Last visit was: 17 Jul 2024, 12:30 It is currently 17 Jul 2024, 12:30
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 19 Aug 2009
Posts: 72
Own Kudos [?]: 996 [26]
Given Kudos: 46
Send PM
Most Helpful Reply
User avatar
Intern
Intern
Joined: 27 Oct 2009
Affiliations: CA - India
Posts: 27
Own Kudos [?]: 1307 [10]
Given Kudos: 5
Location: India
Concentration: Finance
Schools:ISB - Hyderabad, NSU - Singapore
Send PM
General Discussion
User avatar
VP
VP
Joined: 29 Aug 2007
Posts: 1015
Own Kudos [?]: 1733 [0]
Given Kudos: 19
Send PM
User avatar
Senior Manager
Senior Manager
Joined: 23 Apr 2010
Posts: 476
Own Kudos [?]: 359 [0]
Given Kudos: 7
Send PM
Re: Numbers 2 [#permalink]
Bunuel, the first part is systematic. The second part is kind of fuzzy:

Quote:
Now, all these numbers ending with 1, when divided by 5 give result ending in XXXX.2


What if instead of five there were a different number.

Is there a more systematic approach to these kind of problems?

Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 94383
Own Kudos [?]: 641746 [0]
Given Kudos: 85693
Send PM
Re: Numbers 2 [#permalink]
Expert Reply
nonameee wrote:
Bunuel, the first part is systematic. The second part is kind of fuzzy:

Quote:
Now, all these numbers ending with 1, when divided by 5 give result ending in XXXX.2


What if instead of five there were a different number.

Is there a more systematic approach to these kind of problems?

Thank you.


Solution above is pretty systematic.

If you are interested in the easiest approach for different numbers then it'll depend on that numbers and answer choices.
User avatar
Manager
Manager
Joined: 12 Oct 2011
Posts: 100
Own Kudos [?]: 763 [0]
Given Kudos: 23
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
Send PM
Re: (3^32)/50 gives remainder and {.} denotes fractional part of [#permalink]
Can anybody explain to me why 1 was divided by 5? If I divide a number that ends with 1 by 50, all kinds of different remainders and therefore digits could result.
Math Expert
Joined: 02 Sep 2009
Posts: 94383
Own Kudos [?]: 641746 [1]
Given Kudos: 85693
Send PM
Re: (3^32)/50 gives remainder and {.} denotes fractional part of [#permalink]
1
Kudos
Expert Reply
BN1989 wrote:
Can anybody explain to me why 1 was divided by 5? If I divide a number that ends with 1 by 50, all kinds of different remainders and therefore digits could result.


That's not true. ANY number with 1 as the units digit when divided by 50 gives 2 as the last digit after decimal point:
1/50=0.02;
21/50=0.42;
1001/50=20.02;
...
Manager
Manager
Joined: 16 Jan 2011
Posts: 72
Own Kudos [?]: 743 [0]
Given Kudos: 15
Send PM
Re: (3^32)/50 gives remainder and {.} denotes fractional part of [#permalink]
for such kind of problems how to realize from what power of an integer should i start looking for the pattern?
since, if start listing the powers of three from 0, ill get the unit digit of 3^32=...7
3^0=1
3^1=3
3^2=9
3^3=27
...
suppose its possible to face with a problem when it'll be crucial to know this
Math Expert
Joined: 02 Sep 2009
Posts: 94383
Own Kudos [?]: 641746 [0]
Given Kudos: 85693
Send PM
Re: (3^32)/50 gives remainder and {.} denotes fractional part of [#permalink]
Expert Reply
Galiya wrote:
for such kind of problems how to realize from what power of an integer should i start looking for the pattern?
since, if start listing the powers of three from 0, ill get the unit digit of 3^32=...7
3^0=1
3^1=3
3^2=9
3^3=27
...
suppose its possible to face with a problem when it'll be crucial to know this


When looking for a pattern of the last digit of a^n ALWAYS start from n=1 (otherwise if you start from n=0 then all integers will have 1 as the first number in pattern).

For more check: math-number-theory-88376.html
avatar
Intern
Intern
Joined: 23 May 2012
Posts: 25
Own Kudos [?]: 88 [0]
Given Kudos: 11
Send PM
Re: (3^32)/50 gives remainder and {.} denotes fractional part of [#permalink]
virtualanimosity wrote:
(3^32)/50 gives remainder and {.} denotes fractional part of that.The fractional part is of the form (0.bx). The value of x could be
1. 2
2. 4
3. 6


\(= 3^{32}\)

\(= (3^{4})^{8}\)

\(3^{4} =81 =50 +31\)

\(= (M50 + 31)^{8}\)

\(= 31^{8}\)

Last digit 1

For division by 10 & multiple thereof ... find the last digit

So remainder is 1/50

i.e 0.02 --- 0.bx

x=2

Option 1
User avatar
Tutor
Joined: 20 Aug 2015
Posts: 349
Own Kudos [?]: 1408 [1]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Send PM
(3^32)/50 gives remainder and {.} denotes fractional part of [#permalink]
1
Kudos
Expert Reply
virtualanimosity wrote:
(3^32)/50 gives remainder and {.} denotes fractional part of that.The fractional part is of the form (0.bx). The value of x could be
1. 2
2. 4
3. 6


This question tests your knowledge about cyclicity of the numbers.
Cyclicity: The power after which the units digit of a number repeats itself

Eg:\(2^1\) = 2, \(2^2\)= 4, \(2^3\) = 8, \(2^4\) = 16,\(2^5\) = 32
The units digit repeats after 4 powers hence cyclicity = 4
2, 3, 7, 8: Cyclicity 4
5, 6: Cyclicity 1
4,9: Cyclicity 2


\(3^{32}\) will end with the units digit 1
\(3^{32}\) will be of the form ----1
Therefore \(3^{32}\)/50 will be of the form ----.b2
Hence x = 2
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33999
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: (3^32)/50 gives remainder and {.} denotes fractional part of [#permalink]
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.
GMAT Club Bot
Re: (3^32)/50 gives remainder and {.} denotes fractional part of [#permalink]
Moderator:
Math Expert
94383 posts