In the figure shown above, line segment QR has length 12,

Expert replies

Previous Topic Next Topic

AAPL: Moderator; Posts: 2685; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Fri Aug 31, 2018 5:16 am

Timer

00:00

Answers

Stats

Difficulty—

Official Guide

In the figure shown above, line segment has length of 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

OA B.

Like this post

Source: Beat The GMAT — Problem Solving | Fri Aug 31, 2018 5:16 am

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun Sep 02, 2018 10:53 pm

AAPL wrote:Official Guide

In the figure shown above, line segment has length of 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

OA B.

The question is posted correctly.

The correct version is this:

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

Area of MPRS = Area of MPQT + Area of TQRS

Say the length of the square MPQT = x, thus, Area of MPQT = x^2

And, Area of TQRS = 12.x

So, 540 = x^2 + 12x => x = 18.

Area of TQRS = 12*18 = 216

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review

Locations: Manhattan Review Dilsukhnagar | GMAT Prep Begumpet | GRE Prep Visakhapatnam | Warangal GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Like this post

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Sep 03, 2018 4:35 am

AAPL wrote:Official Guide

In the figure shown above, line segment QR has length of 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

\[? = S\]
\[540 = \frac{S}{{12}}\left( {12 + \frac{S}{{12}}} \right)\,\,\mathop = \limits^{x\,\,\left( {aux} \right)\,\, = \,\,\,S/12} \,\,\,x\left( {12 + x} \right)\]
\[540 = 54 \cdot 10 = 27 \cdot 2 \cdot 10 = {3^3} \cdot {2^2} \cdot 5\,\,\,\,\mathop \Rightarrow \limits^{12\,\,{\text{difference}}} \left\{ \begin{gathered}
\boxed{x = {3^2} \cdot 2 = 18} \hfill \\
12 + x = 3 \cdot 2 \cdot 5 = 30 \hfill \\
\end{gathered} \right.\]
\[\frac{S}{{12}} = x = 18\,\,\, \Rightarrow \,\,? = S = 12 \cdot 18 = 180 + 36 = 216\]

This solution follows the notations and rationale taught in the GMATH method.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8188; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Sep 07, 2018 4:22 pm

AAPL wrote:Official Guide

In the figure shown above, line segment has length of 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

Since PQMT is a square, we can let PQ = PM = n. Since QR = 12, PR = n + 12. Finally, since the area of rectangle MPRS is 540, we have:

n(n + 12) = 540

n^2 + 12n = 540

n^2 + 12n - 540 = 0

(n + 30)(n - 18) = 0

n = -30 or n = 18

Since n can't be negative, n = 18, and the area of square MPQT is 18 x 18 = 324. Thus, the area of rectangle TQRS is 540 - 324 = 216. (Or the area of rectangle TQRS is 18 x 12 = 216.)

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 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