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

 It is currently 17 Oct 2019, 18:29 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  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  Joined: 22 Jun 2010
Posts: 31
On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

4
13 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:07) correct 33% (02:05) wrong based on 330 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
Math Expert V
Joined: 02 Sep 2009
Posts: 58402

Show Tags

5
6
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 $$\pi\approx{\frac{22}{7}}$$).

_________________
General Discussion
Intern  Joined: 22 Jun 2010
Posts: 31

Show Tags

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. $$Area=\pi{r^2}\approx{\frac{3.14*49}{64}}\approx{2.4}$$.

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

Show Tags

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

Show Tags

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 V
Joined: 22 May 2016
Posts: 3548
On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

2
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 can be confusing. We have a "scale factor" issue, as you note.

In one sense, however, when scaling up or down, linear change is one kind of step (ONE change in one length), and area change is a different kind of step (TWO changes, one for each length).

"...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 using the change from one linear unit to another (distance in inches -> distance in miles) ...
what you do to one length (scale it up), you must do to the other.

And to calculate area, we use two lengths. You converted only one of the two lengths.

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:

$$\frac{1in}{2mi}$$ -- 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 sq. 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 = length * length, so 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. _________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2816
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

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

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

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  B
Joined: 30 Jul 2014
Posts: 106
GPA: 3.72
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

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 Joined: 09 Sep 2013
Posts: 13246
Re: On an aerial photograph, the surface of a pond appears as  [#permalink]

Show Tags

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.
_________________ Re: On an aerial photograph, the surface of a pond appears as   [#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

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