In the figure, square LMNO has a side of length 2x + 1

Expert replies

sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Tue Jul 02, 2013 11:17 am

In the figure, square LMNO has a side of length 2x + 1 and the two smaller squares have sides of length 3 and 6. If the area of the shaded region is 76, what is the value of x ? (please note the shaded region is not inside of the two small squares)

A). 5
B). 6
C). 7
D). 11
E). 14

OA is A

[spoiler]This question is from kaplan. The explanation says that area of square LMNO equals the sum of the shaded area and the area of two small squares. So, after performing some calculations an equation is formed:-

(2x + 1)² = 121
Shortest method now, which i completely agree
2x = 10
x = 5 (ans)

But i took a turn which was long and i thought that i will get the same answer; unfortunately i didn't. Can you please tell me where i am making a mistake in the following method ?
Actually, i solved the quadratic equation. It gives me 6 as the answer.

121 = 4x² + 1 + 4x
0 = 4x² - 4x - 120
0 = x² - x - 30
0 = x² - 6x + 5x - 30
0 = x(x - 6) + 5 (x - 6)
so, x = 6, x = -5
I am getting 6 here.[/spoiler]

Thanks
Sachin

You do not have the required permissions to view the files attached to this post.

Never surrender

Source: Beat The GMAT — Problem Solving | Tue Jul 02, 2013 11:17 am

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Tue Jul 02, 2013 11:27 am

Quote: 0 = 4x² - 4x - 120

This should instead be 0 = 4x²+ 4x - 120
solving this gives (x+6)*(x-5)=0
or x = 5 (since x cannot be -6)

Therefore x = 5

sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Tue Jul 02, 2013 12:02 pm

srcc25anu wrote:Quote: 0 = 4x² - 4x - 120

This should instead be 0 = 4x²+ 4x - 120
solving this gives (x+6)*(x-5)=0
or x = 5 (since x cannot be -6)

Therefore x = 5

My bad. I have done a very big careless mistake, and it must not have been done. Moreover, i could not believe myself after reading your above post.

Thanks

Never surrender

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jul 03, 2013 3:00 am

sachin_yadav wrote:In the figure, square LMNO has a side of length 2x + 1 and the two smaller squares have sides of length 3 and 6. If the area of the shaded region is 76, what is the value of x ? (please note the shaded region is not inside of the two small squares)

A). 5
B). 6
C). 7
D). 11
E). 14

Total area = smaller inner square + larger inner square + shaded area = 3² + 6² + 76 = 121.

In a square, area = (side)².
Since each side = 2x+1, we get:
121 = (2x + 1)²
11 = 2x + 1
x = 5.

The correct answer is A.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Sun Jul 14, 2013 2:34 am

Thanks Mitch

GMATGuruNY wrote:
Total area = smaller inner square + larger inner square + shaded area = 3² + 6² + 76 = 121.

In a square, area = (side)².
Since each side = 2x+1, we get:
121 = (2x + 1)²
11 = 2x + 1
x = 5.

The correct answer is A.

Never surrender

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

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