Geometry question

Expert replies

w0283767: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Apr 30, 2008 12:12 pm; Thanked: 5 times

by w0283767 » Mon Aug 25, 2008 5:23 pm

This is from MGMAT geometry page 22.

If the perimeter of a rectangular flower bed is 30 feet, and its area is 44 square feet, what is the length of each of its shorter sides?

I know how to solve this problem, but i am trying to learn the way MGMAT solves this problem by using the substitution method.

44= l x w => l = (44/w)

30= 2(l + w)

30 = 2 (44/w + w)

I understand up until this part, but then they say to multiply the entire equation by w/2. I don't understand why.

Once they do that they get

15w = 44 + w^2

w^2 - 15w + 44 = 0 I get the quadratic part but how do they make
the jump from the original equation to get the
(w - 11) (w - 4) = 0 15w = 44 + w^2?

Thanks in advance, any input would be greatly appreciated.
[/list]

Like this post

Source: Beat The GMAT — Problem Solving | Mon Aug 25, 2008 5:23 pm

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: Geometry question

by Ian Stewart » Mon Aug 25, 2008 6:50 pm

w0283767 wrote:
44= l x w
30= 2(l + w)

I find that solution unnecessarily complicated. From the above, we know

lw = 44
l + w = 15

That is, we are looking for two numbers that multiply to 44 and add to 15. We look for pairs of numbers like this every time we factor a quadratic, and in this case the numbers must be 4 and 11.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

w0283767: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Apr 30, 2008 12:12 pm; Thanked: 5 times

thanks

by w0283767 » Mon Aug 25, 2008 6:55 pm

Thank you, but the object of my question is to enhance my math not find the easy solution. I am also shooting for a 700 and I believe knowing this substitution trick can help out on more difficult questions.

Do you agree that it would be a useful skill or should i not worry about it.

Like this post

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

Re: thanks

by Stuart@KaplanGMAT » Mon Aug 25, 2008 11:25 pm

w0283767 wrote:Thank you, but the object of my question is to enhance my math not find the easy solution. I am also shooting for a 700 and I believe knowing this substitution trick can help out on more difficult questions.

Do you agree that it would be a useful skill or should i not worry about it.

Knowing how to substitute to solve equations is a key skill for the GMAT. However, the question you posted seems overly complicated, at least the way it's explained.

If the perimeter of a rectangular flower bed is 30 feet, and its area is 44 square feet, what is the length of each of its shorter sides?

So:

lw = 44
l + w = 30
l = 30 - w

(30 - w)w = 44
30w - w^2 = 44
0 = w^2 -30w + 44

is a MUCH simpler way to get to the same equation. By starting with the addition equation, we keep the whole thing much simpler.

As an aside, I 100% agree with Ian - no matter how good you are at math, either using common sense or backsolving would be a far far quicker way of solving this question. From the answer choices, this question could be backsolved in under 30 seconds.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: thanks

by Ian Stewart » Tue Aug 26, 2008 1:03 am

Stuart's approach to substitution here is much better than that taken in the original solution to the problem. I'd just point out one typo, in case anyone finds it confusing-

Stuart Kovinsky wrote: l + w = 30

should read l + w = 15 (the perimeter is 30, so the length and width sum to 15), and the remaining 30s should all be 15s.

Like this post

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

Re: thanks

by Stuart@KaplanGMAT » Tue Aug 26, 2008 12:02 pm

Ian Stewart wrote:Stuart's approach to substitution here is much better than that taken in the original solution to the problem. I'd just point out one typo, in case anyone finds it confusing-

Stuart Kovinsky wrote: l + w = 30
should read l + w = 15 (the perimeter is 30, so the length and width sum to 15), and the remaining 30s should all be 15s.

Thanks!

Like this post

kandyhot27: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sun Apr 20, 2008 3:23 pm

Re: Geometry question

by kandyhot27 » Wed Aug 27, 2008 4:30 am

w0283767 wrote:This is from MGMAT geometry page 22.

If the perimeter of a rectangular flower bed is 30 feet, and its area is 44 square feet, what is the length of each of its shorter sides?

I know how to solve this problem, but i am trying to learn the way MGMAT solves this problem by using the substitution method.

44= l x w => l = (44/w)

30= 2(l + w)

30 = 2 (44/w + w)

I understand up until this part, but then they say to multiply the entire equation by w/2. I don't understand why.

Once they do that they get

15w = 44 + w^2

w^2 - 15w + 44 = 0 I get the quadratic part but how do they make
the jump from the original equation to get the
(w - 11) (w - 4) = 0 15w = 44 + w^2?

Thanks in advance, any input would be greatly appreciated.
[/list]

they are complicating things by stating the obvious.
For solving
30 = 2 (44/w + w)
indirectly you are multiplying w/2 on both sides anyways.
Take it in steps you would first do the following:

15 = 44/w + w

and then multiply by w on both sides to get the quadratic equation
Jumping from there to (w-11) (w-4) is just skipping two steps to solve the quadratic equation. Just matter of practice

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review