GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 08 Apr 2020, 14:46

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

If a square mirror has a 20-inch diagonal, what is the

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 23 Apr 2010
Posts: 96
Location: Tx
Schools: NYU,UCLA,BOOTH,STANFORD
If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post Updated on: 07 Dec 2012, 05:56
5
16
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (01:20) correct 28% (01:28) wrong based on 1268 sessions

HideShow timer Statistics

If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 120

My aprroach is;

\(20= X \sqrt{2}\)

then \(X=10\sqrt{2}\)

\(4*X \sqrt{2} = 45,6\)

so should i round it to 40 or 60?

Originally posted by fatihaysu on 18 Aug 2010, 07:44.
Last edited by Bunuel on 07 Dec 2012, 05:56, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62637
Re: Look easy but something wrong  [#permalink]

Show Tags

New post 18 Aug 2010, 07:57
4
3
fatihaysu wrote:
If a square mirror has a 20-inch diagonal,what is the approx. perimeter of the mirror,in inches?

a)40
b)60
c)80
d)100
e)120

My aprroach is;

20= X \sqrt{2}

then X=10\sqrt{2}

4*X \sqrt{2} = 45,6

so should i round it to 40 or 60?


You made an error in calculation: \(P=4*10\sqrt{2}\approx{56.6}\) (\(\sqrt{2}\approx{1.4}\)), 56.6 is closer to 60 than to 40, thus answer is B.

If P were 45.6 (as you calculated) then the answer would be A, as 45.6 is closer to 40 than to 60.

Hope it's clear.
_________________
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 19 Nov 2012
Posts: 2
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 01 Sep 2013, 11:39
6
1
fatihaysu wrote:
If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 120

My aprroach is;

\(20= X \sqrt{2}\)

then \(X=10\sqrt{2}\)

\(4*X \sqrt{2} = 45,6\)

so should i round it to 40 or 60?
.

Here is my approach, i think it will be very simple and do not need any calculations.
if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B
General Discussion
Manager
Manager
avatar
Joined: 23 Apr 2010
Posts: 96
Location: Tx
Schools: NYU,UCLA,BOOTH,STANFORD
Re: Look easy but something wrong  [#permalink]

Show Tags

New post 18 Aug 2010, 07:59
1
Bunuel wrote:
fatihaysu wrote:
If a square mirror has a 20-inch diagonal,what is the approx. perimeter of the mirror,in inches?

a)40
b)60
c)80
d)100
e)120

My aprroach is;

20= X \sqrt{2}

then X=10\sqrt{2}

4*X \sqrt{2} = 45,6

so should i round it to 40 or 60?


You made an error in calculation: \(P=4*10\sqrt{2}\approx{56.6}\) (\(\sqrt{2}\approx{1.4}\)), 56.6 is closer to 60 than to 40, thus answer is B.

If P were 45.6 (as you calculated) then the answer would be A, as 45.6 is closer to 40 than to 60.

Hope it's clear.


It is definelty clear Bunuel. I am triped up by not remembering it is 1,14 or 1,4.

thank you
Senior Manager
Senior Manager
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 414
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
If a square mirror has a 20-inch diagonal, what is the approxima  [#permalink]

Show Tags

New post 26 Oct 2012, 01:50
memorize the fact that diagonal of a square with side s = s * root ( 2)

u ll get the answer half a min
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992
Manager
Manager
avatar
Joined: 17 Jul 2010
Posts: 109
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 09 May 2013, 18:31
I'm I doing the last step correctly?

\(10\sqrt{2}\) = 10 x 1.4 = 14 right, therefore 14x4 = 56.

Thanks.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62637
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 10 May 2013, 00:12
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 150
If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 28 May 2015, 05:25
Question:

Diagonal of a square = x * sqrt2

20 = x * sqrt2
x = 20 / sqrt2

Why are you all using x = 10 / sqrt2 ? I got to the same result with 20 / sqrt2 as length of one side, but where is my mistake?

Thanks!!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62637
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 28 May 2015, 05:28
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 150
If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post Updated on: 28 May 2015, 05:46
Bunuel wrote:
noTh1ng wrote:
Diagonal of a square = x * sqrt2

20 = x * sqrt2
x = 20 / sqrt2

Why are you all using x = 10 / sqrt2 ? I got to the same result with 20 / sqrt2 as length of one side, but where is my mistake?

Thanks!!


\(\frac{20}{\sqrt{2}}=\frac{20*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=10\sqrt{2}\).



Thank you Bunuel the calculation is clear, but I just don't get why we do that?!extending?

Why isn't 20 / sqrt2 sufficient?

Originally posted by noTh1ng on 28 May 2015, 05:35.
Last edited by noTh1ng on 28 May 2015, 05:46, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62637
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 28 May 2015, 05:42
noTh1ng wrote:
Bunuel wrote:
noTh1ng wrote:
Diagonal of a square = x * sqrt2

20 = x * sqrt2
x = 20 / sqrt2

Why are you all using x = 10 / sqrt2 ? I got to the same result with 20 / sqrt2 as length of one side, but where is my mistake?

Thanks!!


\(\frac{20}{\sqrt{2}}=\frac{20*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=10\sqrt{2}\).



Thank you Bunuel the calculation is clear, but I just don't get why we do that?!


Because \(10\sqrt{2}\) is considered to be more simplified (rationalized) than \(\frac{20}{\sqrt{2}}\).

This algebraic manipulation is called rationalization and is performed to eliminate irrational expression in the denominator.

Questions involving rationalization to practice:
if-x-0-then-106291.html
if-n-is-positive-which-of-the-following-is-equal-to-31236.html
consider-a-quarter-of-a-circle-of-radius-16-let-r-be-the-131083.html
in-the-diagram-not-drawn-to-scale-sector-pq-is-a-quarter-139282.html
in-the-diagram-what-is-the-value-of-x-129962.html
the-perimeter-of-a-right-isoscles-triangle-is-127049.html
which-of-the-following-is-equal-to-98531.html
if-x-is-positive-then-1-root-x-1-root-x-163491.html
1-2-sqrt3-64378.html

Hope it helps.
_________________
Current Student
User avatar
B
Joined: 10 Mar 2013
Posts: 452
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A$)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 07 Jul 2015, 09:01
The diagonal of a square splits it in 2 right triangles --> the area of one traingle = (B*H)/2 = 100 (Height is 50% of the diagonal)
So the square have an area of 2*100=200 which is almost 14^2 ----> 4*14 = 56 nearest to 60 (B)
CEO
CEO
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3476
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 07 Jul 2015, 14:09
3
fatihaysu wrote:
If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 120



If the Square has side = \(x\)
then the diagonal of Square = \(x\sqrt{2}\)

i.e. \(x\sqrt{2} = 20\)
i.e. \(x = 20/\sqrt{2} = 10\sqrt{2}\)

Perimeter = 4*Side = \(4*x = 4*10\sqrt{2}\)

i.e. Perimeter = \(40\sqrt{2}\) = \(40*1.4 = 56\)inch

Answer: Option B
_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
Click Here for Uneditable GOOGLE reviews

Click here for Our VERBAL & QUANT private tutoring package details
My Recent Posts Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Standard Deviation l Q-4-Functions
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Intern
Intern
avatar
Joined: 05 Sep 2015
Posts: 1
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 05 Sep 2015, 09:04
Can somebody solve this with Trigonometry.
Thank you.
CEO
CEO
avatar
G
Joined: 20 Mar 2014
Posts: 2543
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 05 Sep 2015, 10:37
merwalpiyush19 wrote:
Can somebody solve this with Trigonometry.
Thank you.


Sure, look below.

If you draw the diagonal in a square, it will divide the square into 2 congruent triangles such that the diagonal makes \(45^{\circ}\) with the sides.

Consider, triangle ABC,

\(\frac{AB}{AC}\) = sin (\(\angle {ABC}\)) = sin (45) = \(\frac{1}{\sqrt{2}}\) , where AC =20

Thus, AB = \(\frac{20}{\sqrt{2}}\) = \(\frac{20*\sqrt{2}}{2}\)= 10*\(\sqrt{2}\) = 10*1.4 = 14
Thus, the perimeter of the square = 4*AB = 4*14 =56.

B is the closest answer
Attachments

2015-09-05_14-34-36.jpg
2015-09-05_14-34-36.jpg [ 9.97 KiB | Viewed 18134 times ]

CEO
CEO
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3476
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 06 Sep 2015, 06:14
2
merwalpiyush19 wrote:
Can somebody solve this with Trigonometry.
Thank you.


Since this question was pretty simple with Trigonometry as shown in the explanation above so my only curiosity is

WHY do you want to know the solution of such question with Trigonometry when your base is already not strong enough in it?

over an above that WHY trigonometry when this is not what GMAT ever expects from students?


Writing here just out of concern so that other readers don't get influenced by Solutions by trigonometry as tool of solving such questions of GMAT.

Please be careful while referring to the source of material, types of solutions etc. for GMAT preparation. If it's not what GMAT expects from you then It can only ruin your direction of healthy preparation.
_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
Click Here for Uneditable GOOGLE reviews

Click here for Our VERBAL & QUANT private tutoring package details
My Recent Posts Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Standard Deviation l Q-4-Functions
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2801
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 09 Jun 2016, 13:09
3
fatihaysu wrote:
If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 120



We are given that a square has a 20-inch diagonal, and we must solve for the perimeter of the square. This means we first need to know the length of a side of the square. To determine the length of a side we can use the diagonal formula for a square. We know that:

diagonal of a square = side√2 = s√2

20 = s√2

s = 20/√2

To help with our math we can multiply 20/√2 by √2/√2. This gives us:

s = 20/√2 × √2/√2 = 20√2/√4

s = 20√2/2 = 10√2

We also should have memorized that the approximate value of √2 is 1.4. Thus one side of the square is about 10 x 1.4 = 14 inches.

Finally, the perimeter of the square is 4 x 14 = 56. Since we are asked to approximate, the closest answer is 60.

Answer B.
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
User avatar
B
Joined: 06 Sep 2016
Posts: 122
Location: Italy
Schools: EDHEC (A$)
GMAT 1: 650 Q43 V37
GPA: 3.2
WE: General Management (Human Resources)
If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 04 Jul 2017, 06:44
I solved it using this reasoning:

When I know the diagonal I have to divide it by \(\sqrt{2}\) to get the side.
I also know that \(\sqrt{2}\) is something less than 2.

Consideration 1: 20/2 would be 10 so the perimeter would be 40
Consideration 2: If I assume that 20 is the side 20x4 gives me a perimeter of 80

So the answer must lie between 40 and 80... thus 60...
Clearly this only works because of the type of answer choices... but this is what GMAT often expects from us, right?
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1220
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 06 Apr 2018, 01:25
Bunuel wrote:
fatihaysu wrote:
If a square mirror has a 20-inch diagonal,what is the approx. perimeter of the mirror,in inches?

a)40
b)60
c)80
d)100
e)120

My aprroach is;

20= X \sqrt{2}

then X=10\sqrt{2}

4*X \sqrt{2} = 45,6

so should i round it to 40 or 60?


You made an error in calculation: \(P=4*10\sqrt{2}\approx{56.6}\) (\(\sqrt{2}\approx{1.4}\)), 56.6 is closer to 60 than to 40, thus answer is B.

If P were 45.6 (as you calculated) then the answer would be A, as 45.6 is closer to 40 than to 60.

Hope it's clear.


Bunuel hello,

one question if one side of square is \(10\sqrt{2}\) and perometr of square is 4a

shouldnt we have as an answer \(4\) * \(10\sqrt{2}\) = \(40\sqrt{2}\) :?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62637
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

Show Tags

New post 06 Apr 2018, 01:42
1
dave13 wrote:
Bunuel wrote:
fatihaysu wrote:
If a square mirror has a 20-inch diagonal,what is the approx. perimeter of the mirror,in inches?

a)40
b)60
c)80
d)100
e)120

My aprroach is;

20= X \sqrt{2}

then X=10\sqrt{2}

4*X \sqrt{2} = 45,6

so should i round it to 40 or 60?


You made an error in calculation: \(P=4*10\sqrt{2}\approx{56.6}\)(\(\sqrt{2}\approx{1.4}\)), 56.6 is closer to 60 than to 40, thus answer is B.

If P were 45.6 (as you calculated) then the answer would be A, as 45.6 is closer to 40 than to 60.

Hope it's clear.


Bunuel hello,

one question if one side of square is \(10\sqrt{2}\) and perometr of square is 4a

shouldnt we have as an answer \(4\) * \(10\sqrt{2}\) = \(40\sqrt{2}\):?


You did not read carefully thus your question does not make sense.

From the solution you quote: \(P=4*10\sqrt{2}\)

Your question: "shouldnt we have as an answer \(4\) * \(10\sqrt{2}\) = \(40\sqrt{2}\)"

The SAME perimeter.
_________________
GMAT Club Bot
Re: If a square mirror has a 20-inch diagonal, what is the   [#permalink] 06 Apr 2018, 01:42

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

If a square mirror has a 20-inch diagonal, what is the

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





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