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

It is currently 19 Apr 2019, 07:54

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

Older television screens have an aspect ratio of 4:3. That is, the rat

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54371
Older television screens have an aspect ratio of 4:3. That is, the rat  [#permalink]

Show Tags

New post 27 Mar 2019, 00:17
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (02:30) correct 40% (02:34) wrong based on 20 sessions

HideShow timer Statistics

Older television screens have an aspect ratio of 4:3. That is, the ratio of the width to the height is 4:3. The aspect ratio of many movies is not 4:3, so they are sometimes shown on a television screen by "letterboxing" - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of 2:1 and is shown on an older television screen with a 27-inch diagonal. What is the height, in inches, of each darkened strip?

(A) 2
(B) 2.25
(C) 2.5
(D) 2.7
(E) 3

_________________
Intern
Intern
avatar
Joined: 25 Apr 2016
Posts: 2
Location: India
Schools: ISB '21, IIM
Re: Older television screens have an aspect ratio of 4:3. That is, the rat  [#permalink]

Show Tags

New post 27 Mar 2019, 00:33
Answer D

As TV aspect ratio is 4:3 and diagonal length is 27 inches.

Taking width 4x and height 3x we have
(4x)^2 + (3x)^2 = 27^2
25x^2= 27^2
X= 27/5= 5.2

now the movie ratio is 2:1 i.e (4:2) and the TV ratio is (4:3).
Hence total 1/3 is used for letterboxing i.e X= 5.4

So each darkened strip is 5.4/2= 2.7

Answer D

Posted from my mobile device
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 2998
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: Older television screens have an aspect ratio of 4:3. That is, the rat  [#permalink]

Show Tags

New post 27 Mar 2019, 03:27
Bunuel wrote:
Older television screens have an aspect ratio of 4:3. That is, the ratio of the width to the height is 4:3. The aspect ratio of many movies is not 4:3, so they are sometimes shown on a television screen by "letterboxing" - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of 2:1 and is shown on an older television screen with a 27-inch diagonal. What is the height, in inches, of each darkened strip?

(A) 2
(B) 2.25
(C) 2.5
(D) 2.7
(E) 3


ratio 4:3 has diagonal 27
or say
√(4x)^2+(3x)^2 = (27)
solve for x = 27/5 ; 5.4
also width of darkened strip = 3x-y
and 2y=4x, 2x=y
so 3x-y = 3x-2x = x
height of each strip x/2 ; 5.4/2 = 2.7
IMO D
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5784
Location: United States (CA)
Re: Older television screens have an aspect ratio of 4:3. That is, the rat  [#permalink]

Show Tags

New post 29 Mar 2019, 08:54
Bunuel wrote:
Older television screens have an aspect ratio of 4:3. That is, the ratio of the width to the height is 4:3. The aspect ratio of many movies is not 4:3, so they are sometimes shown on a television screen by "letterboxing" - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of 2:1 and is shown on an older television screen with a 27-inch diagonal. What is the height, in inches, of each darkened strip?

(A) 2
(B) 2.25
(C) 2.5
(D) 2.7
(E) 3



First, let’s find the width and height of the TV screen. Since the TV screen has an aspect ratio of 4:3, let the width be 4x and the height be 3x, for some x. Since we know that the diagonal is 27, we can use the Pythagorean theorem to set up the equation:

(4x)^2 + (3x)^2 = 27^2

16x^2 + 9x^2 = 27^2

25x^2 = 27^2

x^2 = 27^2/25

x = √(27^2/25) = 27/5

So the width of the screen is 4(27/5) = 108/5, and the height is 3(27/5) = 81/5. Now, since the movie has an aspect ratio of 2:1, its width will match that of the screen. That is, the width of movie is 108/5, but its height will be only half of this, or 54/5. Since the height of the screen is 81/5 and the height of the movie is 54/5, the height of each of the two darkening strips is (81/5 - 54/5)/2 = (27/5)/2 = 27/10 = 2.7.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 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

Intern
Intern
avatar
B
Joined: 26 Mar 2018
Posts: 6
Re: Older television screens have an aspect ratio of 4:3. That is, the rat  [#permalink]

Show Tags

New post 30 Mar 2019, 04:20
Bunuel wrote:
Older television screens have an aspect ratio of 4:3. That is, the ratio of the width to the height is 4:3. The aspect ratio of many movies is not 4:3, so they are sometimes shown on a television screen by "letterboxing" - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of 2:1 and is shown on an older television screen with a 27-inch diagonal. What is the height, in inches, of each darkened strip?

(A) 2
(B) 2.25
(C) 2.5
(D) 2.7
(E) 3



16x^2 + 9x^2 = 27^2
25x^2 = 27^2
5x = 27
x = 27/5= 5.4
Now,
tv ratio= 4:3
movie ratio= 2:1=4:2
height diff= 3x-2x=1x=5.4
5.4 is divided equally in the top and bottom
i.e., 5.4/2= 2.7

Answer is D
GMAT Club Bot
Re: Older television screens have an aspect ratio of 4:3. That is, the rat   [#permalink] 30 Mar 2019, 04:20
Display posts from previous: Sort by

Older television screens have an aspect ratio of 4:3. That is, the rat

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.