1999 will be 20000. so annual rent collected in 1999 is same as 1997
Hence Insuff

stmnt2 - here x cannot be less than y and therefore for any set of values satisfying this equation rent collected in 1999 will be more than 1997. hence suff
Intern
Joined: 25 Jul 2009
Posts: 17
Location: Lahore, Pakistan
Schools: going to Melbourne Business School

### Show Tags

29 Dec 2009, 12:23
@ kp1811

please explain why you choose these values ?

I chose value = 100
x% = 10
y% = 5

my results were:

97 = 100
98 = 110
99 = 104.5

equation for 98 = 100 + x
equation for 99 = 100 + x - y(100+x)/100

elaborating eq 2; 100 +x-y-(xy)/100 (B) seems true but so does (A)

kindly elaborate.
Intern
Joined: 23 Nov 2009
Posts: 35

### Show Tags

29 Dec 2009, 13:01
kirankp 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

Hi,
My answer is C. Both statements together are sufficient.

Let us call rent in 1997 as p
Let us call rent in 1998 as q
Let us call rent in 1999 as r

q= p+(x/100)p --- (1)
r=q-(y/100)q --- (2)

We need to compare p and r?

replacing (1) in (2) we get:

r = p+(x/100)p - y/100(p+(x/100)p)
r = p+(x/100)p -(y/100)p - (xy/10000)p

x>y
implies (x/100)p - (y/100)p is positive, but we do not know if the result is greater than (xy/10000)p. Therefore insufficeint

xy/100 < x-y Insufficient since we do not know if x - y is positive or negative

Combining A and B
We get that x-y-xy/100 is a positive quantity
and hence r>p
_________________
A kudos would greatly help

Tuhin
Senior Manager
Joined: 30 Aug 2009
Posts: 255
Location: India
Concentration: General Management

### Show Tags

29 Dec 2009, 19:56
hamza wrote:
@ kp1811

please explain why you choose these values ?

I chose value = 100
x% = 10
y% = 5

my results were:

97 = 100
98 = 110
99 = 104.5

equation for 98 = 100 + x
equation for 99 = 100 + x - y(100+x)/100

elaborating eq 2; 100 +x-y-(xy)/100 (B) seems true but so does (A)

kindly elaborate.

hamza....annual rent was taken randomly....100...20000...even A,R,B,C will suffice ...however values of x and y needs to be selected/checked in a way that we can prove if the statement is either suff or insuff

now in the example given by you "I chose value = 100
x% = 10
y% = 5

my results were:

97 = 100
98 = 110
99 = 104.5
"
this example of yours makes the statement sufficient but in the below examples we can prove that statement1 is insuff

if y% = 100/11 then for 99 we would get rent as 100 which is same as 97

if we take x = 25% and y=20% we get same value for 99 and 97
if we take x=50% and y = 100/3% again we get the same value for 99 and 97

in all these cases x>y. hope this helps
Intern
Joined: 25 Jul 2009
Posts: 17
Location: Lahore, Pakistan
Schools: going to Melbourne Business School

### Show Tags

29 Dec 2009, 23:24
Thanks a lot for help.

The general point here is that 50% increase in A will always be less than 50% decrease in 1.5A.(Even 49% will be larger, or 45% too, if initial price is large)(now I see why kp1811 took 20,000 )

Value = 100
x = 50%
y = 40% (for ease of calculation, otherwise I would have liked to use 49.9% to prove it WRONG )

1997 = 100
1998 = 150 [1.5+50/100(100)]
1999 = 90 [150-40/100(150)]

value of 99 < value of 97

for B I see a sequence already, lets say value = 100

97 = 100
98 = 100+x
99 = (100+x) - (100+x)y/100

expanding 99 eq. => 100+x-y-xy/100

BUT, I would prefer keeping same approach to check both statements ( As i see a pattern in B, so plugging no.s later)

100+x-y-xy/100.
(x=50,y=40)

=100+50-40-(50*40)/100
=100+10-20
=90
Senior Manager
Joined: 22 Dec 2009
Posts: 288

### Show Tags

01 Jan 2010, 17:50
1
1
OA is B..

Explanation:

Let the rent paid in 1997 be R
Therefore rent paid in 1998 = $$R(1+\frac{X}{100})$$
and rent paid in 1999 = $$R(1+\frac{X}{100})(1-\frac{Y}{100})$$

$$R(1+\frac{X}{100})(1-\frac{Y}{100}) > R$$

$$(1+\frac{X}{100})(1-\frac{Y}{100}) > 1$$

$$1+\frac{X}{100}-\frac{Y}{100} - \frac{XY}{10000} > 1$$

$$\frac{X}{100}-\frac{Y}{100} - \frac{XY}{10000} > 0$$

$$X-Y > \frac{XY}{100}$$ ----- [1]

Statement 1:
x > y - Not sufficient as nothing can be said about equation [1]

Statement 2:
Sufficient as the same is given as true!

Cheers!
JT
_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~
Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 479

### Show Tags

16 May 2011, 13:44
the solution by bunnuel is perfect it may take too much time. what to do?
_________________
Director
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 941

### Show Tags

16 May 2011, 20:19
Intern
Joined: 16 Nov 2013
Posts: 23
The annual rent collected by a corporation from a certain building  [#permalink]

### Show Tags

31 Dec 2014, 03:27
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

Can i state this?

1997 1998 1999

100 100+x 100+x-y

So: 100+x-y>100 and x>y.. What's wrong with this? E.G: If the price of a stock is x in 1997 and is 25 percent more in 1998 so the price in 1998 is 100+25=125 percent

Thank you
Manager
Joined: 22 Oct 2014
Posts: 87
Concentration: General Management, Sustainability
GMAT 1: 770 Q50 V45
GPA: 3.8
WE: General Management (Consulting)
Re: The annual rent collected by a corporation from a certain building  [#permalink]

### Show Tags

31 Dec 2014, 03:49
1

Statement 1: is obviously not enough. If rent goes up 51% this year and decreases 50% the next, we end up lower than where we started from, if it only decreases by 1%, we are still higher than before.

Statement 2: Sufficient.

$$R_{1998}=(1+\frac{x}{100})*R_{1997}$$

$$R_{1999}=(1-\frac{y}{100})*R_{1998}=(1-\frac{y}{100})*(1+\frac{x}{100})*R_{1997}$$

$$R_{1999}=(1-\frac{y}{100}+\frac{x}{100}-\frac{xy}{10000})*R_{1997}$$

$$R_{1999}=(1+\frac{x-y-0.01*xy}{100})*R_{1997}$$

With the statement we know that the fraction is positive. Therefore, the rent after the decrease of y% is still higher than it was before it increased by x%.

_________________
$$\sqrt{-1}$$ $$2^3$$ $$\Sigma$$ $$\pi$$ ... and it was delicious!

Please consider giving +1 Kudos if deserved!
Math Expert
Joined: 02 Sep 2009
Posts: 57025
Re: The annual rent collected by a corporation from a certain  [#permalink]

### Show Tags

31 Dec 2014, 04:11
gmatmania17 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

Can i state this?

1997 1998 1999

100 100+x 100+x-y

So: 100+x-y>100 and x>y.. What's wrong with this? E.G: If the price of a stock is x in 1997 and is 25 percent more in 1998 so the price in 1998 is 100+25=125 percent

Thank you

MERGING TOPICS.

PLEASE SEARCH BEFORE POSTING. THANK YOU.
_________________
VP
Joined: 05 Mar 2015
Posts: 1007
Re: The annual rent collected by a corporation from a certain  [#permalink]

### Show Tags

12 Jun 2016, 04:02
kirankp 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

Let the rent in 1997 be A.
(1)Let the amount be increased by x=25%
then if Y=22%(or 20<y<25%)
then we have a NO ans to our Ques.
But if Y=5%(or any smaller amount than 20)
then we have a YES ans to our Ques.
Insuff...
(2) rent in 1999=A(1+x/100)(1-y/100)
=A(1-y/100+x/100-xy/10000)
=A+A/100(x-y-xy/100)
given x-y-xy/100>0
so rent in 1999 is A+A/100(x-y-xy/100) must be greater than rent in 1997 which is A
suff..

Ans B
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2820
Re: The annual rent collected by a corporation from a certain  [#permalink]

### Show Tags

08 Jan 2018, 12:06
1
kirankp 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

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. Let’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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 12006
Re: The annual rent collected by a corporation from a certain  [#permalink]

### Show Tags

06 Aug 2019, 18:59
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.
_________________
Re: The annual rent collected by a corporation from a certain   [#permalink] 06 Aug 2019, 18:59
Display posts from previous: Sort by