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

It is currently 08 Apr 2020, 14:03

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

In the figure above, V represents an observation point at on

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 172
In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 19 Dec 2012, 05:05
2
11
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

90% (02:00) correct 10% (02:30) wrong based on 733 sessions

HideShow timer Statistics

Attachment:
observation.png
observation.png [ 11.05 KiB | Viewed 19684 times ]
In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object?

(A) \(10-5\sqrt{3}\)
(B) \(10-5\sqrt{2}\)
(C) 2
(D) 2 1/2
(E) 4
Most Helpful Community Reply
Manager
Manager
avatar
Joined: 07 May 2013
Posts: 87
Re: In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 17 Nov 2013, 19:38
8
3
No need of using Pythagorean theorem. Observe triangle VPR. VP:VR=5:10=1:2. Angle opposite VR is 90. When does this happen? It happens only when VPR is a 30-60-90 triangle. So, VP:VR:PR=5:10:5\(\sqrt{3}\).So, answer is 10-5\(\sqrt{3}\)
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62637
Re: In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 19 Dec 2012, 05:09
2
2
Image
In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object?

(A) \(10-5\sqrt{3}\)
(B) \(10-5\sqrt{2}\)
(C) 2
(D) 2 1/2
(E) 4

Attachment:
observation2.png
observation2.png [ 12.99 KiB | Viewed 17865 times ]

\(PR=\sqrt{VR^2-VP^2}=\sqrt{10^2-5^2}=5\sqrt{3}\);

Thus, \(RS=PS-PR=10-5\sqrt{3}\).

Answer: A.
_________________
Manager
Manager
avatar
Joined: 25 Feb 2014
Posts: 56
Concentration: Healthcare, Finance
GMAT 1: 700 Q49 V35
GPA: 3.5
Reviews Badge
Re: In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 16 Apr 2014, 10:04
madn800 wrote:
No need of using Pythagorean theorem. Observe triangle VPR. VP:VR=5:10=1:2. Angle opposite VR is 90. When does this happen? It happens only when VPR is a 30-60-90 triangle. So, VP:VR:PR=5:10:5\(\sqrt{3}\).So, answer is 10-5\(\sqrt{3}\)


How can you determine this is a 30-60-90 and not a 45-45-90?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62637
Re: In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 18 Apr 2014, 10:05
atl12688 wrote:
madn800 wrote:
No need of using Pythagorean theorem. Observe triangle VPR. VP:VR=5:10=1:2. Angle opposite VR is 90. When does this happen? It happens only when VPR is a 30-60-90 triangle. So, VP:VR:PR=5:10:5\(\sqrt{3}\).So, answer is 10-5\(\sqrt{3}\)


How can you determine this is a 30-60-90 and not a 45-45-90?


In right triangle VPR the ratio of one side (VP) to hypotenuse (VR) is 1:2. This only happens for 30-60-90 right triangle.

MUST KNOW FOR THE GMAT:
• A right triangle where the angles are 30°, 60°, and 90°.
Image
This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is: The sides are always in the ratio \(1 : \sqrt{3}: 2\).
Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

• A right triangle where the angles are 45°, 45°, and 90°.
Image
This is one of the 'standard' triangles you should be able recognize on sight. A fact you should also commit to memory is: The sides are always in the ratio \(1 : 1 : \sqrt{2}\). With the \(\sqrt{2}\) being the hypotenuse (longest side). This can be derived from Pythagoras' Theorem. Because the base angles are the same (both 45°) the two legs are equal and so the triangle is also isosceles.

For more check Triangles chapter of our Math Book: math-triangles-87197.html

Hope it helps.
_________________
Manager
Manager
avatar
Joined: 25 Feb 2014
Posts: 56
Concentration: Healthcare, Finance
GMAT 1: 700 Q49 V35
GPA: 3.5
Reviews Badge
Re: In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 18 Apr 2014, 10:30
Yes thank you Bunuel. I was missing the fact that VR was 10 which gave the Leg:hypotenuse the 1:2 ratio. Greatly appreciated!!
Intern
Intern
avatar
Joined: 10 Apr 2012
Posts: 22
Concentration: Finance, Economics
GMAT 1: 760 Q50 V44
In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 10 Jul 2014, 08:49
1
See Image for plugging in strategy
Attachments

Observatory.jpg
Observatory.jpg [ 44.41 KiB | Viewed 15331 times ]

Senior Manager
Senior Manager
User avatar
Joined: 15 Oct 2015
Posts: 297
Concentration: Finance, Strategy
GPA: 3.93
WE: Account Management (Education)
GMAT ToolKit User
Re: In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 03 Mar 2016, 01:32
Walkabout wrote:
Attachment:
observation.png
In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object?

(A) \(10-5\sqrt{3}\)
(B) \(10-5\sqrt{2}\)
(C) 2
(D) 2 1/2
(E) 4


I think this is the fastest route to the answer.
Knowing the popular right-triangle and applying that knowledge when u meet a question of this sort rewards you massively.
2:1:√3 for 30 60 90
1: 1: √2 for 40 40 90.

And the fastest means of telling is finding the ratio of the sides regardless of if it's a 15360000: 7680000: x that you saw.
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9972
Location: United States (CA)
Re: In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 23 Jun 2016, 08:31
Walkabout wrote:
Attachment:
observation.png
In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object?

(A) \(10-5\sqrt{3}\)
(B) \(10-5\sqrt{2}\)
(C) 2
(D) 2 1/2
(E) 4


We are being asked to determine the length of RS. To determine this length we need to know the length from point R to the right angle in the given figure. If we label the point at the right angle as T, we see that we need to determine the length of TR.

If we draw a line segment connecting V and R, we will see that VR, VT and TR create a right triangle. Furthermore, we are told in the question stem that VR (the hypotenuse) is 10, and that one of the sides, VT, is 5, so we now plug these values into the Pythagorean Theorem.

TR^2 + VT^2 = VR^2

TR ^2 + 5^2 = 10^2

TR ^2 + 25 = 100

TR ^2 = 75

TR = √75

TR = √25 x √3

TR = 5√3

So TR is 5√3. We subtract this from the total length TS, which is 10, to determine the length from R to S:

10 - 5√3

Answer is A.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@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.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14508
Re: In the figure above, V represents an observation point at on  [#permalink]

Show Tags

New post 05 Apr 2020, 13:47
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.
_________________
GMAT Club Bot
Re: In the figure above, V represents an observation point at on   [#permalink] 05 Apr 2020, 13:47
Display posts from previous: Sort by

In the figure above, V represents an observation point at on

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





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