It is currently 24 Mar 2018, 16:45

### 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.

Author Message
TAGS:

### Hide Tags

Intern
Joined: 25 Jun 2017
Posts: 2
Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

08 Jul 2017, 17:53
great article. A suggestion - if you could add some examples of questions for each principle, it would be great for retention of the material. Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 44423
Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

09 Jul 2017, 02:54
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
Intern
Joined: 29 May 2017
Posts: 9
Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

21 Oct 2017, 02:06
ctrlaltdel wrote:
If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is divided by t?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45

Ans: Using the technique: remainder = 0.12*t => the answer is multiple of 12. but none of the options match...did i miss something or is my understanding wrong ops :stupid

I tried with below approach in all type of above Q and i solved it each time within secs.
Let's see .

given : s/t = 64.12
consider only 0.12
so 0.12=12/100 = 3/25. Now what we have to do is to find the multiple of 3 in given Ans. There will be one correct ans which will satisfy the Q. Hence , here only 45 is the multiple of 3 ...so that's the ans.
Manager
Joined: 06 Sep 2016
Posts: 141
Location: Italy
Schools: EDHEC (A)
GMAT 1: 650 Q42 V37
GPA: 3.2
WE: General Management (Human Resources)
Re: Compilation of tips and tricks to deal with remainders. [#permalink]

### Show Tags

26 Jan 2018, 08:14
sriharimurthy wrote:
Hi guys,
This is in conjunction with another post which has questions dealing with remainders (http://gmatclub.com/forum/collection-of ... 74776.html). I'm just trying to put together a list of tips and tricks which we can use to solve these kind of problems with greater accuracy and speed. Please feel free to comment and make suggestions. Hopefully we can add onto this list and cover all sorts of strategies that would help us deal with remainders!
Cheers.

1) Take your time with these points. Some of them might be a little difficult to follow in the first reading, but don't give up. The concepts are fairly simple.
2) These tips if mastered will be extremely valuable in the GMAT to help solve a variety of questions not limited specifically to remainders. I have been using them for quite a while now and they have not only helped me improve my accuracy but also my speed.
3) If you have any doubts, please do not hesitate to ask (no matter how stupid you might think them to be!). If you do not ask, you will never learn.
4) Lastly, have fun while trying to understand these tips and tricks as that, according to me, is the best possible way to learn.

All the best!

-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-
NOTE: Where ever you see R of 'x' it just stands for Remainder of x.

1) The possible remainders when a number is divided by ‘n’ can range from 0 to (n-1).
Eg. If n=10, possible remainders are 0,1,2,3,4,5,6,7,8 and 9.

2) If a number is divided by 10, its remainder is the last digit of that number. If it is divided by 100 then the remainder is the last two digits and so on.
This is good for questions such as : ' What is the last digit of.....' or ' What are the last two digits of.....' .

3) If a number leaves a remainder ‘r’ (the number is the divisor), 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 a number when divided by 21 is 5, then the remainder of that same number when divided by 7 (which is a factor of 21) will also be 5.

If the value of ‘r’ is greater than the value of the factor, then we have to take the remainder of ‘r’ divided by the factor to get the remainder.
Eg. If remainder of a number when divided by 21 is 5, then the remainder of that same number when divided by 3 (which is a factor of 21) will be remainder of 5/3, which is 2.

4) 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 $$n^x$$.

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.

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 : http://gmatclub.com/forum/numbers-86325.html]

7) If you take the decimal portion of the resulting number when you divide by "n", and multiply it to "n", you will get the remainder. [Special thanks to h2polo for this one]

Note: Converse is also true. If you take the remainder of a number when divided by 'n', and divide it by 'n', it will give us the remainder in decimal format.

Eg. $$\frac{8}{5} = 1.6$$

In this case, $$0.6 * 5 = 3$$

Therefore, the remainder is $$3$$.

This is important to understand for problems like the one below:

If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is divided by t?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45

OA :
[Reveal] Spoiler:
E

sriharimurthy In the points 5 and 6 what means the simbol ROF?
Re: Compilation of tips and tricks to deal with remainders.   [#permalink] 26 Jan 2018, 08:14

Go to page   Previous    1   2   3   4   5   6   [ 104 posts ]

Display posts from previous: Sort by