NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 21:44 It is currently 26 Apr 2024, 21:44
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

10^25 – 560 is divisible by all of the following EXCEPT:

SORT BY:
Date
Kudos
   1   2 
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
jlgdr
VP
VP
Joined: 06 Sep 2013
Posts: 1345
Own Kudos [?]: 2391 [0]
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Send PM
GMAT ToolKit User
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   08 Jan 2014, 15:29
enigma123 wrote:
10^25 – 560 is divisible by all of the following EXCEPT:

A.11
B. 8
C. 5
D. 4
E. 3

Guys any idea what concept has been Tested over here and what will be the answer?

I have started doing it this way but got stuck. So can someone please help?

I have started from

10^5 - 560 = 99,440 i.e. it has two 9s followed by 440.
.
.
10^10 - 560 = 99,99,440 ------------------------------> Am I doing it right this way?


You will have 9X + 8

Since 8 is not divisible by 3 then answer is E

Cheers!
J :)
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7208 [0]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   25 Mar 2014, 00:43
One more method to check divisibility by 11

Add / substract 1 to the equation

\(10^{25} + 1 - 560 - 1\)

\(= 10^{25} + 1 - (560 + 1)\)

\(= (10^{25} + 1) - 561\)

Any odd power of 10 added to 1 is always divisible by 11

\(10^1 + 1 = 11\)

\(10^3 + 1 = 1001\)

\(10^5 + 1 = 100001\)

In the same way, \(10^{25} + 1\) is divisible by 11

Also 561 is divisible by 11; so the possibility of 11 is ruled out

Rest all options can be worked out in similar ways given in the earlier posts
avatar
B
Argo
Manager
Manager
Joined: 03 Jul 2016
Posts: 51
Own Kudos [?]: 46 [0]
Given Kudos: 166
Send PM
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   04 Aug 2016, 22:04
Here is my approach :

10^25 - 560 --> 5x2^4(10^21X125 - 7) . We can rule out B, C, D options.

5x2^4(10^21X125 - 7) = 124999..3 is no way divisible by 3 but can be divisible by 11.

So 'E'
avatar
B
mikeyg51
Intern
Intern
Joined: 07 Jun 2016
Posts: 24
Own Kudos [?]: 8 [0]
Given Kudos: 106
Schools: Ross Weekend"19 UNC Kenan-Flagler Booth PT '19 Kelley Online MBA"19
GPA: 3.8
WE:Supply Chain Management (Manufacturing)
Send PM
GMAT ToolKit User
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   06 Oct 2016, 18:36
Bunuel wrote:
enigma123 wrote:
10^25 – 560 is divisible by all of the following EXCEPT:
a)11
b)8
c)5
d)4
e) 3

Guys any idea what concept has been Tested over here and what will be the answer?

I have started doing it this way but got stuck. So can someone please help?

I have started from

10^5 - 560 = 99,440 i.e. it has two 9s followed by 440.
.
.
10^10 - 560 = 99,99,440 ------------------------------> Am I doing it right this way?


Yes, you were on a right track.

10^(25) is a 26 digit number: 1 with 25 zeros. 10^(25)-560 will be 25 digit number: 22 9's and 440 in the end: 9,999,999,999,999,999,999,999,440 (you don't really need to write down the number to get the final answer). From this point you can spot that all 9's add up to some multiple of 3 (naturally) and 440 add up to 8 which is not a multiple of 3. So, the sum of all the digits is not divisible by 3 which means that the number itself is not divisible by 3.

Answer: E.

You can also quickly spot that the given number is definitely divisible:
By 2 as the last digit is even;
By 4 as the last two digits are divisible by 4;
By 8 as the last three digits are divisible by 8;
By 11 as 11 99's as well as 440 have no reminder upon division by 11 (or by applying divisibility by 11 rule).

Check Divisibility Rules chapter of Number Theory: math-number-theory-88376.html


Thank you Bunuel. I used this tactic after seeing you reference it in other posts. I learned this before but had not committed it to memory until now. Great explanation as always
User avatar
S
SchruteDwight
Manager
Manager
Joined: 03 Sep 2018
Posts: 178
Own Kudos [?]: 90 [0]
Given Kudos: 924
Location: Netherlands
Schools: HEC MiM "22 (S) LBS MiM "21 (A)
GPA: 4
Send PM
Reviews Badge
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   14 Jan 2019, 04:25
I am wondering whether the following test for divisibility by 11 is valid:

\((11-1)^{25}-560\) \(\implies\) \(Remainders: -1-10=-11\) \(\implies\) \(Remainder_{total} = 0\)

I am unsure whether from \((11-1)^{25}\) it follows that the remainder is \(-1\) as for instance the remainder of \((11-1)^2\) is \(-10\). So how do I know that the remainder is only -1 when the exponent of \((11-1)^{25}\) is odd?
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8020
Own Kudos [?]: 4098 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   10 Feb 2020, 00:40
value of 10^25 has 25 zeroes & 1 one ; last three digits would be 440
440 factors 11*4*5*2 ;
not possible value ; 3
IMO E


enigma123 wrote:
10^25 – 560 is divisible by all of the following EXCEPT:

A. 11
B. 8
C. 5
D. 4
E. 3


Show Spoiler
Guys any idea what concept has been Tested over here and what will be the answer?

I have started doing it this way but got stuck. So can someone please help?

I have started from

10^5 - 560 = 99,440 i.e. it has two 9s followed by 440.
.
.
10^10 - 560 = 99,99,440 ------------------------------> Am I doing it right this way?
avatar
B
bluefalkin
Intern
Intern
Joined: 21 Feb 2018
Posts: 11
Own Kudos [?]: 4 [0]
Given Kudos: 16
Send PM
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   27 Mar 2020, 01:59
This was my approach.

10^25 will be a huge number with 100..000 we know if we subtract the 560 the number will become 9999....460. We have to focus on the 460 and its divisors.

I took 460 and performed a prime factorization, this results in the factors of 11, 5, 2, 2 , 2 (the building blocks to make 460).

I then took to prime factors of the answer choices.

A) 11 - prime factor is 11 and 11 is a prime factor for 460, therefore out.
B) 8 - 2, 2, 2 - 460 has three prime factors of 2, therefore out
C) 5 - this is also a prime factor of 460, therefore out
D) 4 - 2, 2 - 460 contains at least two prime factors of 2 therefore out
E) 3 - is not a prime factor of 460, therefore, cannot be a divisor

Please let me know if there are any errors using this approach.
User avatar
G
Ravixxx
Manager
Manager
Joined: 24 Feb 2020
Posts: 119
Own Kudos [?]: 538 [0]
Given Kudos: 118
Location: Italy
WE:Analyst (Investment Banking)
Send PM
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   07 Apr 2020, 00:23
Fast Approach:
10^25 – 560 is divisible by all of the following EXCEPT:

A. 11
B. 8
C. 5
D. 4
E. 3


We know that 10^25 finish with zero.

Suppose 1000 - 560 = 440.

440 is an even number, so we can eliminate all the even answer choices: B and D.
440 is also a multiple of 5, so we can eliminate C.

We remain with A (11) and E (3).
440 can be expressed as: 11*40, thus 440 is divisible by 11.

We remain with only 3.

Answer E.
User avatar
S
gurmukh
Senior Manager
Senior Manager
Joined: 18 Dec 2017
Posts: 270
Own Kudos [?]: 203 [0]
Given Kudos: 20
Send PM
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   07 Apr 2020, 01:16
10^25 = 3a +1
Where a is the natural numbers
560 =3b +2
Where b is the natural number
10^25- 560
3a +1- 3b - 2
3(a-b) -1
Not divisible by 3
Option E is the answer

Posted from my mobile device
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8020
Own Kudos [?]: 4098 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   15 Sep 2020, 05:21
10^25 – 560
will give us 22*9 & 440 in end
given is even so options b,c,d can be eliminated
among a & e ; 22 times 9 and 440 would be divisble by 11
left with 3 which does not divide the value
option E


enigma123 wrote:
10^25 – 560 is divisible by all of the following EXCEPT:

A. 11
B. 8
C. 5
D. 4
E. 3


Show Spoiler
Guys any idea what concept has been Tested over here and what will be the answer?

I have started doing it this way but got stuck. So can someone please help?

I have started from

10^5 - 560 = 99,440 i.e. it has two 9s followed by 440.
.
.
10^10 - 560 = 99,99,440 ------------------------------> Am I doing it right this way?
User avatar
P
Nipungupta9081
School Moderator - INSEAD Masters
Joined: 07 Jan 2020
Posts: 510
Own Kudos [?]: 265 [0]
Given Kudos: 193
Location: India
GPA: 4
WE:Analyst (Accounting)
Send PM
Re: 10^25 – 560 is divisible by all of the following EXCEPT: [#permalink] New post   29 Oct 2020, 13:08
enigma123 wrote:
10^25 – 560 is divisible by all of the following EXCEPT:

A. 11
B. 8
C. 5
D. 4
E. 3



My Approach is Kinda Different.

Rather then multiplying 10^25 we can just take 1000 - 560 which will yield = 440

Which means it is divisible by all numbers except 3

Answer = E
User avatar
B
lotif
Intern
Intern
Joined: 16 Jan 2019
Posts: 20
Own Kudos [?]: 3 [0]
Given Kudos: 27
Send PM
Reviews Badge
Re: 10^25 560 is divisible by all of the following EXCEPT: [#permalink] New post   20 May 2023, 15:17
Bunuel wrote:
enigma123 wrote:
10^25 – 560 is divisible by all of the following EXCEPT:
a)11
b)8
c)5
d)4
e) 3

Guys any idea what concept has been Tested over here and what will be the answer?

I have started doing it this way but got stuck. So can someone please help?

I have started from

10^5 - 560 = 99,440 i.e. it has two 9s followed by 440.
.
.
10^10 - 560 = 99,99,440 ------------------------------> Am I doing it right this way?


Yes, you were on a right track.

10^(25) is a 26 digit number: 1 with 25 zeros. 10^(25)-560 will be 25 digit number: 22 9's and 440 in the end: 9,999,999,999,999,999,999,999,440 (you don't really need to write down the number to get the final answer). From this point you can spot that all 9's add up to some multiple of 3 (naturally) and 440 add up to 8 which is not a multiple of 3. So, the sum of all the digits is not divisible by 3 which means that the number itself is not divisible by 3.

Answer: E.

You can also quickly spot that the given number is definitely divisible:
By 2 as the last digit is even;
By 4 as the last two digits are divisible by 4;
By 8 as the last three digits are divisible by 8;
By 11 as 11 99's as well as 440 have no reminder upon division by 11 (or by applying divisibility by 11 rule).

Check Divisibility Rules chapter of Number Theory: https://gmatclub.com/forum/math-number- ... 88376.html


Hi

Why does the bit above in bold show that the number has no remainder upon division by 11?
Thanks
GMAT Club Bot
gmatclubot
Re: 10^25 560 is divisible by all of the following EXCEPT: [#permalink]
20 May 2023, 15:17
   1   2 
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions