What is the perimeter of quadrilateral Q?

Expert replies

Previous Topic Next Topic

VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sun Apr 14, 2019 9:42 am

Timer

00:00

Answers

Stats

Difficulty—

What is the perimeter of quadrilateral Q?

(1) Q is a rectangle.
(2) The area of Q is 25.

[spoiler]OA=E[/spoiler]

Source: Princeton Review

Like this post

Source: Beat The GMAT — Data Sufficiency | Sun Apr 14, 2019 9:42 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Sat Apr 20, 2019 5:44 am

What is the perimeter of quadrilateral Q?

(1) Q is a rectangle.
(2) The area of Q is 25.

OA=E

Source: Princeton Review

Hi Vjesus12.

The perimeter of the quadrilateral Q is given by $p= w+x+y+z $, where $w, x, y, z$ are the lengths of each side of the quadrilateral.

Statement 1:

(1) Q is a rectangle.

Since Q is a rectangle, then we have that $ w=y$ and $ x=z$, so the perimeter is $p= 2x+2y$, but we don't know the values of $x$ and $y$. Hence, this statement is NOT SUFFICIENT.

Statement 2:

(2) The area of Q is 25.

Now, we don't know what type of quadrilateral Q is. So, we can't get anything from the area. Therefore, this statement is NOT SUFFICIENT.

Statement 1 and Statement 2:

If Q is a rectangle with area equal to 25, we can get several cases, for example,

(i) Q is a square of side 5, then the perimeter of Q is 20.
(ii) Q is a rectangle with sides 25/2 and 2 respectively, therefore the perimeter of Q is 29.

Since we've got two different answers then we conclude that using both statements is NOT SUFFICIENT.

In conclusion, the correct answer is the option _E_.

I hope it helps.

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Apr 20, 2019 5:48 am

VJesus12 wrote:What is the perimeter of quadrilateral Q?

(1) Q is a rectangle.
(2) The area of Q is 25.

[spoiler]OA=E[/spoiler]

Source: Princeton Review

Target question: What is the perimeter of quadrilateral Q?

If we recognize that each statement alone is not sufficient, we can jump straight to......

Statements 1 and 2 combined
There are several quadrilaterals satisfy BOTH statements. Here are two:
Case a: Q is a rectangle with width 1 and length 25. In this case, the perimeter of quadrilateral Q is 1 + 1 + 25 + 25 = 52
Case b: Q is a rectangle with width 5 and length 5. In this case, the perimeter of quadrilateral Q is 5 + 5 + 5 + 5 = 20
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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