It is currently 21 Nov 2017, 05:30

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

Bill owns a large collection of fishing lures consisting of

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

Hide Tags

3 KUDOS received
Intern
Intern
avatar
Joined: 11 May 2013
Posts: 8

Kudos [?]: 28 [3], given: 0

Bill owns a large collection of fishing lures consisting of [#permalink]

Show Tags

New post 07 Oct 2013, 16:41
3
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:25) correct 39% (01:48) wrong based on 224 sessions

HideShow timer Statistics

Bill owns a large collection of fishing lures consisting of small, medium, and large lures that weigh 3, 4, and 5 grams each, respectively. If the product of the lure weights that Bill sold to his friend is 216,000 grams, how many medium lures did he sell?

A. 6
B. 5
C. 4
D. 3
E. 2

[Reveal] Spoiler:
Analyze the Question:

Bill sold some small, medium, and large lures to his friend. The product of the weights of the lures is 216,000 grams. We know the weights of the individual lures, but we do not know how many of each type he sold. We can factor the product to find the number of 4-gram weights sold. The answer choices are very close together, and these values can help guide the solution process.

Identify the Task:

We will determine the number of 4-gram lures Bill sold to his friend by determining the number of factors of 4 there are in 216,000.

Approach Strategically:

Number properties are the key to solving this problem quickly. Since 3, 4, and 5 do not have any common factors with each other, the number of 4-gram lures Bill sold must be the number of factors of 4 in 216,000. Dividing 216,000 by 4 yields 54,000, and 54,000 is still a multiple of 4 due to its last two digits of 00. Dividing 54,000 by 4 yields 13,500, and 13,500 is still a multiple of 4 due to its last two digits of 00. Dividing 13,500 by 4 yields 3,375, and 3,375 is not a multiple of 4 as its last two digits, 75, are not divisible by 4. That’s three factors of 4 for 216,000, so Bill sold three 4-gram lures to his friend.

The correct answer is Choice (D).

Confirm Your Answer:

We can factor 216,000 completely using the given weights and see that 216,000 = 3^3× 4^3× 5^3. This is the only possible way to get 216,000 from 3, 4, and 5, so we know that three of each of these lures were sold.
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Oct 2013, 00:48, edited 1 time in total.
RENAMED THE TOPIC.

Kudos [?]: 28 [3], given: 0

Intern
Intern
avatar
Status: Determined..700 will be my Revenge
Joined: 27 Sep 2012
Posts: 9

Kudos [?]: 5 [0], given: 5

Location: United States
Re: How many medium lures did Bill sell? [#permalink]

Show Tags

New post 07 Oct 2013, 18:21
The answer should be D.

Start with doing the Prime Factorization of the number 216000.

You will get (2)with exponent 6.

Which is nothing but 4 with exponent 3.

Thanks

Kudos [?]: 5 [0], given: 5

Intern
Intern
avatar
Joined: 30 May 2012
Posts: 2

Kudos [?]: [0], given: 9

GMAT ToolKit User
Re: How many medium lures did Bill sell? [#permalink]

Show Tags

New post 07 Oct 2013, 19:13
total weight = 216000

weight of medium lure - 4 gm
by factoring we get 5*5*5*3*3*3*4*4*4
THUS MEDIUM LURE = 3

Kudos [?]: [0], given: 9

Expert Post
2 KUDOS received
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 535 [2], given: 16

Location: India
Re: How many medium lures did Bill sell? [#permalink]

Show Tags

New post 07 Oct 2013, 20:51
2
This post received
KUDOS
Expert's post
1. Let the number of small, medium and large lures sold be x,y and z resp.
2. The product of the weights of the lures is 3^x * 4^y * 5^z
3. But it is also given the product is 216,000 = 3^3 * 4^3 * 5^3 by factorization.
4. So y=3.
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Premium Material
Standardized Approaches

Kudos [?]: 535 [2], given: 16

Expert Post
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10143

Kudos [?]: 3523 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: Bill owns a large collection of fishing lures consisting of [#permalink]

Show Tags

New post 24 Dec 2014, 16:10
Hi All,

Everyone who posted in this thread seems comfortable with prime factorization, but for anyone coming across this post who isn't completely comfortable with the "math", here's how prime factorization "works" - every positive integer (except the number 1) is either a prime number OR the product of a bunch of prime numbers.

For example, 2 and 3 are both prime numbers, but 4 is the product of 2 and 2.

Here, we're given a BIG number and asked to figure out the numbers that make up its PRODUCT. Since the numbers 3 and 5 are prime and 4 = 2^2, this is a big "clue" that we can use prime factorization to get to the correct answer.

So, let's prime factor 216,000

You can break this number up any way you choose, but I usually look for a logical "split"...

(216)(1,000)

(216) =
(4)(54)
(4)(6)(9)
(4)(2)(3)(3)(3)

**NOTICE that we have one 4 and one 2**

(1,000)
(10)(10)(10)
(2)(5)(2)(5)(2)(5)

**NOTICE that we have three 2s***

We now have enough information to determine how many 3s, 4s and 5s make up 216,000:

Three 3s
Three 5s
We have one 4 and four 2s. The 2s can be "paired up" to create a 4, so we have
Three 4s

Final Answer:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3523 [0], given: 173

1 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1851

Kudos [?]: 2717 [1], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Bill owns a large collection of fishing lures consisting of [#permalink]

Show Tags

New post 31 Dec 2014, 00:33
1
This post received
KUDOS
216000 = 216 * 1000

216 is a perfect cube of 6, 1000 is a perfect cube of 10

\(216000 = 6^3 * 10^3\)

\(= 2^3 * 3^3 * 2^3 * 5^3\)

\(= (2*2)^3 * 3^3 * 5^3\)

\(= 4^3 * 3^3 * 5^3\)

Answer = 3 = D
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2717 [1], given: 193

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 437

Kudos [?]: 141 [0], given: 169

Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: Bill owns a large collection of fishing lures consisting of [#permalink]

Show Tags

New post 10 Jan 2015, 13:13
Just as an equation, using sort of the unknown mupltiplier approach:

(3^x)*(4^x)*(5^x)= 216.000. Here you need the prime factorization of 216.000, which I will not show as it has been shown above.

Then you get this:
(3^x)*(4^x)*(5^x) = (3^3)*(4*3)*(5^3), so 4^x = 4*3 and x=3.

Does this make any sense?

Kudos [?]: 141 [0], given: 169

Board of Directors
User avatar
G
Joined: 17 Jul 2014
Posts: 2676

Kudos [?]: 432 [0], given: 200

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Bill owns a large collection of fishing lures consisting of [#permalink]

Show Tags

New post 09 Oct 2016, 11:11
jabronyo wrote:
Bill owns a large collection of fishing lures consisting of small, medium, and large lures that weigh 3, 4, and 5 grams each, respectively. If the product of the lure weights that Bill sold to his friend is 216,000 grams, how many medium lures did he sell?

A. 6
B. 5
C. 4
D. 3
E. 2



pretty straight forward question...find the prime factorization of 216,000 and tell the exponent number for 4 or 2^2.

first step:
216,000 = 216 * 1000
1000 = 10^3 or 5^3 * 2^3.
216 = 2 * 108 = 2*2* 54
54 = 2*27 = 2*3^3.
total, we have:
2^3(from 1000) * 5^3(from 1000) * 2^3(from 216) * 3^3(from 2016)
combine:
2^6 * 5^3 * 3^3
we can rewrite 2^6 as 4^3.
since we are asked for the exponent for 4, the answer should be 3 - D

Kudos [?]: 432 [0], given: 200

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 837

Kudos [?]: 267 [0], given: 15

Bill owns a large collection of fishing lures consisting of [#permalink]

Show Tags

New post 17 Oct 2017, 20:50
Bill owns a large collection of fishing lures consisting of small, medium, and large lures that weigh 3, 4, and 5 grams each, respectively. If the product of the lure weights that Bill sold to his friend is 216,000 grams, how many medium lures did he sell?

A. 6
B. 5
C. 4
D. 3
E. 2

the product of one set of three lures--s,m,l--will=3*4*5=60 grams
the product of three sets of three lures will=60^3=216,000 grams
in three sets there will be 3 medium lures
D

Kudos [?]: 267 [0], given: 15

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1821

Kudos [?]: 934 [0], given: 3

Location: United States (CA)
Re: Bill owns a large collection of fishing lures consisting of [#permalink]

Show Tags

New post 19 Oct 2017, 10:20
jabronyo wrote:
Bill owns a large collection of fishing lures consisting of small, medium, and large lures that weigh 3, 4, and 5 grams each, respectively. If the product of the lure weights that Bill sold to his friend is 216,000 grams, how many medium lures did he sell?

A. 6
B. 5
C. 4
D. 3
E. 2


We can break down 216,000 into primes:

216,000 = 216 x 1000 = 6^3 x 10^3 = 2^3 x 3^3 x 2^3 x 5^3 = 2^6 x 3^3 x 5^3

However, we really want to break the number 216,000 into factors of 3, 4, and 5 to match the weights of the lures that he sold. Thus, we should rewrite the product as:

216,000 = 2^6 x 3^3 x 5^3 = 4^3 x 3^3 x 5^3

Since each medium lure weighed 4 grams, he sold 3 medium lures.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Kudos [?]: 934 [0], given: 3

Re: Bill owns a large collection of fishing lures consisting of   [#permalink] 19 Oct 2017, 10:20
Display posts from previous: Sort by

Bill owns a large collection of fishing lures consisting of

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


cron

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®.