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

 It is currently 11 Dec 2019, 04:44

### 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

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

# If a square region has area n, what is the length of the dia

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59675
If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

05 Feb 2014, 02:19
2
28
00:00

Difficulty:

5% (low)

Question Stats:

83% (00:52) correct 17% (01:05) wrong based on 851 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) $$\sqrt{2n}$$
(B) $$\sqrt{n}$$
(C) $$2\sqrt{n}$$
(D) 2n
(E) 2n^2

Problem Solving
Question: 76
Category: Geometry Area; Pythagorean theorem
Page: 71
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 59675
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

05 Feb 2014, 02:20
4
10
SOLUTION

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) $$\sqrt{2n}$$
(B) $$\sqrt{n}$$
(C) $$2\sqrt{n}$$
(D) 2n
(E) 2n^2

The area of a square is $$\frac{diagonal^2}{2}$$.

$$\frac{diagonal^2}{2}=n$$ --> $$diagonal=\sqrt{2n}$$.

_________________
Intern
Joined: 26 Feb 2012
Posts: 14
GMAT 3: 640 Q49 V29
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

05 Feb 2014, 05:03
5
4
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) $$\sqrt{2n}$$
(B) $$\sqrt{n}$$
(C) $$2\sqrt{n}$$
(D) 2n
(E) 2n^2

Area of square = n,
Hence each of the sides of the square are $$\sqrt{n}$$

Now the sides of any rectangular isosceles triangle have a ratio of 1:1:$$\sqrt{2}$$.

Applying this ratio to a rectangular isosceles triangle whose equal sides are $$\sqrt{n}$$, the ratio of the sides for this triangle becomes:
$$\sqrt{n}:\sqrt{n}:\sqrt{2}\sqrt{n}$$

Which is equivalent to
$$\sqrt{n} : \sqrt{n} : \sqrt{2n}$$

##### General Discussion
Manager
Joined: 20 Dec 2013
Posts: 222
Location: India
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

05 Feb 2014, 08:19
1
Ans A

Area of square=n=(side)^2
\sqrt{n}=side
(Diagonal)^2= (\sqrt{n})^2 + (\sqrt{n})^2
Diagonal=\sqrt{n+n}
=\sqrt{2n}
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15696
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

21 May 2015, 20:30
2
Hi All,

This question can be solved by TESTing VALUES.

We're told that a square has an AREA of N. We're asked for the length of the diagonal of that square.....

IF...
Side of the square = 3....
the area of the square = N = (3)(3) = 9....
the diagonal of the square = 3√2

Answer A: √(2N) = √(18) = 3√2 This IS a match.
Answer B: √N = √9 = 3 NOT a match.
Answer C: 2√N = 2√9 = 6 NOT a match.
Answer D: 2N = 18 NOT a match.
Answer E: 2N^2 = 162 NOT a match.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 25 Mar 2013
Posts: 225
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

20 Jan 2017, 11:33
Area = s^2
Area represented as n
n = s^2
each side s = $$\sqrt{n}$$
Diagonal of a square =$$s\sqrt{2}$$
Diagonal = $$\sqrt{n}$$$$\sqrt{2}$$
$$\sqrt{2n}$$
A
VP
Joined: 09 Mar 2016
Posts: 1229
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

21 Feb 2018, 01:35
Bunuel wrote:
SOLUTION

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) $$\sqrt{2n}$$
(B) $$\sqrt{n}$$
(C) $$2\sqrt{n}$$
(D) 2n
(E) 2n^2

The area of a square is $$\frac{diagonal^2}{2}$$.

$$\frac{diagonal^2}{2}=n$$ --> $$diagonal=\sqrt{2n}$$.

Hi Bunuel,

can you please explain one thing. Square has all sides of equal lenght. And if Diagonal divides square into two triangles.

How can such triangle be a RIGHT trangle ? It has two sides equal and two angles equal which is an Isosceles Triangle. Right?

Have an awesome day
Math Expert
Joined: 02 Sep 2009
Posts: 59675
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

21 Feb 2018, 01:45
1
dave13 wrote:
Bunuel wrote:
SOLUTION

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) $$\sqrt{2n}$$
(B) $$\sqrt{n}$$
(C) $$2\sqrt{n}$$
(D) 2n
(E) 2n^2

The area of a square is $$\frac{diagonal^2}{2}$$.

$$\frac{diagonal^2}{2}=n$$ --> $$diagonal=\sqrt{2n}$$.

Hi Bunuel,

can you please explain one thing. Square has all sides of equal lenght. And if Diagonal divides square into two triangles.

How can such triangle be a RIGHT trangle ? It has two sides equal and two angles equal which is an Isosceles Triangle. Right?

Have an awesome day

Don't we have a right angle there? We'll get two isosceles right triangles. You could draw a square and divide it into two triangles with a diagonal, should be easy to check.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15696
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

21 Feb 2018, 20:43
dave13 wrote:
Bunuel wrote:
SOLUTION

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) $$\sqrt{2n}$$
(B) $$\sqrt{n}$$
(C) $$2\sqrt{n}$$
(D) 2n
(E) 2n^2

The area of a square is $$\frac{diagonal^2}{2}$$.

$$\frac{diagonal^2}{2}=n$$ --> $$diagonal=\sqrt{2n}$$.

Hi Bunuel,

can you please explain one thing. Square has all sides of equal lenght. And if Diagonal divides square into two triangles.

How can such triangle be a RIGHT trangle ? It has two sides equal and two angles equal which is an Isosceles Triangle. Right?

Have an awesome day

Hi dave13,

When you cut a square in half (from corner to opposite corner), you always end up with two 45/45/90 right triangles (and yes, they are Isosceles triangles). With tougher Geometry questions on the GMAT, you should look for common shapes (such as right triangles) inside of larger (or more complex) shapes. Sometimes the 'key' to solving those types of prompts is to redraw a picture by 'breaking' it into pieces and then using the appropriate Geometry formulas to complete the calculations.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 06 Sep 2018
Posts: 171
Location: Pakistan
Concentration: Finance, Operations
GPA: 2.87
WE: Engineering (Other)
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

10 Sep 2018, 09:35
let side of square is $$x$$
so, $$area=x^2$$
$$x^2=n$$
$$x=\sqrt{n}$$
As the diagonal length of a square with side length $$x$$ is = $$\sqrt{2}x$$
so, diagonal length of square with side length $$\sqrt{n}$$ = $$\sqrt{2}\sqrt{n}$$ = $$\sqrt{2n}$$

Alternately you can use pathagoras theorem to find diagonal length of square with side length $$\sqrt{n}$$
Director
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

29 Sep 2018, 10:33
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) $$\sqrt{2n}$$
(B) $$\sqrt{n}$$
(C) $$2\sqrt{n}$$
(D) 2n
(E) 2n^2

Problem Solving
Question: 76
Category: Geometry Area; Pythagorean theorem
Page: 71
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Area of square = x^2

Since we are given the area = n then the side equals $$\sqrt{n}$$

A diagonal in a square creates two 45:45:90 triangles.

45:45:90
x:x:x$$\sqrt{2}$$
since the side equals $$\sqrt{n}$$ then the diagonal would be $$\sqrt{n} * \sqrt{2} = \sqrt{2n}$$

Non-Human User
Joined: 09 Sep 2013
Posts: 13737
Re: If a square region has area n, what is the length of the dia  [#permalink]

### Show Tags

25 Oct 2019, 07:32
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.
_________________
Re: If a square region has area n, what is the length of the dia   [#permalink] 25 Oct 2019, 07:32
Display posts from previous: Sort by