Last visit was: 17 Jul 2025, 21:05 It is currently 17 Jul 2025, 21:05
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
505-555 Level|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,605
Own Kudos:
742,308
 [3]
Given Kudos: 98,220
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,605
Kudos: 742,308
 [3]
The width, length, and diagonal of a rectangle could be represented by 20 Nov 2015, 00:48
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

82% (01:20) correct 18% (01:21) wrong based on 218 sessions

History

Date
Time
Result
Not Attempted Yet
The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, \(\sqrt{13}\)
II. \(\sqrt{10}\), 4, 6
III. 3, 10, 11

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
ShowHide Answer
Official Answer
A
User avatar
Skywalker18
User avatar
Retired Moderator
Joined: 08 Dec 2013
Last visit: 15 Nov 2023
Posts: 2,052
Own Kudos:
9,701
Given Kudos: 171
Status:Greatness begins beyond your comfort zone
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Products:
My Reviews
Posts: 2,052
Kudos: 9,701
The width, length, and diagonal of a rectangle could be represented by 20 Nov 2015, 01:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The width, length, and diagonal of a rectangle will be Pythagorean triples .
(width)^2 + (length)^2 = (diagonal)^2

1. 2^2 + 3^2 = (13^(1/2))^2 = 13
=> 4+9 = 13
Yes.
2.
(10^(1/2))^2 + 4^2 = 10 + 16 = 26
which is not equal to 6^2= 36
No.
3. 3^2 + 10^2 = 9 +100 = 109
not equal to 11^2 = 121
No.

Answer A
User avatar
nipunjain14
User avatar
Joined: 07 May 2015
Last visit: 12 Aug 2017
Posts: 152
Own Kudos:
81
 [1]
Given Kudos: 21
Location: India
Schools: ISB '19 Kellogg '20 Yale '20 HEC Dec"18
GMAT 1: 660 Q48 V31
GPA: 3
Schools: ISB '19 Kellogg '20 Yale '20 HEC Dec"18
GMAT 1: 660 Q48 V31
Posts: 152
Kudos: 81
 [1]
The width, length, and diagonal of a rectangle could be represented by 20 Nov 2015, 19:41
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
1. 2, 3, sqrt(13)
squaring all numbers: 4, 9 , 13
since third number is sum of other 2: 4+9 = 13

2. sqrt(10), 4, 6
squaring all numbers: 16, 36 , 10
since third number is not the sum of other 2: 16+10 = 26 which is not equal to 36
Not possible

3.3, 10 , 11
squaring all numbers: 9, 100 , 110
since third number is not the sum of other 2: 100+9 = 109 which is not equal to 110
Not possible

Ans: A
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,118
 [1]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,118
 [1]
The width, length, and diagonal of a rectangle could be represented by 21 Nov 2015, 15:15
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, \(\sqrt{13}\)
II. \(\sqrt{10}\), 4, 6
III. 3, 10, 11

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

NOTE: The width, length, and diagonal create a RIGHT TRIANGLE, with the diagonal as the hypotenuse.
For these to be valid lengths, the Pythagorean Theorem must apply.
That is, it MUST be the case that width² + length² = diagonal²

Let's check the 3 sets of values BEGINNING WITH III

III. Does 3² + 10² = 11²? NO.
This means that 3, 10, 11 CANNOT represent the width, length, and diagonal of a rectangle.
This means we can ELIMINATE C, D and E

II. Does (√10)² + 4² = 6²? NO.
This means that √10, 4, 6 CANNOT represent the width, length, and diagonal of a rectangle.
This means we can ELIMINATE B

Answer: A

Cheers,
Brent
avatar
rakshithbabu
avatar
Joined: 14 Jun 2015
Last visit: 20 Jun 2017
Posts: 80
Own Kudos:
35
Given Kudos: 33
Location: India
GMAT 1: 680 Q46 V37
GMAT 2: 750 Q50 V40
GPA: 3.5
WE:Information Technology (Telecommunications)
GMAT 2: 750 Q50 V40
Posts: 80
Kudos: 35
The width, length, and diagonal of a rectangle could be represented by 22 Nov 2015, 02:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, 13‾‾‾√
II. 10‾‾‾√, 4, 6
III. 3, 10, 11

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


The Three dimensions of a rectangle in the given order represents the two side and the hypotenuse of a right angle trianlge.
Only set that obeys pythogerous theorem is I.
So Ans: A
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,443
Own Kudos:
1,013
Posts: 37,443
Kudos: 1,013
The width, length, and diagonal of a rectangle could be represented by 17 Nov 2022, 12:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
102605 posts
Krunaal
PS Forum Moderator
698 posts