It is currently 18 Jan 2018, 02:17

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

What is the lowest positive integer that is divisible by both 5,000,00

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43318

Kudos [?]: 139367 [0], given: 12787

What is the lowest positive integer that is divisible by both 5,000,00 [#permalink]

Show Tags

New post 15 Nov 2016, 09:10
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:31) correct 29% (01:41) wrong based on 77 sessions

HideShow timer Statistics

What is the lowest positive integer that is divisible by both 5,000,000 and 256?

A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000
[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 [?]: 139367 [0], given: 12787

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2016
Posts: 263

Kudos [?]: 55 [1], given: 212

Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Re: What is the lowest positive integer that is divisible by both 5,000,00 [#permalink]

Show Tags

New post 15 Nov 2016, 09:24
1
This post received
KUDOS
Bunuel wrote:
What is the lowest positive integer that is divisible by both 5,000,000 and 256?

A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000


5,000,000= 5^1*10^6==> 5^7*2^6
256= 2^8
Required= LCM(5,000,000, 256)= 5^7*2^8 = 2*10^7
C

Alternate way
Both values of 5,000,000 and 256 must divide the values in the option

A. 5,000,000 ==== (5^7 * 2^6)/2^8 Not completely divisible
B. 10,000,000 === (5^7 * 2^7)/2^8 Not completely divisible
C. 20,000,000 === (5^7 * 2^8)/2^8 Divisible lowest positive integer
D. 50,000,000 === (5^8 * 2^7)/2^8 Not completely divisible
E. 100,000,000 === (5^8 * 2^8)/2^8 Divisible

Kudos [?]: 55 [1], given: 212

Senior Manager
Senior Manager
User avatar
P
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 423

Kudos [?]: 157 [0], given: 422

Location: India
GPA: 3.64
GMAT ToolKit User Premium Member Reviews Badge
Re: What is the lowest positive integer that is divisible by both 5,000,00 [#permalink]

Show Tags

New post 15 Nov 2016, 09:26
Finding the Least Common Multiple of 256 and 5,000,000 gives 20,000,000.
Hence answer is C.
_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Kudos [?]: 157 [0], given: 422

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3224

Kudos [?]: 1174 [0], given: 327

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
What is the lowest positive integer that is divisible by both 5,000,00 [#permalink]

Show Tags

New post 15 Nov 2016, 10:13
Bunuel wrote:
What is the lowest positive integer that is divisible by both 5,000,000 and 256?

A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000


\(5000000 = 2^6 * 5^7\)
\(256 = 2^8\)

Lowest positive integer that is divisible by both 5,000,000 and 256 = LCM of ( \(2^6 x 5^7 , 2^8\) ) = \(2^6 * 5^7\) = \(20,000,000\)

Hence, answer will be (C) \(20,000,000\)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1174 [0], given: 327

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2014

Kudos [?]: 1084 [0], given: 4

Location: United States (CA)
Re: What is the lowest positive integer that is divisible by both 5,000,00 [#permalink]

Show Tags

New post 17 Nov 2016, 13:44
Bunuel wrote:
What is the lowest positive integer that is divisible by both 5,000,000 and 256?

A. 5,000,000
B. 10,000,000
C. 20,000,000
D. 50,000,000
E. 100,000,000


Taking a quick scan of our answer choices, we see that all answer choices are divisible by 5,000,000, so we really need to determine which of the answer choices is the smallest value divisible by 256.

Breaking 256 into primes, we see that 256 = 2^8. Thus, we need to find the smallest value that has 8 twos among the answer choices. Let’s start with answer A.

A) 5,000,000 = 5 x 1,000,000 = 5 x 10^6 = 5 x 5^6 x 2^6

Since 5,000,000 only has 6 twos, it is not divisible by 256.

B) 10,000,000 = 10^7 = 2^7 x 5^7

Since 10,000,000 only has 7 twos, it is not divisible by 256.

C) 20,000,000 = 2 x 10,000,000 = 2 x 10^7 = 2^1 x 2^7 x 5^7 = 2^8 x 5^7.

Since 20,000,000 has 8 twos, it’s divisible by 256, and thus, 20,000,000 is the lowest positive integer that is divisible by both 5,000,000 and 256.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Kudos [?]: 1084 [0], given: 4

Intern
Intern
avatar
B
Joined: 25 May 2017
Posts: 9

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

GMAT 1: 750 Q49 V44
Re: What is the lowest positive integer that is divisible by both 5,000,00 [#permalink]

Show Tags

New post 04 Dec 2017, 11:46
256 has only eight 2's --> \(2^8\)

5,000,000 has six 0's and each zero = 5 x 2 --> therefore it has six 2's

There are therefore two 2's leftover from 256 that are not counted in 5,000,000, we simply have to multiply 5,000,000 by \(2^2\)
= 5,000,000 x 4 = 20,000,000
_________________

GmatIvyPrep
Yale MBA Graduate and GMAT-Focused Tutor for 4+ years
Contact: gmativyprep@gmail.com for a consultation and private tutoring rates

Image

Material offered free of charge along with full end-to-end GMAT Quantitative Course:
- High-level (700+) practice question sets for Quantitative section by topic
- AWA writing template that helped students get a full score on the Essay
- Complete pack of Verbal Material for SC, RC and CR

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

Re: What is the lowest positive integer that is divisible by both 5,000,00   [#permalink] 04 Dec 2017, 11:46
Display posts from previous: Sort by

What is the lowest positive integer that is divisible by both 5,000,00

  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®.