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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the figure shown above, line segment QR has length 12 and rectangle

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VP  D
Joined: 09 Mar 2016
Posts: 1229
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

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oss198 wrote: In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?

(A) 144
(B) 216
(C) 324
(D) 360
(E) 396

Attachment:
Picture 1.png

why isn't E an answer if QR has length 12, and rectangle MPQT is a square -- hence area of square is 144

if area of rectangle TQRS? is 540 so 540-144 = 396

so whats wrong with my reasoning ?
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12
In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

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1
dave13 wrote:
oss198 wrote: In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?

(A) 144
(B) 216
(C) 324
(D) 360
(E) 396

Attachment:
The attachment Picture 1.png is no longer available

why isn't E an answer if QR has length 12, and rectangle MPQT is a square -- hence area of square is 144

if area of rectangle TQRS? is 540 so 540-144 = 396

so whats wrong with my reasoning ?

Hi dave13

Attachment: Picture 1.png [ 9.84 KiB | Viewed 466 times ]

As you can see, we are given the following details

1. Length of a line segment of QRST which might be a square/rectangle - QR = 12
2. MPQT(the highlighted portion) is a square.

We have been asked to find the area of QRST, and know that MPQT is a square.
That's the reason your reasoning is wrong!

Hope that clears the confusion.
_________________
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Director  P
Joined: 20 Sep 2016
Posts: 640
Location: India
Concentration: Strategy, Operations
GPA: 3.95
WE: Operations (Real Estate)
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

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How to solve LARGE COEFFICIENT quadratic equations?
ax^2 +bx+c =0 (where a ,b and c are constants/coefficient)

Example
For example, try factoring . (3x^2+10x-1000)
It's relatively simple to factor it to (3x-50)(X+20) but that would take a little while or at least longer than the way that I'm about to discuss.

We begin with the expression
.(3x^2+10x-1000)
Then we divide the second coefficient by 10
and the third by 100,
and we are left with the expression (3x^2+x-10=0)
which we can easily factor to (3x-5)(X+2).
Finally, we multiply the second term in each factor by 10
we have (3x-50)(X+20)=0 . Looks familiar, doesn't it?

Basically, what I have done is that I divided the second coefficient by any one of its factors (in this case 10) and then divided the third coefficient by the square of that factor while leaving the first untouched.

This method applies to irrational and imaginary coefficients as well.

Do the same for
PQ^2+12PQ-540=0

HCF of 12 and 540 = 6
Now divide constant"b" ( in this case 12) with 6
And divide constant"c" with 36( sqayre of 6)
== pq^2+2-15=0
== (PQ+5)(qp-3)=0
Multiply 6 to both the constant of both the factors.
(PQ+30)(pq-18)=0

USE THIS FOR LARGER COEFFICIENTS.

Posted from my mobile device
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4055
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

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Top Contributor
oss198 wrote: In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?

(A) 144
(B) 216
(C) 324
(D) 360
(E) 396

Attachment:
Picture 1.png Let x = the length of each side of square MPQT GIVEN: The area of rectangular region MPRS is 540

In other words: (base)(height) = 540
Substitute values to get: (x + 12)(x) = 540
Expand: x² + 12x = 540
Set equal to zero: x² + 12x - 540 = 0
Factor: (x + 30)(x - 18) = 0
So, EITHER x = -30 OR x = 18

Since the length cannot be negative, it must be the case that x = 18

What is the area of rectangular region TQRS?
Area = (base)(height) = (12)(18) = 216

Cheers,
Brent
_________________ Re: In the figure shown above, line segment QR has length 12 and rectangle   [#permalink] 15 Oct 2019, 13:26

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