keep its area unchanged

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Jul 31, 2010 4:27 am

The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be:
A. kept unchanged.
B. increased by 25%.
C. reduced by 25%.
D. increased by 20%.
E. reduced by 20%.

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Source: Beat The GMAT — Problem Solving | Sat Jul 31, 2010 4:27 am

nithi_mystics: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Mon Sep 07, 2009 9:11 pm; Location: California; Thanked: 4 times

by nithi_mystics » Sat Jul 31, 2010 5:27 am

Answer is E.

Let initial length be l and width be b.
let x be the decrease in percentage of the width.

l * b = (l+0.25l) * (b-xb)

l*b = l*b + 0.25lb - 1.25lxb

==> 0.25lb = 1.25lxb
==> x= 0.25/1.25 = 0.2

Therefore the decrease in width should be 20%

sanju09 wrote:The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be:
A. kept unchanged.
B. increased by 25%.
C. reduced by 25%.
D. increased by 20%.
E. reduced by 20%.

[spoiler]Source: winningprep.com[/spoiler]

Thanks
Nithi

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atb135: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sat Jul 31, 2010 8:19 am

by atb135 » Sat Jul 31, 2010 9:53 am

It is always good to use numbers to make the calculations easier:

In the current problem let us consider l=4 and b=3, Area= 12.

Now if we are to increase l by 25% then l=5 and b=? according to the problem statement.

since area should be equal for the two: 4*3=5*x

resulting in x (new width)=2.4

2.4 is 80% of the original value 3, Hence we have to decrease the original width by 20%, Answer E

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Jul 31, 2010 10:22 am

sanju09 wrote:The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be:
A. kept unchanged.
B. increased by 25%.
C. reduced by 25%.
D. increased by 20%.
E. reduced by 20%.

[spoiler]Source: winningprep.com[/spoiler]

We can use logic/common sense/GMAT knowledge to answer this question in under 15 seconds.

First, if we increase one dimension, we need to decrease the other to keep area constant: eliminate A, B and D.

Second, there's no way that the percentage decrease will be the same as the percentage increase (a common GMAT trap is answers that just repeat numbers from the question stem): eliminate C.

Choose E (without doing any math)!

* * *

If for some reason you do want to do math, then:

l*w = (5/4)l * (x)w

1 = (5/4)(x)

4/5 = x

So, width gets decreased by 1 - 4/5 = 1/5

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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pradeepkaushal9518: Legendary Member; Posts: 1309; Joined: Wed Mar 17, 2010 11:41 pmFollowed by: 5 members; Thanked: 33 times

by pradeepkaushal9518 » Sat Jul 31, 2010 11:19 am

boss take lenght 100 and width 20 and solve the problem

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Aug 02, 2010 1:16 am

pradeepkaushal9518 wrote:boss take lenght 100 and width 20 and solve the problem

why not take both 100, btw Stuart Kovinsky's logical approach serves the best when time is the limiting factor, eliminate as much as you can to avoid doing math where it's really not required

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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getso: Master | Next Rank: 500 Posts; Posts: 141; Joined: Sat Feb 28, 2009 8:19 am; Thanked: 1 times

by getso » Tue Aug 03, 2010 1:50 am

Stuart Kovinsky wrote:
sanju09 wrote:The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be:
A. kept unchanged.
B. increased by 25%.
C. reduced by 25%.
D. increased by 20%.
E. reduced by 20%.

[spoiler]Source: winningprep.com[/spoiler]
We can use logic/common sense/GMAT knowledge to answer this question in under 15 seconds.

First, if we increase one dimension, we need to decrease the other to keep area constant: eliminate A, B and D.

Second, there's no way that the percentage decrease will be the same as the percentage increase (a common GMAT trap is answers that just repeat numbers from the question stem): eliminate C.

Choose E (without doing any math)!

* * *

If for some reason you do want to do math, then:

l*w = (5/4)l * (x)w

1 = (5/4)(x)

4/5 = x

So, width gets decreased by 1 - 4/5 = 1/5

wonderful explanation!!!
In a hurry to solve problems ,I tend to overlook such problems which needs common sense approach.
Thanks Stuart

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