Compilation of tips and tricks to deal with remainders. : GMAT Quantitative Section - Page 2
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 20 Jan 2017, 08:45

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Compilation of tips and tricks to deal with remainders.

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

### Hide Tags

Manager
Joined: 23 Oct 2009
Posts: 84
Location: New Delhi, India
Schools: Chicago Booth, Harvard, LBS, INSEAD, Columbia
Followers: 7

Kudos [?]: 16 [0], given: 76

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

08 Dec 2009, 03:23
Thanks a lot for this thread!!! Remainder questions have been a bit of a problem for me...and this really helps!!!
_________________

Read about my GMAT prep at http://gmatting.blogspot.com/
1st Feb '11 -- Actual GMAT : 730 (Q48 V42) AWA 6.0

My Practice GMAT Scores
29th Jan '11 -- GMATPrep#2 : 700 (Q47 V38)
23rd Jan '11 -- MGMAT Practice Test #3 : 670 (Q45 V36)
19th Jan '11 -- GMATPrep#1 v.1 : 710 (Q49 V37)
15th Jan '11 -- GMATPrep#1 : 720 (Q47 V42)
11th Jan '11 -- MGMAT Practice Test #2 : 740 (Q47 V44)
6th Jan '11 -- Kaplan#2 : 620 (Q40 V35)
28th Dec '10 -- PowerPrep#1 : 670 (Q47 V35)
30th Oct '10 -- MGMAT Practice Test #1 : 660 (Q45 V35)
12th Sept '10 -- Kaplan Free Test : 610 (Q39 V37)
6th Dec '09 -- PR CAT #1 : 650 (Q44 V37)
25th Oct '09 -- GMATPrep#1 : 620 (Q44 V34)

If you feel like you're under control, you're just not going fast enough.
A goal without a plan is just a wish.
You can go higher, you can go deeper, there are no boundaries above or beneath you.

Intern
Joined: 10 Dec 2009
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

10 Dec 2009, 09:34
Wondering if it is a good way to solve it as follows:

.12 = 12/100 = 3/25 implies that the remainder is 3 or multiple of 3.

Manager
Joined: 08 Jul 2009
Posts: 171
Followers: 0

Kudos [?]: 25 [0], given: 26

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

10 Dec 2009, 15:06
brownybuddy wrote:
Wondering if it is a good way to solve it as follows:

.12 = 12/100 = 3/25 implies that the remainder is 3 or multiple of 3.

I tested it with some numbers. (8/5, 9/4, 57/12, 57/15, 57/20) They are work using the way you described. I don't know how to prove it mathematically though. Does anyone know? This is a smart way if it works for all numbers!
Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
Followers: 103

Kudos [?]: 1281 [0], given: 18

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

10 Dec 2009, 23:24
wilbase wrote:
sriharimurthy wrote:

Eg. $$R of \frac{(23)*(27)}{25} = R of \frac{(-2)*(2)}{24} = -4.$$ Now, since it is negative, we have to add it to 25.$$R = 25 + (-4) = 21$$

Is the "24" on the second part of the equation suppose to be "25"?

Yes. It is supposed to be 25. Thanks for spotting that. I have edited it.

brownybuddy wrote:
Wondering if it is a good way to solve it as follows:

.12 = 12/100 = 3/25 implies that the remainder is 3 or multiple of 3.

Yes. It follows from property number 7.

Since we are asked to find the remainder when 's' is divided by 't' and we are given the resulting number, we can write an equation as follows :

Remainder = (Decimal portion of the resulting number) * (Number we are dividing by)

Remainder = 0.12 * t

R = $$\frac{12}{100}*t$$ = $$\frac{3}{25}*t$$

So as you can see, the remainder 'R' must be a multiple of '3' provided 't' is an integer.

Since we know that 't' is an integer, we can safely conclude that 'R' is a multiple of '3'.

Note : In cases of remainder problems, even if 't' is not an integer it can be made into an integer. Eg. Remainder of 6/2.5 will be the same as Remainder of 12/5.
_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!
1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html

Manager
Joined: 08 Jul 2009
Posts: 171
Followers: 0

Kudos [?]: 25 [0], given: 26

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

11 Dec 2009, 09:36
Oh, right, property #7. That makes sense to me now. Thanks for the reply.
Intern
Joined: 21 Nov 2009
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

12 Dec 2009, 07:04
sry, i din get a chance to luk thru all the tips... but the 1 problem on remainder posted above is very interesting n helpful... thanks for the post.
Intern
Joined: 10 Dec 2009
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

13 Dec 2009, 03:14
s = Numerator
t = Denominator
q = Quotient (>= 0)
r = Remainder

where,

s/t = q + r/t

In 64.12, q = 64, so

r/t = .12 = 12/100 = 3/25

where 25 is the least possible value of 't' and 1603 is the least possible value of 's'. The other possible values of 't' will include 25, 50, 75 and so on (i.e. multiple of 25). The values of 'r' and 's' will also change accordingly.
Intern
Affiliations: IEEE, PMI, MIEEE, PMP, New Nigeria Club
Joined: 08 Dec 2009
Posts: 5
Location: Lagos , Nigeria
Schools: Wharton, Kellogg,NYU STERN, Jones, Simon
Followers: 0

Kudos [?]: 1 [0], given: 7

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

19 Dec 2009, 01:17
Hi ,

I am new on this forum , and i will tell you that what i have gained reading all the posts in the various sections have been mind blowing .

I wish to study indepth before i sit for my GMAT. I am quite ambitious with the kind of score i desire and i think you guys are the best in terms of detailing the requirements .

Please kindly explain the 3rd to 5th Rule on the remainder lecture ... i cant seem to grasp the rules!!

Thank you

Easy
_________________

Easy does it , an extra effort does not hurt...

Manager
Status: Applying Now
Joined: 21 Nov 2009
Posts: 63
WE: Project Management (Manufacturing)
Followers: 3

Kudos [?]: 154 [0], given: 3

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

21 Dec 2009, 02:18
Property 3 says that

Quote:
3) If a number has a remainder of ‘r’, all its factors will have the same remainder ‘r’ provided the value of ‘r’ is less than the value of the factor.
Eg. If remainder of 21 is 5, then remainder of 7 (which is a factor of 21) will also be 5.

But if we see 21/5 remainder is 1
7 is a factor of 21
7/5 and the remainder is 2.

Why the contradiction ??
_________________

If you like my post, consider giving me a kudos. THANKS!

Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
Followers: 103

Kudos [?]: 1281 [0], given: 18

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

21 Dec 2009, 03:56
msunny wrote:
Property 3 says that

Quote:
3) If a number has a remainder of ‘r’, all its factors will have the same remainder ‘r’ provided the value of ‘r’ is less than the value of the factor.
Eg. If remainder of 21 is 5, then remainder of 7 (which is a factor of 21) will also be 5.

But if we see 21/5 remainder is 1
7 is a factor of 21
7/5 and the remainder is 2.

Why the contradiction ??

Hi,

To make this example more clear : If any number when divided by 21 leaves a remainder of 5, then that number when divided by any factor of 21 will also leave a remainder of 5 provided the remainder is less than the factor.

Eg. R of 26/21 = 5

Factors of 21 are 3 and 7

Since 7 is greater than 5, R of 26/7 = 5

Since 3 is less than 5, R of 26/3 = R of 5/3 = 2

Hope this makes it clear.

I think I will edit the main post to make this point less confusing.

Cheers.
_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!
1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html

Manager
Status: Applying Now
Joined: 21 Nov 2009
Posts: 63
WE: Project Management (Manufacturing)
Followers: 3

Kudos [?]: 154 [0], given: 3

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

21 Dec 2009, 04:08
Oh ok. Thanks so much for the explanation.
21 is the divisor.
_________________

If you like my post, consider giving me a kudos. THANKS!

Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
Followers: 103

Kudos [?]: 1281 [0], given: 18

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

21 Dec 2009, 04:17
Hi ,

I am new on this forum , and i will tell you that what i have gained reading all the posts in the various sections have been mind blowing .

I wish to study indepth before i sit for my GMAT. I am quite ambitious with the kind of score i desire and i think you guys are the best in terms of detailing the requirements .

Please kindly explain the 3rd to 5th Rule on the remainder lecture ... i cant seem to grasp the rules!!

Thank you

Easy

Hi,

3rd Rule : I have explained the 3rd rule in the above post.

4th Rule : The cycle of powers is useful to know because it tells us the only possible values that the units place can hold for any particular number when it is raised to an integer power.

Go through the following example to see the usefulness of this rule :

Quote:
If n and m are positive integers, what is the remainder when 3^(4n + 2 + m) is divided by 10 ?
(1) n = 2
(2) m = 1

The Concept tested here is cycles of powers of 3.

The cycles of powers of 3 are : 3,9,7,1

St I) n = 2. This makes 3^(4*2 +2 + m) = 3^(10+m). we do not know m and hence cannot figure out the unit digit.

St II) m=1 . This makes 3^(4*n +2 + 1).
4n can be 4,8,12,16...
3^(4*n +2 + 1) will be 3^7,3^11, 3^15,3^19 ..... in each case the unit digit will be 7. SUFF
Hence B

5th Rule : Again for this rule, the best way to understand it is to work through a couple of questions (numbers-86325.html). Go through my solutions for the two problems in the post I have linked and see how rules 5 and 6 relate to them.

It might take a while for these concepts to get cemented but have a little patience and you will be rewarded.

If you have any specific doubts you would like me to address then please let me know.

Cheers.
_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!
1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html

Intern
Joined: 23 Dec 2009
Posts: 49
Schools: HBS 2+2
WE 1: Consulting
WE 2: Investment Management
Followers: 1

Kudos [?]: 40 [0], given: 7

Practice these tricks! [#permalink]

### Show Tags

30 Dec 2009, 02:08
Practice sri's wonderful tips and tricks: 4GMAT Home >> GMAT Test Prep Questions >> Number Systems...

(Can't post hyperlinks yet, sorry!)

I was wondering if someone could show me how to do this problem (found at the said site) quicker than my method (detailed below):

8. What is the remainder when the product of 1044, 1047, 1050, and 1053 is divided by 33?

I used sri's trick and found that 1056 is a multiple of 33. This resulted in remainders of (-12)(-9)(-6)(-3), respectively.
Multiplied together, you get 1944. The remainder of 1944, when divided by 33, is 30, the correct answer.

Is there a quicker way than multiplying (-12)(-9)(-6)(-3) out?

_________________

My GMAT quest...

...over!

Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
Followers: 103

Kudos [?]: 1281 [1] , given: 18

Re: Practice these tricks! [#permalink]

### Show Tags

30 Dec 2009, 08:12
1
KUDOS
R2I4D wrote:
Practice sri's wonderful tips and tricks: 4GMAT Home >> GMAT Test Prep Questions >> Number Systems...

(Can't post hyperlinks yet, sorry!)

I was wondering if someone could show me how to do this problem (found at the said site) quicker than my method (detailed below):

8. What is the remainder when the product of 1044, 1047, 1050, and 1053 is divided by 33?

I used sri's trick and found that 1056 is a multiple of 33. This resulted in remainders of (-12)(-9)(-6)(-3), respectively.
Multiplied together, you get 1944. The remainder of 1944, when divided by 33, is 30, the correct answer.

Is there a quicker way than multiplying (-12)(-9)(-6)(-3) out?

Hi,

Im glad you found these tips helpful. There is in fact a quicker way to solve it.

R of $$\frac{(-12)*(-3)*(-9)*(-6)}{33}$$ = R of $$\frac{(36)*(54)}{33}$$ = R of $$\frac{(3)*(21)}{33}$$ = R of $$\frac{63}{33}$$ = $$30$$

As you can see, you don't really need to do any complex multiplications. Just multiply numbers is groups that yield a number closest to the denominator. That way you can keep simplifying to smaller numbers and avoid big calculations.

Let me know if anything needs to be clarified.

Cheers.
_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!
1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html

Senior Manager
Joined: 22 Dec 2009
Posts: 362
Followers: 11

Kudos [?]: 375 [0], given: 47

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

31 Jan 2010, 01:56
sriharimurthy wrote:
Cycle of powers : This is used to find the remainder of $$n^x$$, when divided by 10, as it helps us in figuring out the last digit of $$n^x$$.[/size]

The cycle of powers for numbers from 2 to 10 is given below:

2: 2, 4, 8, 6 → all $$2^{4x}$$ will have the same last digit.

3: 3, 9, 7, 1 → all $$3^{4x}$$ will have the same last digit.

4: 4, 6 → all $$4^{2x}$$ will have the same last digit.

5: 5 → all $$5^x$$ will have the same last digit.

6: 6 → all $$6^x$$ will have the same last digit.

7: 7, 9, 3, 1 → all $$7^{4x}$$ will have the same last digit.

8: 8, 4, 2, 6 → all $$8^{4x}$$ will have the same last digit.

9: 9, 1 → all $$9^{2x}$$ will have the same last digit.

10: 0 → all $$10^x$$ will have the same last digit.

Hi sriharimurthy...... Thanks a lot for this post...its outstanding..... Kudos x 10 for this

I have a few questions on the cycle of powers part... didnt get this too well...

2: 2, 4, 8, 6 → all $$2^{4x}$$ will have the same last digit.
Why do you show this as $$2^{4x}$$... what is $$4x$$ all about.... ?
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Senior Manager
Joined: 22 Dec 2009
Posts: 362
Followers: 11

Kudos [?]: 375 [0], given: 47

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

31 Jan 2010, 03:42
sriharimurthy wrote:

5) Many seemingly difficult remainder problems can be simplified using the following formula :
$$R of \frac{x*y}{n} = R of \frac{(R of \frac{x}{n})*(R of \frac{y}{n})}{n}$$

Eg. $$R of \frac{20*27}{25} = R of \frac{(R of \frac{20}{25})*(R of \frac{27}{25})}{25} = R of \frac{(20)*(2)}{25} = R of \frac{40}{25} = 15$$

Eg. $$R of \frac{225}{13} = R of \frac{(15)*(15)}{13} = R of {(2)*(2)}{13} = R of \frac{4}{13} = 4$$

6) $$R of \frac{x*y}{n}$$ , can sometimes be easier calculated if we take it as $$R of \frac{(R of \frac{(x-n)}{n})*(R of \frac{(y-n)}{n})}{n}$$
Especially when x and y are both just slightly less than n. This can be easier understood with an example:

Eg. $$R of \frac{(19)*(21)}{25} = R of \frac{(-6)*(-4)}{25} = 24$$

NOTE: Incase the answer comes negative, (if x is less than n but y is greater than n) then we have to simply add the remainder to n.

Eg. $$R of \frac{(23)*(27)}{25} = R of \frac{(-2)*(2)}{25} = -4.$$ Now, since it is negative, we have to add it to 25.$$R = 25 + (-4) = 21$$

[Note: Go here to practice two good problems where you can use some of these concepts explained : numbers-86325.html]

I have a question here.....

You explained the remainder formula as :
Quote:
size=130]6) $$R of \frac{x*y}{n}$$ , can sometimes be easier calculated if we take it as $$R of \frac{(R of \frac{(x-n)}{n})*(R of \frac{(y-n)}{n})}{n}$$ [/size]
Especially when x and y are both just slightly less than n.

And in you example:
Quote:
Eg. $$R of \frac{(19)*(21)}{25} = R of \frac{(-6)*(-4)}{25} = 24$$

shouldn't this be Eg. $$R of \frac{(19)*(21)}{25} = R of \frac{(R of \frac{(19-25)}{25})*R of \frac{(21-25)}{25}}{25} = R of \frac{(R of \frac{(-6)}{25})*R of \frac{(-4)}{25}}{25}$$????

After this I am upside down
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Intern
Joined: 15 Jan 2010
Posts: 1
Schools: HBS,LSB stanford, wharton,MIT
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

21 Feb 2010, 09:18
great sri

this is really helpful
Intern
Joined: 14 Dec 2009
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

04 Mar 2010, 11:49
Excellent...collection..Kudos to you for assembling this.
Manager
Joined: 20 Nov 2009
Posts: 167
Followers: 8

Kudos [?]: 203 [0], given: 64

Which of the following must be a divisor of a? [#permalink]

### Show Tags

02 Apr 2010, 01:29
Great post. Was very useful. Thanks.
_________________

But there’s something in me that just keeps going on. I think it has something to do with tomorrow, that there is always one, and that everything can change when it comes.
http://aimingformba.blogspot.com

Intern
Joined: 03 Apr 2010
Posts: 6
Followers: 2

Kudos [?]: 0 [0], given: 10

Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

03 Apr 2010, 13:08
Hi
Please can u explain me more about 4, 5 and 6. I don't understand when u say cycle of powers and how to apply the formulas in 5 and 6.

Thanks a lot.

Jonyjo
Re: Compilation of tips and tricks to deal with remainders.   [#permalink] 03 Apr 2010, 13:08

Go to page   Previous    1   2   3   4   5    Next  [ 95 posts ]

Similar topics Replies Last post
Similar
Topics:
1 A few tricks to solve remainder problems fast. 2 26 Jan 2016, 02:18
63 Tips and Tricks: Mixtures 6 30 Apr 2013, 13:45
169 Tips and Tricks: Inequalities 28 14 Apr 2013, 08:20
2 The lucky number trick: Remainder when divided by 9 2 08 May 2011, 02:31
Math formulas, tips/tricks 2 06 Feb 2008, 20:46
Display posts from previous: Sort by

# Compilation of tips and tricks to deal with remainders.

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.