It is currently 17 Oct 2017, 23:18

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The price of a diamond varies inversely with the square of the percent

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128641 [1], given: 12181

The price of a diamond varies inversely with the square of the percent [#permalink]

Show Tags

New post 07 Jul 2017, 02:13
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:09) correct 40% (01:29) wrong based on 129 sessions

HideShow timer Statistics

The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400
(B) $500
(C) $1000
(D) $4000
(E) $8000
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 128641 [1], given: 12181

Manager
Manager
avatar
G
Joined: 14 Oct 2015
Posts: 205

Kudos [?]: 83 [0], given: 388

Reviews Badge
The price of a diamond varies inversely with the square of the percent [#permalink]

Show Tags

New post 07 Jul 2017, 03:35
Bunuel wrote:
The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400
(B) $500
(C) $1000
(D) $4000
(E) $8000


It should be A.

P is proportional to square of impurities.

First Diamond
\(0.02^2 = 0.0004\)

Second Diamond
\(0.05^2 = 0.025\)

Ratio of square of increase in impurities = \(0.025/0.04 = 6.25.\)

Price of diamond would decrease by the same ratio -> \(2500/6.25 = 400\)

This is a very crude calculation and I would appreciate someone providing a proper mathematical equation for this.
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Kudos [?]: 83 [0], given: 388

1 KUDOS received
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Jun 2015
Posts: 300

Kudos [?]: 107 [1], given: 47

Concentration: Finance
GPA: 3.5
Re: The price of a diamond varies inversely with the square of the percent [#permalink]

Show Tags

New post 07 Jul 2017, 04:22
1
This post received
KUDOS
1
This post was
BOOKMARKED
p = k/(impurity)^2
2500 = k/(0.02)^2
k = 1

p = 1/(o.o5)^2
p = 1/0.0025 = 400. Ans - A.
_________________

I used to think the brain was the most important organ. Then I thought, look what’s telling me that.

Kudos [?]: 107 [1], given: 47

Director
Director
avatar
P
Joined: 22 May 2016
Posts: 802

Kudos [?]: 254 [0], given: 544

The price of a diamond varies inversely with the square of the percent [#permalink]

Show Tags

New post 08 Jul 2017, 11:43
Bunuel wrote:
The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400
(B) $500
(C) $1000
(D) $4000
(E) $8000

Hmm. I got D. I translated .02% to .0002. (Initially I got A, but then it occurred to me that the problem says .02% -- not .02.)
Quote:
The price of a diamond varies inversely with the square of the percentage of impurities

1. Where P is price, k is constant, and x is the square of the percentage of impurities

\(P = \frac{k}{x}\), or \(P*x = k\)

2. Find k from "the cost of a diamond with .02% impurities is $2500."

.02% = \(.0002\), and

\((.0002)^2 = .00000004\), or \(4 * 10^{-8}\), thus:

\(2500 * 4 * 10^{-8} = .001\) = \(k\)

3. What is the cost of a diamond with 0.05% impurities? Start with x.

.05% = .0005

\(x = (.0005)^2\) = \(.00000025\), or

\(25 * 10^{-8}\)

4. Find price. \(P = \frac{k}{x}\)

Make k easier to work with: .001 = \(100 * 10^{-5}\)

P = \(100 * 10^{-5}\) / \(25 * 10^{-8}\) =

\(4 * 10^{-5 - (-8)}\) =

\(4 * 10^3 = 4,000\)

Answer D? (Seems a little odd that a larger percentage of impurities -- prior to squaring -- would yield a more expensive diamond. Once squared, however, .05% impurities < .02% impurities.)

Kudos [?]: 254 [0], given: 544

Director
Director
avatar
S
Joined: 21 Mar 2016
Posts: 529

Kudos [?]: 28 [0], given: 96

Reviews Badge CAT Tests
The price of a diamond varies inversely with the square of the percent [#permalink]

Show Tags

New post 09 Jul 2017, 08:49
Bunuel wrote:
The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400
(B) $500
(C) $1000
(D) $4000
(E) $8000



can be solved with ratios..
let the price be x
2500 -->> 1/0.0004 ..(1)
x--> 1/0.0025 ..(2)

divide both the equations

2500/x = 25/4

x = 2500 *4 /25
x = 400
ans A

Kudos [?]: 28 [0], given: 96

1 KUDOS received
Manager
Manager
User avatar
G
Joined: 30 May 2012
Posts: 220

Kudos [?]: 77 [1], given: 151

Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Premium Member
Re: The price of a diamond varies inversely with the square of the percent [#permalink]

Show Tags

New post 10 Jul 2017, 20:05
1
This post received
KUDOS
Here's how I solved it:

Given, price of the diamond decreases as the square of impurities increase.

\(Diamond_{0.0004%}\) = 2500

So, obviously if the impurities increase, the price MUST be less than 2500. So, rule out option D and E

Now, how much of 0.0004 is 0.0025 [I have squared both the impurities as per the given info]? That will be 6.25. In other words, if you multiplied 0.0004 by 6.25, you will get 0.0025.

Since, the price and impurities and inversely proportional - I will divide the price by 6.25

\(Diamond_{0.0025%}\) = \(\frac{2500}{6.25}\), which is 400. Hope what I did was correct :)

Kudos [?]: 77 [1], given: 151

Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 827 [2], given: 5

Re: The price of a diamond varies inversely with the square of the percent [#permalink]

Show Tags

New post 12 Jul 2017, 16:35
2
This post received
KUDOS
Expert's post
Bunuel wrote:
The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400
(B) $500
(C) $1000
(D) $4000
(E) $8000


We can let k = the constant of proportionality, and we have:

k/(0.0002)^2 = 2500

k/0.00000004 = 2500

k = 0.0001

Thus:

0.0001/(0.0005)^2 = 0.0001/0.00000025 = 400

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

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

Kudos [?]: 827 [2], given: 5

Manager
Manager
avatar
B
Joined: 07 Jun 2017
Posts: 111

Kudos [?]: 3 [0], given: 454

Re: The price of a diamond varies inversely with the square of the percent [#permalink]

Show Tags

New post 11 Aug 2017, 01:30
jedit wrote:
Bunuel wrote:
The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400
(B) $500
(C) $1000
(D) $4000
(E) $8000


It should be A.

P is proportional to square of impurities.

First Diamond
\(0.02^2 = 0.0004\)

Second Diamond
\(0.05^2 = 0.025\)

Ratio of square of increase in impurities = \(0.025/0.04 = 6.25.\)

Price of diamond would decrease by the same ratio -> \(2500/6.25 = 400\)

This is a very crude calculation and I would appreciate someone providing a proper mathematical equation for this.

For this part that you did \(0.025/0.04 = 6.25.\),
Do you actually mean--> 0.0025/ 0.0004?

Kudos [?]: 3 [0], given: 454

Re: The price of a diamond varies inversely with the square of the percent   [#permalink] 11 Aug 2017, 01:30
Display posts from previous: Sort by

The price of a diamond varies inversely with the square of the percent

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.