A rectangular circuit board is designed to have width w inch

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guerrero: Master | Next Rank: 500 Posts; Posts: 227; Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members; Thanked: 12 times

by guerrero » Wed Sep 11, 2013 12:37 pm

A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) w^2 + pw + k = 0
(B) w^2 - pw + 2k = 0
(C) 2w^2 + pw + 2k = 0
(D) 2w^2 - pw - 2k = 0
(E) 2w^2 - pw + 2k = 0

OAE

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Source: Beat The GMAT — Problem Solving | Wed Sep 11, 2013 12:37 pm

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by [email protected] » Wed Sep 11, 2013 1:43 pm

Hi guerrero,

I'm going to give you a nudge and have you try this question again:

1) Draw a picture of a rectangle.
2) TEST VALUES. Pick a value for the width and the length
3) Calculate anything else that you need to calculate

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Wed Sep 11, 2013 7:01 pm

Suppose,

L= 2 in, W= 4 in

Then Area=8 in and Perimeter = 12 inches, let us test the equations

(A) w^2 + pw + k = 0 16+48+8 not equal to zero
(B) w^2 - pw + 2k = 0 16-48-16 not equal to zero
(C) 2w^2 + pw + 2k = 0 32+48+16 not equal to zero
(D) 2w^2 - pw - 2k = 0 32-48-16 not equal to zero
(E) 2w^2 - pw + 2k = 0 32-48+16 equals zero

Option E

Also we could have eliminated options A and C since if the equations have to be equal to zero, then we need at least one expression as negative.

Hope it helps!

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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guerrero: Master | Next Rank: 500 Posts; Posts: 227; Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members; Thanked: 12 times

by guerrero » Wed Sep 11, 2013 10:40 pm

[email protected] wrote:Hi guerrero,

I'm going to give you a nudge and have you try this question again:

1) Draw a picture of a rectangle.
2) TEST VALUES. Pick a value for the width and the length
3) Calculate anything else that you need to calculate

GMAT assassins aren't born, they're made,
Rich

thanks Rich , I used height as "H" & Width as "W" . Equated the assumed value( H )in Perimeter and Area formula and got the required equation in ~1 Min .

Did not realize it was that simple

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sanjoy18: Senior | Next Rank: 100 Posts; Posts: 81; Joined: Tue Jun 11, 2013 10:24 pmFollowed by: 1 member; Thanked: 7 times

by sanjoy18 » Wed Sep 11, 2013 10:49 pm

Let Length =a width = w (given)

hence perimeter = 2*(a+w)=p ----(A)
areq= a*w=k
>> a= k/w -----------(B)

2* ((k/w)+w)=p using (B)
> 2W^2 -pw+ 2k=0

hence E

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Wed Sep 11, 2013 11:41 pm

guerrero wrote:A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) w^2 + pw + k = 0
(B) w^2 - pw + 2k = 0
(C) 2w^2 + pw + 2k = 0
(D) 2w^2 - pw - 2k = 0
(E) 2w^2 - pw + 2k = 0

OAE

Since w,p, and k are all positive, eliminate A and C.
p = 2w + 2l (l is the length)
k = lw
2k = (2l) w
2k = (p - 2w)w
2k = pw - 2w^2
2w^2 - pw + 2k = 0

Choose E

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by [email protected] » Thu Sep 12, 2013 11:07 am

Hi vinay1983, guerrero et al,

TESTing values makes these types of questions really easy to solve.

Here's another tactic that can save you some time:

Notice how the answer choices have similar "pieces"? For example, "pw" shows up in each answer. Rather than do THAT calculation 5 separate times, you can do it ONCE and plug the result into all 5 answers. This approach, when available, can create a significant shortcut and save you time.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Mon Dec 18, 2017 7:52 am

guerrero wrote:A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) w^2 + pw + k = 0
(B) w^2 - pw + 2k = 0
(C) 2w^2 + pw + 2k = 0
(D) 2w^2 - pw - 2k = 0
(E) 2w^2 - pw + 2k = 0

We can let n = the length of the rectangle and create the following equation:

2w + 2n = p

2n = p - 2w

n = (p - 2w)/2

Since area = n x w:

k = (n)(w)

k = [(p - 2w)/2]w

2k = pw - 2w^2

2w^2 - pw + 2k = 0

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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