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

It is currently 14 Aug 2018, 16:23

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

Questions about operations on remainders

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

Hide Tags

Intern
Intern
avatar
B
Joined: 07 Sep 2017
Posts: 30
Questions about operations on remainders  [#permalink]

Show Tags

New post 08 Dec 2017, 02:57
I was just fooling around with remainders and had a query.

Suppose I want to find the remainder when \(7^{30}\) is divided by 100. I know I can solve this using cyclicity, but why don't I get the right answer using the following method?

I can express \((7^{30})/100\) as \([(7^{15})/10]^{2}\). Now why can't I find the remainder of \((7^{15})/10\) and simply square it to obtain the desired answer?

(Answer is 49)
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6509
Re: Questions about operations on remainders  [#permalink]

Show Tags

New post 08 Dec 2017, 07:13
1
dejavu619 wrote:
I was just fooling around with remainders and had a query.

Suppose I want to find the remainder when \(7^{30}\) is divided by 100. I know I can solve this using cyclicity, but why don't I get the right answer using the following method?

I can express \((7^{30})/100\) as \([(7^{15})/10]^{2}\). Now why can't I find the remainder of \((7^{15})/10\) and simply square it to obtain the desired answer?

(Answer is 49)



hi...

by this method you are NOT getting the remainder because you are changing the DIVISOR from 100 to 10

if you were to find the remainder when 10 is divisor it is OK..
\(\frac{7^{30}}{10}=\frac{(7^{15})^2}{10}\)
Now you find remainder of 7^15 and the square it..

A very small example is..
remainder of 49 when divided by 36.. ans 49-36=13
but if you look at it as SQUARE, 7^2 divided by 6^2..
\(\frac{7^2}{6^2}=(\frac{7}{6})^2\) so 1^2=1.. NO
_________________

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

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 1887
Re: Questions about operations on remainders  [#permalink]

Show Tags

New post 30 Dec 2017, 01:03
dejavu619 wrote:
I was just fooling around with remainders and had a query.

Suppose I want to find the remainder when \(7^{30}\) is divided by 100. I know I can solve this using cyclicity, but why don't I get the right answer using the following method?

I can express \((7^{30})/100\) as \([(7^{15})/10]^{2}\). Now why can't I find the remainder of \((7^{15})/10\) and simply square it to obtain the desired answer?

(Answer is 49)



We know that any number can be written in terms of its Divisor, Quotient and Remainder.

Thus, we can write \(N = QD + R\) ......(i)

According to your logic, if the remainder when N divided by D is R, then the remainder when \(N^2\) is divided by \(D^2\) should be \(R^2\).

If you square equation (i), you will be able to see it clearly that your assumption is not correct. :)

\(N^2 = (QD + R)^2\)

\(N^2 = Q^2* D^2 + R^2 + 2 * Q * R * D\)

Keep in mind that you are dividing \(N^2\) by \(D^2\) now..

\(Q^2 * D^2\) is diivisble by \(D^2\).

But what about \(2*Q * R * D\), do we know if this is perfectly divisble by \(D^2\)?

No, we don't! :)

Hence, it is wrong to make such assumption that if \(N/D\) give \(R\) as remainder then \(N^2/D^2\) will give \(R^2\) as the remainder or vice versa.



Regards,
Saquib
e-GMAT
Quant Expert
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: Questions about operations on remainders &nbs [#permalink] 30 Dec 2017, 01:03
Display posts from previous: Sort by

Questions about operations on remainders

  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®.