GMAT Changed on April 16th - Read about the latest changes here

 It is currently 23 Apr 2018, 08:28

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Apr 2010
Posts: 117
Location: Tx
Schools: NYU,UCLA,BOOTH,STANFORD
If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

Updated on: 07 Dec 2012, 06:56
4
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

72% (00:58) correct 28% (01:05) wrong based on 1027 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;

[Reveal] Spoiler:
$$20= X \sqrt{2}$$

then $$X=10\sqrt{2}$$

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

so should i round it to 40 or 60?
[Reveal] Spoiler: OA

_________________

This is not finished here...Watch me.....

Originally posted by fatihaysu on 18 Aug 2010, 08:44.
Last edited by Bunuel on 07 Dec 2012, 06:56, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 44636
Re: Look easy but something wrong [#permalink]

### Show Tags

18 Aug 2010, 08:57
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.
_________________
Manager
Joined: 23 Apr 2010
Posts: 117
Location: Tx
Schools: NYU,UCLA,BOOTH,STANFORD
Re: Look easy but something wrong [#permalink]

### Show Tags

18 Aug 2010, 08:59
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
_________________

This is not finished here...Watch me.....

Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 486
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

26 Oct 2012, 02:50
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
Joined: 17 Jul 2010
Posts: 117
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

09 May 2013, 19:31
I'm I doing the last step correctly?

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

Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 44636
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

10 May 2013, 01:12
laythesmack23 wrote:
I'm I doing the last step correctly?

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

Thanks.

Yes, that's correct.
_________________
Intern
Joined: 19 Nov 2012
Posts: 2
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

01 Sep 2013, 12:39
5
KUDOS
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;

[Reveal] Spoiler:
$$20= X \sqrt{2}$$

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
Manager
Joined: 07 Apr 2015
Posts: 177
If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

28 May 2015, 06:25
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
Joined: 02 Sep 2009
Posts: 44636
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

28 May 2015, 06:28
Expert's post
1
This post was
BOOKMARKED
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!!

$$\frac{20}{\sqrt{2}}=\frac{20*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=10\sqrt{2}$$.
_________________
Manager
Joined: 07 Apr 2015
Posts: 177
If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

Updated on: 28 May 2015, 06:46
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, 06:35.
Last edited by noTh1ng on 28 May 2015, 06:46, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 44636
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

28 May 2015, 06:42
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
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.
_________________
Director
Joined: 10 Mar 2013
Posts: 563
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

07 Jul 2015, 10:01
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)
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

SVP
Joined: 08 Jul 2010
Posts: 2067
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

07 Jul 2015, 15:09
1
KUDOS
Expert's post
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

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Joined: 05 Sep 2015
Posts: 1
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

05 Sep 2015, 10:04
Can somebody solve this with Trigonometry.
Thank you.
Current Student
Joined: 20 Mar 2014
Posts: 2652
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

05 Sep 2015, 11:37
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.

Attachments

2015-09-05_14-34-36.jpg [ 9.97 KiB | Viewed 10591 times ]

SVP
Joined: 08 Jul 2010
Posts: 2067
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

06 Sep 2015, 07:14
2
KUDOS
Expert's post
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 I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2273
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

09 Jun 2016, 14:09
1
KUDOS
Expert's post
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 06 Sep 2016
Posts: 140
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

04 Jul 2017, 07:44
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?
Senior Manager
Joined: 09 Mar 2016
Posts: 441
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

06 Apr 2018, 02:25
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
Joined: 02 Sep 2009
Posts: 44636
Re: If a square mirror has a 20-inch diagonal, what is the [#permalink]

### Show Tags

06 Apr 2018, 02:42
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.
_________________
Re: If a square mirror has a 20-inch diagonal, what is the   [#permalink] 06 Apr 2018, 02:42
Display posts from previous: Sort by