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

 It is currently 20 Jun 2019, 00:52 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.  What is the lowest positive integer that is divisible by both 5,000,00

Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55718
What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 63% (01:43) correct 38% (01:56) wrong based on 141 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

_________________
Senior Manager  Joined: 06 Jun 2016
Posts: 258
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

1
1
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 V
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1021
Location: India
GPA: 3.64
Re: What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

Show Tags

Finding the Least Common Multiple of 256 and 5,000,000 gives 20,000,000.
_________________
Please give kudos, if you like my post

When the going gets tough, the tough gets going...
Board of Directors P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4504
Location: India
GPA: 3.5
What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

Show Tags

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 )
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6589
Location: United States (CA)
Re: What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

Show Tags

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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@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.

Intern  B
Joined: 25 May 2017
Posts: 10
GMAT 1: 750 Q49 V44 Re: What is the lowest positive integer that is divisible by both 5,000,00  [#permalink]

Show Tags

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 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
Non-Human User Joined: 09 Sep 2013
Posts: 11396
Re: What is the lowest positive integer that is divisible by both 5,000,00  [#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: What is the lowest positive integer that is divisible by both 5,000,00   [#permalink] 28 Jan 2019, 08:49
Display posts from previous: Sort by

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