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

It is currently 14 Aug 2018, 22:05

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

Is x is divisible by 25? (1) x^2 is a multiple of 50 (2) x^3 is

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

Hide Tags

SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2132
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Is x is divisible by 25? (1) x^2 is a multiple of 50 (2) x^3 is  [#permalink]

Show Tags

New post Updated on: 05 Feb 2018, 07:11
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

52% (01:08) correct 48% (01:16) wrong based on 69 sessions

HideShow timer Statistics

Is Integer x divisible by 25?

(1) \(x^2\) is a multiple of 50
(2) \(x^3\) is a multiple of 625

Source: http://www.GMATinsight.com

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION


Originally posted by GMATinsight on 05 Feb 2018, 03:44.
Last edited by GMATinsight on 05 Feb 2018, 07:11, edited 3 times in total.
Intern
Intern
avatar
B
Joined: 26 Sep 2017
Posts: 28
CAT Tests
Re: Is x is divisible by 25? (1) x^2 is a multiple of 50 (2) x^3 is  [#permalink]

Show Tags

New post 05 Feb 2018, 05:59
Answer c

1) let us assume x as 10
10^2=100 which is multiple of 50. But x which is 10 is not divisible by 25

2) let us assume x as 5
5^3=625
Again 5 is not divisible by 25

Together least value should be 1250, which is divisible by 25...

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1338
Location: India
Premium Member
Re: Is x is divisible by 25? (1) x^2 is a multiple of 50 (2) x^3 is  [#permalink]

Show Tags

New post 05 Feb 2018, 08:13
1
GMATinsight wrote:
Is Integer x divisible by 25?

(1) \(x^2\) is a multiple of 50
(2) \(x^3\) is a multiple of 625

Source: http://www.GMATinsight.com


If x is an integer, then its square and cube will also be integers.

(1) x^2 is a multiple of 50. Now 50 = 2 * 5^2
This tells us that prime factorisation of x^2 has at least one 2 and at least two 5's.
If x^2 has at least two 5's, then x will have at least one 5. So x will be divisible by 5, but we cannot be sure if it will be divisible by 25.

Eg., if x^2 = 100, then x = 10, not divisible by 25. But if x^2 = 2500, then x = 50, which is divisible by 25.
So not sufficient.


(2) x^3 is a multiple of 625. Now 625 = 5^4
So this tells us that cube of x has at least four 5's. So x also must have '5' in its prime factorisation.
But if x has only one 5 in its prime factorisation, then its cube will have only three 5's, and this given condition will not be satisfied. Case rejected
Only if x has at least two 5's in its prime factorisation, will then its cube have at least six 5's, and then only will its cube be divisible by 625.

This tells us that x must have at least two 5's in its prime factorisation, making it divisible by 25. So sufficient.


Hence B answer
Intern
Intern
avatar
B
Joined: 26 Sep 2017
Posts: 28
CAT Tests
Re: Is x is divisible by 25? (1) x^2 is a multiple of 50 (2) x^3 is  [#permalink]

Show Tags

New post 05 Feb 2018, 08:28
amanvermagmat wrote:
GMATinsight wrote:
Is Integer x divisible by 25?

(1) \(x^2\) is a multiple of 50
(2) \(x^3\) is a multiple of 625

Source: http://www.GMATinsight.com


If x is an integer, then its square and cube will also be integers.

(1) x^2 is a multiple of 50. Now 50 = 2 * 5^2
This tells us that prime factorisation of x^2 has at least one 2 and at least two 5's.
If x^2 has at least two 5's, then x will have at least one 5. So x will be divisible by 5, but we cannot be sure if it will be divisible by 25.

Eg., if x^2 = 100, then x = 10, not divisible by 25. But if x^2 = 2500, then x = 50, which is divisible by 25.
So not sufficient.


(2) x^3 is a multiple of 625. Now 625 = 5^4
So this tells us that cube of x has at least four 5's. So x also must have '5' in its prime factorisation.
But if x has only one 5 in its prime factorisation, then its cube will have only three 5's, and this given condition will not be satisfied. Case rejected
Only if x has at least two 5's in its prime factorisation, will then its cube have at least six 5's, and then only will its cube be divisible by 625.

This tells us that x must have at least two 5's in its prime factorisation, making it divisible by 25. So sufficient.


Hence B answer

Thanks, you're right

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
Re: Is x is divisible by 25? (1) x^2 is a multiple of 50 (2) x^3 is &nbs [#permalink] 05 Feb 2018, 08:28
Display posts from previous: Sort by

Is x is divisible by 25? (1) x^2 is a multiple of 50 (2) x^3 is

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

Events & Promotions

PREV
NEXT


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®.