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

 It is currently 17 Jan 2019, 13:48

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# Bill owns a large collection of fishing lures consisting of

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 May 2013
Posts: 7
Bill owns a large collection of fishing lures consisting of  [#permalink]

### Show Tags

Updated on: 07 Oct 2013, 23:48
5
2
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:02) correct 32% (02:34) wrong based on 251 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

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.

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).

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.

Originally posted by jabronyo on 07 Oct 2013, 15:41.
Last edited by Bunuel on 07 Oct 2013, 23:48, edited 1 time in total.
RENAMED THE TOPIC.
Intern
Status: Determined..700 will be my Revenge
Joined: 27 Sep 2012
Posts: 9
Location: United States
Re: How many medium lures did Bill sell?  [#permalink]

### Show Tags

07 Oct 2013, 17:21

You will get (2)with exponent 6.

Which is nothing but 4 with exponent 3.

Thanks
Intern
Joined: 30 May 2012
Posts: 2
Re: How many medium lures did Bill sell?  [#permalink]

### Show Tags

07 Oct 2013, 18:13
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
Director
Joined: 17 Dec 2012
Posts: 625
Location: India
Re: How many medium lures did Bill sell?  [#permalink]

### Show Tags

07 Oct 2013, 19:51
2
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 Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13331
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Bill owns a large collection of fishing lures consisting of  [#permalink]

### Show Tags

24 Dec 2014, 15:10
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

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!*****

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1823
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

30 Dec 2014, 23:33
1
216000 = 216 * 1000

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

$$216000 = 6^3 * 10^3$$

$$= 2^3 * 3^3 * 2^3 * 5^3$$

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

$$= 4^3 * 3^3 * 5^3$$

_________________

Kindly press "+1 Kudos" to appreciate

Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 416
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

10 Jan 2015, 12:13
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?
Board of Directors
Joined: 17 Jul 2014
Posts: 2600
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Bill owns a large collection of fishing lures consisting of  [#permalink]

### Show Tags

09 Oct 2016, 10:11
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
VP
Joined: 07 Dec 2014
Posts: 1151
Bill owns a large collection of fishing lures consisting of  [#permalink]

### Show Tags

17 Oct 2017, 19:50
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
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4527
Location: United States (CA)
Re: Bill owns a large collection of fishing lures consisting of  [#permalink]

### Show Tags

19 Oct 2017, 09:20
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.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: Bill owns a large collection of fishing lures consisting of &nbs [#permalink] 19 Oct 2017, 09:20
Display posts from previous: Sort by