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

It is currently 18 Oct 2018, 02:26

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

For any positive number x, the function [x] denotes the greatest integ

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

Hide Tags

ISB, NUS, NTU Moderator
User avatar
G
Joined: 11 Aug 2016
Posts: 265
Reviews Badge CAT Tests
For any positive number x, the function [x] denotes the greatest integ  [#permalink]

Show Tags

New post Updated on: 26 Sep 2018, 08:35
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

38% (01:59) correct 62% (01:32) wrong based on 26 sessions

HideShow timer Statistics

For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.999] = 1.
If k is a positive integer such that \(k^2\) is divisible by 45 and 80, what is the units digit of \([\frac{k^3}{4000}]\)?

A. 0
B. 1
C. 7
D. 4
E. Can not be determined.

_________________

~R.
If my post was of any help to you, You can thank me in the form of Kudos!!


Originally posted by GmatDaddy on 26 Sep 2018, 07:42.
Last edited by GmatDaddy on 26 Sep 2018, 08:35, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6957
Re: For any positive number x, the function [x] denotes the greatest integ  [#permalink]

Show Tags

New post 26 Sep 2018, 08:22
1
2
GmatDaddy wrote:
For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.999] = 1.
If k is a positive integer such that \(k^2\) is divisible by 45 and 80, what is the units digit of \([\frac{k^3}{4000}]\)?

A. 0
B. 1
C. 27
D. 54
E. Can not be determined.


Please correct your choices..
We are looking for units digit and choice C and D give you 2-digit integers.

Anyways..
k^2 divisible by 45 or 3^2*5, so k will surely be a multiple of 3*5
k^2 is also divisible by 80 or 2^4*5 or 2^3*2*5 so k is surely a multiple of 2*2*5
Therefore k will surely be a multiple of LCM of 3*5 and 2*2*5 or 2*2*3*5 or 60
Therefore k^3 = (60a)^3=216000a^3
Therefore k^3/4000=216000a^3/4000=54a^3
Now units digit will depend on a..
Say a is 1 Ans is 4
a is 7, Ans is 4*3 or 2
So cannot be determined

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3863
Location: United States (CA)
Re: For any positive number x, the function [x] denotes the greatest integ  [#permalink]

Show Tags

New post 29 Sep 2018, 17:55
GmatDaddy wrote:
For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.999] = 1.
If k is a positive integer such that \(k^2\) is divisible by 45 and 80, what is the units digit of \([\frac{k^3}{4000}]\)?

A. 0
B. 1
C. 7
D. 4
E. Can not be determined.



If a number is divisible by 45 and 80, then it’s divisible by the least common multiple of 45 and 80, which is 720. The prime factorization of 720 is 9 x 8 x 10 = 3^2 x 2^3 x 2 x 5 = 2^4 x 3^2 x 5. Therefore, k^2 is divisible by 2^4 x 3^2 x 5 and k must be divisible by 2^2 x 3 x 5 = 60. In other words, k is a multiple of 60.

If k = 60, then k^3/4000 = 60^3/4000 = (60 x 60 x 60)/4000 = (6 x 6 x 6)/4 = 54. So the units digit of [k^3/4000] is 4.

If k = 600, then k^3/4000 = 600^3/4000 = (600 x 600 x 600)/4000 = (60 x 60 x 60)/4 = 54,000. So the units digit of [k^3/4000] is 0.

We see that the units digit of [k^3/4000] is not unique. So it can’t be determined.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

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

GMAT Club Bot
Re: For any positive number x, the function [x] denotes the greatest integ &nbs [#permalink] 29 Sep 2018, 17:55
Display posts from previous: Sort by

For any positive number x, the function [x] denotes the greatest integ

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


Copyright

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