BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Doing #120 OG pg. 329 in under 2 min

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Sat Jan 01, 2011 11:57 am
Thanked: 1 times

Doing #120 OG pg. 329 in under 2 min

by OneTwoThreeFour » Mon Feb 07, 2011 10:41 am
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

This problem has been posted many times before on beatthegmat and other gmat related forums. I consider myself pretty fast at doing mental math in my head, but even after repeatedly timing myself for this problem, it still takes me about 2:15 to 2:20 to solve. Usually when I time myself on a problem I have done before, it takes me at most 1:30 to solve it. So my question is, do all of you take more than 2 minutes to solve this problem or are there some of you who can do it under 2 minutes? For those who can do it under 2 minutes, I would love to hear your approach.

Thanks. For those you who haven't done this problem before, the correct answer is

b
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Feb 07, 2011 10:53 am
OneTwoThreeFour 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

This problem has been posted many times before on beatthegmat and other gmat related forums. I consider myself pretty fast at doing mental math in my head, but even after repeatedly timing myself for this problem, it still takes me about 2:15 to 2:20 to solve. Usually when I time myself on a problem I have done before, it takes me at most 1:30 to solve it. So my question is, do all of you take more than 2 minutes to solve this problem or are there some of you who can do it under 2 minutes? For those who can do it under 2 minutes, I would love to hear your approach.

Thanks. For those you who haven't done this problem before, the correct answer is

b
Here's an efficient approach:

Plug in 1997 rent = 100.
Increase in 1998 = (x/100)*100 = x.
Thus, rent in 1998 = 100+x.
Decrease in 1999 = y/100*(100+x) = y + xy/100
The problem asks whether the increase is greater than the decrease. Thus, the question can be rewritten as:

Is x > y + xy/100?

Statement 1: x > y
If x=20 and y=10, then y + xy/100 = 10 + (20*10)/100 = 12.
Is 20 > 12? Yes.

If x=90 and y=80, then y + xy/100 = 80 + (90*80)/100 = 152.
Is 90 > 152? No.
Since the answer can be both yes and no, insufficient.

Statement 2: x-y > xy/100
If x-y > xy/100, then x > y + xy/100.
Sufficient.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Sat Jan 01, 2011 11:57 am
Thanked: 1 times

by OneTwoThreeFour » Mon Feb 07, 2011 11:51 am
Ah, thanks Mitch! I was always under the impression that the fastest approach was do it as

(1+x/100)n97 =n98 and (1- Y/100)n98=n99. (where n97= rent for year 1997)
Thus: (1-Y/100)n98 > n98/ (1 +x/100)

The algebra from this point on is pretty straight forward, but this process is not efficient enough to do it in under two minutes. Looks like I need to tackle hard quant problems from a more conceptual approach. Rather than approaching this problem as the rent of 1997 vs 1999, instead think of it as the increase of rent from 1997 to 1998 vs the decrease in rent from 1998 to 1999.

However I have one minor question on your approach:
x> y + xy/100
If we add one hundred to both sides, then on the left hand side, it would mean the rent from 1997 (rent 1997=100) + X to get the rent for 1998. If add 100 to the right hand side, would it means that y +xy/100 + 100 = the rent for 1999?

Thank you so much once again!
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Mon Feb 07, 2011 12:04 pm
it was staring at me...
___R=1
97` R
98` R*(100+x)/100
99` R*(100+x)/100 * R*(100-y)/100

99 <, >, = 97 ?
[] - sign
Two side modifications ---> R [] R*(100+x)/100 * R*(100-y)/100 --->1 [] 1* (100+x)*(100-y)/10,000 --->
10,000 [] 10,000-100y+100X-xy ---> 0 [] 100x-100y-xy ---> xy [] 100x-100y, xy [] 100(x-y) ? our question {nice staring :)

st(1) x > y, xy [<,>] 100(x-y) ---> different signs {x=1,y=2 ---> 2*1<100(2-1), but x=30, y-29 ---> 30*29>100(30-29) Not Sufficient;
st(2) xy/100 < x - y is equivalent to xy<100(x-y) which is our given statement xy [] 100(x-y) without a sign Sufficient.

B

OneTwoThreeFour 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

This problem has been posted many times before on beatthegmat and other gmat related forums. I consider myself pretty fast at doing mental math in my head, but even after repeatedly timing myself for this problem, it still takes me about 2:15 to 2:20 to solve. Usually when I time myself on a problem I have done before, it takes me at most 1:30 to solve it. So my question is, do all of you take more than 2 minutes to solve this problem or are there some of you who can do it under 2 minutes? For those who can do it under 2 minutes, I would love to hear your approach.

Thanks. For those you who haven't done this problem before, the correct answer is

b
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 273
Joined: Tue Sep 21, 2010 5:37 am
Location: Durham, NC
Thanked: 154 times
Followed by:74 members
GMAT Score:770

by Whitney Garner » Mon Feb 07, 2011 12:11 pm
OneTwoThreeFour 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

This problem has been posted many times before on beatthegmat and other gmat related forums. I consider myself pretty fast at doing mental math in my head, but even after repeatedly timing myself for this problem, it still takes me about 2:15 to 2:20 to solve. Usually when I time myself on a problem I have done before, it takes me at most 1:30 to solve it. So my question is, do all of you take more than 2 minutes to solve this problem or are there some of you who can do it under 2 minutes? For those who can do it under 2 minutes, I would love to hear your approach.

Thanks. For those you who haven't done this problem before, the correct answer is

b
I think the toughest part of this problem is thinking of a good way to keep the information straight. Anytime a problem tells me that something (price, amounts, number of pens, etc) is changing from one time period to the next - I start a list from left to right. Everything is moving in percent changes and we have no starting point, so I start with 100. Then I fill out what I know from left to right (through time):

1997 would just be 100, and then adding x% would just add x to that amount:

1997______1998_____________1999__________
100..........100 + x

1999 is the tough year because we have a percent change on a compound number. But if we think it though we can get there:
We start with the 100+x from 1998, but then we have to take y% of that away, so - (y/100)*(100+x)


1997______1998_____________1999__________
100..........100 + x........(100+x) - (y/100)*(100+x)

So the question asks if 100 < 100 + x - (y/100)*(100+x)

Subtract 100 from both sides and expand the (y/100) just to clean things up.

0 < x - y - (xy/100)

This would make statement (2) a potentially easier statement because it looks a lot like this; let's test it first. [spoiler]One quick manipulation (subtract xy/100 from both sides) reveals that statement (2) is the same inequality as the stem. SUFFICIENT(eliminate choices A, C and E)[/spoiler]

Looking at statement (1), I like to use the knowledge that a 25% increase is offset by a 20% decrease (meaning you get back to where you started). So, if x=25 and y=20, x>y and prices in 1997 and 1999 are equal ($100 --> $125 --> $100). But increase the X at all and test quickly. X=30 and y=20, original price $100 goes up to $130 in 1998 then down to $104 in 1999, x>y but now $1997 > $1999. (aside: using a smaller x, x=22 would have the opposite result, $100 --> $122 --> $98) [spoiler]Because I can show 2 different outcomes, INSUFFICIENT. (eliminate D)[/spoiler]

**The 25-20% trick is a nice thing to have handy when trying to conceptualize percent changes :)

Hope this helps!
:D
Whit
Whitney Garner
GMAT/GRE/EA Instructor & Anxiety/Accommodations Coach
www.whitneygarner.com

Contributor to Beat The GMAT!

Math is a lot like love - a simple idea that can easily get complicated :heart-eyes:
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Feb 07, 2011 12:48 pm
OneTwoThreeFour wrote:Ah, thanks Mitch! I was always under the impression that the fastest approach was do it as

(1+x/100)n97 =n98 and (1- Y/100)n98=n99. (where n97= rent for year 1997)
Thus: (1-Y/100)n98 > n98/ (1 +x/100)

The algebra from this point on is pretty straight forward, but this process is not efficient enough to do it in under two minutes. Looks like I need to tackle hard quant problems from a more conceptual approach. Rather than approaching this problem as the rent of 1997 vs 1999, instead think of it as the increase of rent from 1997 to 1998 vs the decrease in rent from 1998 to 1999.

However I have one minor question on your approach:
x> y + xy/100
If we add one hundred to both sides, then on the left hand side, it would mean the rent from 1997 (rent 1997=100) + X to get the rent for 1998. If add 100 to the right hand side, would it means that y +xy/100 + 100 = the rent for 1999?

Thank you so much once again!
Let 1997 rent = 100.

Then increase in 1998 = x/100 * 100 = x.
Thus, 1998 rent = 100 + x.

Decrease in 1999 = y/100(100 + x) = y + xy/100.
Thus, 1999 rent = 1998 rent - decrease in 1999 = 100 + x - (y + xy/100) = 100 + x - y - xy/100.

It is helpful to be able to recognize the following formulas for repeated percent change:

If a value increases by x% and then by another y%, the total change = x + y + xy/100.
If a value increases by x% and then decreases by y%, the total change = x - y - xy/100.

I haven't seen the following come up on the GMAT, but just in case:

If a value decreases by x% and then by another y%, the total change = -x - y + xy/100
If a value decreases by x% and then increases by y%, the total change = -x + y - xy/100

In the DS above, if we recognize that statement 2 gives a variation of the second formula above, we can see almost immediately that statement 2 is sufficient. Statement 1 can be tested quickly by plugging in values (as I did above).

Hope this helps!
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Sat Jan 01, 2011 11:57 am
Thanked: 1 times

by OneTwoThreeFour » Tue Feb 08, 2011 3:19 pm
Thank you so much for the tips Mitch! With the shortcuts you provided, this question is definitely solvable in under a minute. Also I would like to thank all the other experts who chipped in!
Top
Post new topic Post Reply
• Page 1 of 1