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

It is currently 17 Oct 2018, 04:55

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

On an aerial photograph, the surface of a pond appears as

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

Hide Tags

Intern
Intern
avatar
Joined: 22 Jun 2010
Posts: 33
On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

New post Updated on: 20 May 2012, 12:17
4
10
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:21) correct 34% (02:01) wrong based on 267 sessions

HideShow timer Statistics

On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

Originally posted by mehdiov on 07 Sep 2010, 15:13.
Last edited by Bunuel on 20 May 2012, 12:17, edited 1 time in total.
Edited the question and added the OA
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49960
Re: please help  [#permalink]

Show Tags

New post 07 Sep 2010, 15:31
5
5
mehdiov please post the questions in their original form and provide answer choice with them.

On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

As 1 inch = 2 miles, then 7/16 inches = 2*7/16 = 7/8 miles. So actual radius is 7/8 miles. \(Area=\pi{r^2}\approx{\frac{22}{7}*\frac{49}{64}}\approx{2.4}\) (as we are asked about the approximate value we can take \(\pi\approx{\frac{22}{7}}\)).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
avatar
Joined: 22 Jun 2010
Posts: 33
Re: please help  [#permalink]

Show Tags

New post 07 Sep 2010, 15:35
Bunuel wrote:
mehdiov please post the questions in their original form and provide answer choice with them.

On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

As 1 inch = 2 miles, then 7/16 inches = 2*7/16 = 7/8 miles. So actual radius is 7/8 miles. \(Area=\pi{r^2}\approx{\frac{3.14*49}{64}}\approx{2.4}\).

Answer: B.

thanks. appoligies for that
Intern
Intern
avatar
B
Joined: 06 Apr 2017
Posts: 29
Location: United States (OR)
Concentration: Finance, Leadership
Schools: Haas EWMBA '21
GMAT 1: 730 Q48 V44
GMAT 2: 730 Q49 V40
GPA: 3.98
WE: Corporate Finance (Health Care)
GMAT ToolKit User
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

New post 03 Aug 2017, 12:42
1
Why doesn't converting the area to square inches and then converting from inches to miles work?

\((\frac{7}{16})^2=\frac{49}{256}\)
\(\frac{49}{256}*\frac{22}{7}=\frac{77}{128}\)
\(\frac{77}{12}*2\approx1.2\)

I chose 1.3 because it's the closest answer, but obviously the conversion to miles needs to happen before calculating the area. Why does this matter, and is there a decent framework to do conversions of this sort that involve squaring and cubing? This seems to pop up often, and I find it slightly confusing. Thanks!

SR
Manager
Manager
avatar
B
Joined: 09 Oct 2016
Posts: 89
Location: United States
GMAT 1: 740 Q49 V42
GPA: 3.49
Reviews Badge
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

New post 30 Aug 2017, 05:55
I chose 1.3miles as well but I think they key word here is "square miles". That's the indicator that you need to convert before using the area formula
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2033
Premium Member CAT Tests
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

New post 31 Aug 2017, 13:17
1
spence11 wrote:
Why doesn't converting the area to square inches and then converting from inches to miles work?

\((\frac{7}{16})^2=\frac{49}{256}\)
\(\frac{49}{256}*\frac{22}{7}=\frac{77}{128}\)
\(\frac{77}{12}*2\approx1.2\)

I chose 1.3 because it's the closest answer, but obviously the conversion to miles needs to happen before calculating the area. Why does this matter, and is there a decent framework to do conversions of this sort that involve squaring and cubing? This seems to pop up often, and I find it slightly confusing. Thanks!

SR

spence11 , these problems confuse me too, sometimes, just not on this front. It's a scale factor issue.

"...converting finding the area to in square inches and then converting from inches to miles [does not] work" because you are not converting from inches to miles. You need to convert square inches (in the area you found for the pond on the photo) to square miles.

The scale factor here is (2 miles: 1 inch) = 2. When converting an area, you have to use the scale factor, \(k\), twice. Area conversion requires \(k^2\) because the area of any two dimensional figure, circles included, is length times length. To convert area from one unit to another, what you do to one length (scale it up), you must do to the other.

You chose the correct scale factor of 2. But you need to multiply the area you found by \(k^2\) = \(2^2\) = 4. You are short one factor of \(k\). Close!

(\(\frac{77}{128}\) * 4) = \(\frac{77}{32}\) = 2.4 (sq mi - see below)

Here is one way to look at it:

\(\frac{1 in}{2 mi}\) -- those are one-dimensional lengths. Lines.

Convert them to two-dimensional areas by squaring the number and the unit:

(1 in)\(^2\) = (1 in)*(1 in) = 1 square inch, or 1 in\(^2\)

(2 mi)\(^2\) = (2 mi)(2 mi) = 4 square miles, or 4mi\(^2\). Below, area in square inches is converted to area in square miles. Square inches cancel, leaving square miles as the desired result, but only because I multiply the original area by the scale factor twice:

\(\frac{77}{128}(in*in)\) * \(\frac{2mi}{1in}\) * \(\frac{2mi}{1in}\) = \(\frac{77}{32}\)(mi*mi) =

2.4 miles\(^2\)

So for any conversion from area to area: if you find the original area in small units, multiply that area by the scale factor squared to get the larger actual area.

Bunuel sidestepped the whole issue by multiplying one length (radius in inches) by one scale factor (2) to get [another] one length: the radius in miles. Then he found the area in square miles with normal calculations for a circle's area.

Length: multiply by one scale factor \(k\)

Area: multiply by two scale factors \(k^2\)

Volume: multiply by three scale factors \(k^3\) (b/c V = L * L * L)

It depends on the problem, but often it is easier to convert one length of the smaller figure to one length of the larger figure (here, radius), and then calculate area or volume. If you do it that way, you only deal with the scale factor once: length --> length.

Hope that helps. :-)
_________________

The only thing more dangerous than ignorance is arrogance.
-- Albert Einstein

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

New post 02 Sep 2017, 07:09
1
mehdiov wrote:
On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0


We can create a proportion in which n is the radius of the pond in miles:

1/2 = (7/16)/n

n = 2(7/16)

n = 7/8

Thus, the area of the pond is (7/8)^2 x π. Recall that the fractional approximation of π is 22/7. Thus, we have:

(7/8)^2 x π ≈ 49/64 x 22/7 = 7/32 x 11/1 = 77/32 = 2 13/32 ≈ 2 12/30 = 2 2/5 = 2.4

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

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

Manager
Manager
User avatar
B
Joined: 30 Jul 2014
Posts: 137
GPA: 3.72
Reviews Badge
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

New post 07 Sep 2017, 05:56
Did a very silly calculation mistake -> 8*4 = 64 :(
How to avoid such careless mistakes?
_________________

A lot needs to be learned from all of you.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8429
Premium Member
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

New post 01 Oct 2018, 11:40
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: On an aerial photograph, the surface of a pond appears as &nbs [#permalink] 01 Oct 2018, 11:40
Display posts from previous: Sort by

On an aerial photograph, the surface of a pond appears as

  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®.