Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 30 Aug 2016, 22:26

### 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

# What arithmetic should I memorize?

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

### Hide Tags

Senior Manager
Joined: 25 Mar 2009
Posts: 305
Followers: 7

Kudos [?]: 184 [14] , given: 6

What arithmetic should I memorize? [#permalink]

### Show Tags

25 Jun 2009, 21:39
14
KUDOS
125
This post was
BOOKMARKED
I find myself constantly using long division and multiplication for simple things like 13 x 11.

What are some good arithmetic calcs to memorize? I created a 20x20 multiplication table but this seems like a bit much right?

Perfect squares up to 100? $$\sqrt{3}$$? $$\sqrt{5}$$?

I am not really talking about formulas to memorize since you should definitely memorize things like nCr, nPr, sum of all #'s in an evenly spaced set, etc.
Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 13982
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 3467

Kudos [?]: 20669 [60] , given: 4340

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

25 Jun 2009, 22:18
60
KUDOS
Expert's post
50
This post was
BOOKMARKED
Fantastic question

This file should give you an idea where you are lacking.
I think you should definitely know the squares from 0-10 and preferrably from 10 to 20 as well.
Attachments

Arithmetic Fractions and Percentages.doc [32.5 KiB]

_________________

Founder of GMAT Club

US News 2008 - 2017 Rankings progression - New!
Just starting out with GMAT? Start here...
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 12 May 2009
Posts: 54
Followers: 2

Kudos [?]: 87 [49] , given: 18

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

22 Oct 2009, 00:59
49
KUDOS
33
This post was
BOOKMARKED
As far as common squares are concerned, I only remember the ones with 0 or 5 in the units digit. For the latter category, I use the following process:

For example: 65*65

1) Always write down 25 as this is always the last two digits of the result:
...25

2) Multiply (non-units digits) times (non-units digits + 1)
6 * (6+1) = 42

2c) Combine:
4225

This way I always have the important squares handy... very useful for estimations!

Any other math shortcuts? Anyone

Steve
Intern
Joined: 24 Oct 2009
Posts: 24
Location: Russia
Schools: IESE, SDA Bocconi
Followers: 1

Kudos [?]: 79 [47] , given: 4

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

31 Oct 2009, 09:56
47
KUDOS
29
This post was
BOOKMARKED
I'm new here, and try to go through all the topics - this site is a treasure!

Maybe not the right place to share my experience with "multiplication for simple things like 13 x 11", but anyway...if you need to multiply any two-digits number by 11, just sum those digits and put the result in between. For example,
13x11 -> 1+3=4 -> 143 is the result.
Or, 36x11 -> 3+6=9 -> the result is 36x11=396.

It really saves time.
Senior Manager
Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 292
Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)
Followers: 17

Kudos [?]: 215 [35] , given: 248

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

11 Feb 2010, 10:34
35
KUDOS
16
This post was
BOOKMARKED
Thanks for sharing the Doc bb...@Shelen & @jeckll...Thanks for the tip but I would like to add some more.

What if u need to multiply 3 digits or 4 didgits by 11...the procedure is same as u mentioned but it would be done like below

For 3 digits
133x11 --> 1 1+3 3+3 3=1463
And for 4 digits
1243x11 --> 1 1+2 2+4 4+3 3=13673

And for 5 digits
15453x11 --> 1 1+5 5+4 4+5 5+3 3=169983
and so on.
you can plug other numbers in and check it out.

Hope it helps!
_________________

"I choose to rise after every fall"
Target=770
http://challengemba.blogspot.com
Kudos??

Intern
Joined: 31 Oct 2009
Posts: 38
Followers: 1

Kudos [?]: 48 [23] , given: 0

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

31 Oct 2009, 20:21
23
KUDOS
16
This post was
BOOKMARKED
Shelen wrote:
I'm new here, and try to go through all the topics - this site is a treasure!

Maybe not the right place to share my experience with "multiplication for simple things like 13 x 11", but anyway...if you need to multiply any two-digits number by 11, just sum those digits and put the result in between. For example,
13x11 -> 1+3=4 -> 143 is the result.
Or, 36x11 -> 3+6=9 -> the result is 36x11=396.

It really saves time.

And if it equals more than 10, add a 1 to the first digit

EG

68*11 -> 6+8=14 -> 6 14 8 -> 748
Senior Manager
Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 292
Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)
Followers: 17

Kudos [?]: 215 [11] , given: 248

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

11 Feb 2010, 22:41
11
KUDOS
14
This post was
BOOKMARKED
Guys! I just found another way of checking whether a number is divisible by 8 or not ( the rule is same but another approach or route ). It's for a number with more than two digits.

Let's take 1936
1) First of all check whether last two digits of the number are divisible by 4 or not.
For 1936, we do this way 36/4=9

2) If it is divisible by 4 then add the quotient to the 3rd last digit of the number and if the sum of them is divisible by 2 then the whole number is divisible by 8.

--> 9 (quotient)+ 9 ( 3rd digit from right)= 18, and -->18/2=9
So the whole number is divisible by 8.

Once you understand it and do a little practice, you'll find it easy and fast.
**You can try other numbers to see whether it is true or not
Hope it helps!
_________________

"I choose to rise after every fall"
Target=770
http://challengemba.blogspot.com
Kudos??

Intern
Joined: 21 Apr 2011
Posts: 18
Concentration: General Management, Operations
GMAT 1: Q V
Followers: 0

Kudos [?]: 18 [8] , given: 6

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

03 Nov 2012, 01:09
8
KUDOS
5
This post was
BOOKMARKED
I would like to add one more trick or shortcut to find the square of a number...

Suppose you know square of 13 but you want to know whats the square of 14, then follow this..

13 square = 169

For 14 square, 13 square + 13 - { present number } + 14 - { the next number }

i.e 169 + 13 + 14 = 196 { which is 14 square }

Note - you may calculate 14 square by knowing 15 square also!

14 square = 15 square - 15 {present number} - 14 {previous number}

14 square = 225 - 15 -14

14 square = 196

Additionally if you club this technique with "finding squares of numbers ending with 5" then finding the square of big numbers id just a matter of few seconds.

This technique is very helpful when finding squares of big numbers, it will be mere addition or subtraction.

Consider Kudos if you like this post.
Intern
Joined: 17 Feb 2010
Posts: 1
Followers: 0

Kudos [?]: 6 [5] , given: 0

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

17 Feb 2010, 19:53
5
KUDOS
1
This post was
BOOKMARKED
RE:
What if u need to multiply 3 digits or 4 didgits by 11...the procedure is same as u mentioned but it would be done like below

For 3 digits
133x11 --> 1 1+3 3+3 3=1463
And for 4 digits
1243x11 --> 1 1+2 2+4 4+3 3=13673

And for 5 digits
15453x11 --> 1 1+5 5+4 4+5 5+3 3=169983
and so on.

Hi guys,
When multiplying by 11 I find it much easier to multiply the # by 10 (or add 0) and then add the original # to it.
For example, 1234x11 = 12340 + 1234

When dividing by 11 and the following condition is satisfied one could factor the # as follows:
671/11 = 61x11/11 = 61 because in 671, 6+1=7 which is the # in the middle of 671. This works for 3digit #'s
Intern
Joined: 10 Jul 2011
Posts: 30
Followers: 0

Kudos [?]: 14 [4] , given: 5

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

04 Jan 2012, 16:59
4
KUDOS
8
This post was
BOOKMARKED
These are a few math tricks my brother used when studying for the MCAT. Hope they help!
(attached a word document)

1. A nice math trick is multiplying two integers that have multiple digits relatively quickly. It does not apply to all integers the following has to be met:
TENS DIGIT in both integers HAS TO BE SAME
ONES DIGIT in each integer HAS TO ADD UP TO 10
Also, if the ones digits are 1 and 9 you just write 09.

Example 34x36:
Step 1: Add one to tens place then multiply (1+3)x3 = 12
Step 2: Ones place 4x6 = 24
Step 3: Place Steps 1 & 2 = 1224

Example 1 & 9 in ones place: 21x29
Step 1: Add one to tens place then multiply (1+2)x2 = 6
Step 2: Ones place 1x9= 09
Step 3: Place Steps 1 & 2 together = 609

2. This one is for people having difficulty memorizing a few square root numbers!
sqrt 1 = 1 (as in 1/1 = New Year's Day)
sqrt 2 = 1.4 (as in 2/14 = Valentine's Day)
sqrt 3 = 1.7 (as in 3/17 = St. Patrick's Day)

3. The next math trick is the Babylonian Method it can be useful when estimating square roots.
First guess roughly what you think it would be

Step 1: For a number less than 1 guess bigger.
For a number greater than 1 guess smaller.
Step 2: Divide your guess into the square root number.
Step 3: Take your answer (from step 2) and add it to your guess
Step 4: Divide by 2

Example sqrt(.78):
Step 1: sqrt of .78 < 1 so guess = .85
Step 2. .78/.85 = ~.9
Step 3: (.85+.9) = 1.75
Step 4: 1.75/2 = ~.88 And this should be your answer (or close enough)

If you guess really wildly just use the answer from your first guess and run through the process again. You can do it in seconds once you get good at it.

Wild Guess Example: sqrt 70 = ?
Step 1 sqrt of 70>1 so guess 10
Step 2: 70/10= 7
Step 3: 7+10= 17
Step 4: 17/2 = 8.5
*8.5x8.5 = 72.25 Still off (10 kind of a wild guess, so repeat process with the new answer from step 4)
Step 1: guess = 8.5
Step 2: 70/8.5= 8.2
Step 3: 8.2+8.5= 16.7
Step 4: 16.7/2 = ~8.4
8.4*8.4 = 70.6

4. If two numbers (both even or odd) are close together and their average is an integer, then this method can be used.
Need to recognize that:
x^2 - y^2 = (x + y)(x - y) and vice-versa (x + y)(x - y) = x^2 - y^2
Example 1
48*52 = (50-2)(50+2) = 50^2 - 2^2 = 2496.

Example 2
3^2 - 2^2 = 3 + 2
4^2 - 3^2 = 4 + 3
5^2 - 4^2 = 5 + 4

5. When x and y are consecutive integers, then (x - y) = 1.

It's useful for calculating large squares:

Example: 71^2 = ?
71^2 - 70^2 = 71 + 70
so 71^2 = 70^2 + (141)
= 4900 + 141 = 5041

Example: 53^2 = ?
53^2 – 52^2 = (53 + 52) + (52 + 51) + (51 + 50)
53^2 = 50^2 + (105) + (103) + (101)
= 2500 + 309 = 2809

0.79^2
80^2 - 79^2 = 80 + 79
so 80^2 - (80 + 79) = 79^2
6400 - 159 = 6241 so 0.79^2 = 0.6241
Attachments

math tricks.docx [15.68 KiB]

Intern
Joined: 23 Jun 2014
Posts: 1
GMAT Date: 09-04-2014
Followers: 0

Kudos [?]: 6 [4] , given: 2

What arithmetic should I memorize? [#permalink]

### Show Tags

25 Jul 2014, 04:46
4
KUDOS
2
This post was
BOOKMARKED
Hi,

I've created an excel file I use to test myself on a daily basis to hopefully strengthen my basics while studying for the exam. It tests 20x20 multiplication and some of the the common powers, roots, fractions etc. that bb included in his doc.

Just thought I'd share incase there are others that might find it useful.

Cheers
Rupert
Attachments

Daily Maths Basics.xlsm [31.25 KiB]

Intern
Affiliations: isa.org
Joined: 26 Jan 2010
Posts: 23
Location: Mumbai, India.
Schools: ISB, India.
Followers: 0

Kudos [?]: 9 [3] , given: 2

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

14 Feb 2010, 06:21
3
KUDOS
3
This post was
BOOKMARKED
AtifS wrote:
Guys! I just found another way of checking whether a number is divisible by 8 or not ( the rule is same but another approach or route ). It's for a number with more than two digits.

Let's take 1936
1) First of all check whether last two digits of the number are divisible by 4 or not.
For 1936, we do this way 36/4=9

2) If it is divisible by 4 then add the quotient to the 3rd last digit of the number and if the sum of them is divisible by 2 then the whole number is divisible by 8.

--> 9 (quotient)+ 9 ( 3rd digit from right)= 18, and -->18/2=9
So the whole number is divisible by 8.

Once you understand it and do a little practice, you'll find it easy and fast.
**You can try other numbers to see whether it is true or not
Hope it helps!

hi,
i feel the process is bit complicated as it doesn't give the value of quotient, it just tells you whether no. is divisible by 8.
here is another tric, if the no. formed by last three digits is divisible by 8 then the whole no. is divisible by 8.

953360 is divisible by 8 since 360 is divisible by 8,
529418: not divisible as 418 is not divisible by 8.

plug in different values and try.
_________________

"Great people don't do different things, they do things differently"

Intern
Affiliations: isa.org
Joined: 26 Jan 2010
Posts: 23
Location: Mumbai, India.
Schools: ISB, India.
Followers: 0

Kudos [?]: 9 [2] , given: 2

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

14 Feb 2010, 06:12
2
KUDOS
2
This post was
BOOKMARKED
AtifS wrote:
Thanks for sharing the Doc bb...@Shelen & @jeckll...Thanks for the tip but I would like to add some more.

What if u need to multiply 3 digits or 4 didgits by 11...the procedure is same as u mentioned but it would be done like below

For 3 digits
133x11 --> 1 1+3 3+3 3=1463
And for 4 digits
1243x11 --> 1 1+2 2+4 4+3 3=13673

And for 5 digits
15453x11 --> 1 1+5 5+4 4+5 5+3 3=169983
and so on.
you can plug other numbers in and check it out.

Hope it helps!

welldone dude,
just a small addition which i tried and will help to avoid confusion:

start writing the answer from right hand side in case if the addition of two no. exceeds 10, and add it to consecutive no. on left hand side. try out!!
_________________

"Great people don't do different things, they do things differently"

Intern
Joined: 29 Oct 2012
Posts: 11
Followers: 0

Kudos [?]: 8 [2] , given: 5

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

26 Dec 2012, 18:19
2
KUDOS
1
This post was
BOOKMARKED
I found a trick or a shortcut to find the sum of the first half of consecutive integers( STRAIGHT,EVEN AND ODD) given the sum of one half of the set. This works only when the total number of elements in the set is even. but definitely saves a few seconds.

Let me illustrate with examples:

1. CONSECUTIVE INTEGERS : 6 TO 15
The Sum of the greater 5 numbers in a set of 10 consecutive integers is 65. Find the sum of the first 5 numbers.

Short cut:
Step 1: Multiply the no.of elements in each half : in this case 5 each and the spacing between each number in the set. in this case 1. ie., 5*5*1 = 25
Step 2: If the given sum is that of the greater numbers in the set, then subtract '25' to get the sum of the lower 5 numbers, i.e, 65-25 = 40 is the Answer
or if the given sum is that of the lower 5 consecutive numbers, then add '25' to get the sum of the greater 5 numbers i.e., 40+25 = 65.

2.Lets try this with 6 consecutive EVEN integers:

Find the sum of lower half of the numbers in a set of 6 consecutive even integers if the sum of the latter half is 30.

Step 1: 3*3*2 ( remember each half has 3 elements and the spacing between the elements is 2 as they are even) = 18
step 2: the given sum - step 1= 30 - 18 = 12 ( the sum of the even integers 2,4 and 6) is the answer.

3.Lets try for the 16 consecutive integers from 8 to 23. given sum of the greater 8 numbers in the set = 156

step 1: 8*8*1=64
step 2: given sum - step 1 = 156-64= 92 (which is the sum of numbers starting 8 thru 15)

4. Now lets try 24 consecutive ODD integers:

Find the sum of the second half of the elements of a set when the first half sums up to 168. The set contains Consecutive Odd integers.

Step 1: 12*12*2 = 288 ( Odd numbers are spaced evenly)
Step 2: given sum + 168 = 288+168 = 456

Check it out : the numbers are 3 to 49 inclusive.

try more examples. But remember it works only on CONSECUTIVE INTEGERS WITH EVEN NUMBER OF ELEMENTS. And when the sum of lower half is given, you need to ADD the given sum to step 1 and when the sum of greater half is given u need to SUBTRACT step 1 from the given sum.

Hope this helps!
Manager
Joined: 05 Jul 2009
Posts: 182
Followers: 1

Kudos [?]: 42 [1] , given: 5

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

23 Oct 2009, 22:04
1
KUDOS
1
This post was
BOOKMARKED
@bb: Thanks
@enfinity: good technique but I guess one need time to get familiar and comfortable with it. Up to then the conventional way is better.
Manager
Joined: 22 Sep 2009
Posts: 222
Location: Tokyo, Japan
Followers: 2

Kudos [?]: 21 [1] , given: 8

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

18 Nov 2009, 21:28
1
KUDOS
Good document. Should bump this up for ppl to download and memorize
Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 13982
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 3467

Kudos [?]: 20669 [1] , given: 4340

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

07 Jan 2010, 17:13
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
Also, see this post for some good theory: math-number-theory-88376.html
_________________

Founder of GMAT Club

US News 2008 - 2017 Rankings progression - New!
Just starting out with GMAT? Start here...
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 24 Jul 2009
Posts: 193
Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
Followers: 4

Kudos [?]: 34 [1] , given: 10

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

09 Jan 2010, 20:05
1
KUDOS
Shelen wrote:
I'm new here, and try to go through all the topics - this site is a treasure!

Maybe not the right place to share my experience with "multiplication for simple things like 13 x 11", but anyway...if you need to multiply any two-digits number by 11, just sum those digits and put the result in between. For example,
13x11 -> 1+3=4 -> 143 is the result.
Or, 36x11 -> 3+6=9 -> the result is 36x11=396.

Thanks for the tips. I recently downloaded some math apps to learn shortcuts. I plan to use them minimially though given the geometry and other formulas I need to memorize.
It really saves time.

Posted from my mobile device
_________________

Reward wisdom with kudos.

Intern
Joined: 31 Aug 2012
Posts: 11
Location: United States
Concentration: General Management, Finance
Schools: Sloan '15
GMAT 1: 640 Q44 V34
WE: Architecture (Telecommunications)
Followers: 0

Kudos [?]: 10 [1] , given: 7

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

29 Nov 2012, 10:10
1
KUDOS
One useful tip (from vedic maths) -
multiplying numbers close to 100 or 1000 or so on
e.g. multiply 97 * 98
Take the base as 100 as both numbers are close to 100

Step 1) First, we multiply the offsets 2 and 3
We get 6.
Since our base is 100, which has 2 zeros, the product of offsets must also have 2 digits. Hence we write 6 as 06 and these are our last 2 digits.

Step 2) Now substract one of the integers ( 97 or 98) from the peer number's offset i.e. 97 - 2 or 98 -3. Either will give you 95.
These are our first 2 digits.

So the answer is 9506.
Hope this helps.
Intern
Joined: 21 Jan 2013
Posts: 7
Location: India
WE: Engineering (Telecommunications)
Followers: 0

Kudos [?]: 12 [1] , given: 7

Re: What arithmetic should I memorize? [#permalink]

### Show Tags

05 Jan 2014, 23:40
1
KUDOS
Dividing 1 with any two digit no ends with 9 eg. 1/19, 1/29, 1/39...
Let’s take 1/19
1.Divide 1 by 2(1+1). It will give quotient 0 and reminder 1. Here we will set 0 as our first decimal value and 1 as prefix. So it will be .0 and keep 1 in mind which will be used for our next dividend.
2.Now divide 10(1= reminder and 0=quotient from above point) by 2. It will give quotient=5 and reminder=0. So our next digit is 5. Now it becomes 0.05.
3.Now divide 05(0=reminder and 1=quotient from point no2) by 2. It will give quotient=2 and reminder=1. Now ans is 0.052
You may continue if you want more decimal value.
Now let’s test it for 1/89.
1.Divide 1/9(8+1). We will get 0 as quotient and 1 as reminder. So it becomes 0.0
2. Divide 10 by 9. Q=1, R=1. Second digit is 1 i.e 0.01
3. Divide 11 by 9. Q=1 R=2. Third digit is 1 i.e 0.011
4. Divide 21 by 9. Q=2 R=2. Ans is 0.0112
Re: What arithmetic should I memorize?   [#permalink] 05 Jan 2014, 23:40

Go to page    1   2   3   4    Next  [ 62 posts ]

Similar topics Replies Last post
Similar
Topics:
What to memorize for Quant (decimal equivalence, number properties,?) 1 29 Dec 2015, 23:47
62 What to Memorize in GMAT Quant for the GMAT 8 11 Jul 2013, 07:22
Am I supposed to memorize SQRTs? 2 31 May 2012, 13:46
Memorization? 3 20 Jan 2011, 12:59
3 What math formulas, items, etc. should be memorized 2 15 Aug 2009, 16:34
Display posts from previous: Sort by

# What arithmetic should I memorize?

 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®.