GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Oct 2019, 15:42

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.

Close

Request Expert Reply

Confirm Cancel

Is the length of the diagonal of the rectangle bigger than root(6) ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 07 Feb 2009
Posts: 13
Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

Show Tags

New post 01 Nov 2010, 05:41
2
10
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

53% (01:24) correct 47% (01:15) wrong based on 235 sessions

HideShow timer Statistics

Is the length of the diagonal of the rectangle bigger than \(\sqrt{6}\) ?

(1) The shorter side of the rectangle is 2.
(2) The longer side of the rectangle is 3.


Hi,

In Geomtry I, question 3 the DS question is:

Question: The OA assumes sides as integers, otherwise it should be another answer. Why is assuming integers and not decimals?

Thank you,
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

Show Tags

New post 01 Nov 2010, 06:02
1
You don't need to assume sides as integers.
Statement (1) The shorter side of the rectangle is 2 which means the greater side will be more than 2. Let us say it is just a little more than 2, say 2.01.
The diagonal will be \(\sqrt{{2^2 + (2.01)^2}} = \sqrt{8.04}.\) This is definitely greater than \(\sqrt{6}\). So it doesn't matter what the greater side is, the diagonal will be greater than root 6. Statement (1) is sufficient.
Statement (2) The greater side of the rectangle is 3. The smaller side can be as small as possible, let's say a little more than 0. Still, the diagonal will be \(\sqrt{{3^2 + (0.01)^2}} = \sqrt{9.0001}.\) This is definitely greater than \(\sqrt{6}\). Therefore, statement (2) is sufficient.
Answer (D).
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
Joined: 07 Feb 2009
Posts: 13
Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

Show Tags

New post 01 Nov 2010, 06:06
VeritasPrepKarishma wrote:
You don't need to assume sides as integers.
Statement (1) The shorter side of the rectangle is 2 which means the greater side will be more than 2. Let us say it is just a little more than 2, say 2.01.
The diagonal will be \(\sqrt{{2^2 + (2.01)^2}} = \sqrt{8.04}.\) This is definitely greater than \(\sqrt{6}\). So it doesn't matter what the greater side is, the diagonal will be greater than root 6. Statement (1) is sufficient.
Statement (2) The greater side of the rectangle is 3. The smaller side can be as small as possible, let's say a little more than 0. Still, the diagonal will be \(\sqrt{{3^2 + (0.01)^2}} = \sqrt{9.0001}.\) This is definitely greater than \(\sqrt{6}\). Therefore, statement (2) is sufficient.
Answer (D).




Hi Karishma,

Once posted, I realized it was talking about the diagonal, while I was thinking in the area.
Apologize for my mistake.

Thanks!
Senior Manager
Senior Manager
avatar
B
Joined: 02 Dec 2014
Posts: 354
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

Show Tags

New post 23 Jul 2016, 14:41
Is this really 700+ question?
_________________
"Are you gangsters?" - "No we are Russians!"
Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2012
Posts: 270
Schools: Schulich '16
Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

Show Tags

New post 24 Jul 2016, 01:34
1
Konstantin1983 wrote:
Is this really 700+ question?


maybe during exam condition it can be.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58396
Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

Show Tags

New post 24 Jul 2016, 02:24
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

Show Tags

New post 15 Aug 2017, 15:29
i'm sure it's not a 700 level question. I solved it just by applying logic...

1. if short one is 2, then we can minimize the longer one to be 2 for example too... a^2 + b^2 = c^2. so we have a=2, b=2, and c^2 = 8. c is sqrt(8). we can give only 1 answer so sufficient.
2. if the bigger one is 3, the other one doesn't matter, as 3^2 = 9. and 9+ smth squared will always be bigger than sqrt(6)... sufficient.

D is the answer.
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

Show Tags

New post 02 Nov 2018, 18:03
vivaslluis wrote:
Is the length of the diagonal of the rectangle bigger than \(\sqrt{6}\) ?

(1) The shorter side of the rectangle is 2.
(2) The longer side of the rectangle is 3.

\(a \ge b > 0\,\,\,\,\,\left[ {{\rm{rectangle}}\,\,{\rm{dimensions}}} \right]\)

\({a^2} + {b^2}\,\,\mathop > \limits^? \,\,6\)


\(\left( 1 \right)\,\,a > b = 2\,\,\,\, \Rightarrow \,\,\,{a^2} + {b^2} > {2^2} + {2^2} = 8\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle\)

\(\left( 2 \right)\,\,3 = a > b > 0\,\,\,\, \Rightarrow \,\,\,{a^2} + {b^2} > {3^2} = 9\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle\)


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

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Bot
Re: Is the length of the diagonal of the rectangle bigger than root(6) ?   [#permalink] 02 Nov 2018, 18:03
Display posts from previous: Sort by

Is the length of the diagonal of the rectangle bigger than root(6) ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne