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# What arithmetic should I memorize?

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

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16 Mar 2012, 17:17
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I know this post is quite old, but I'm just discovering this forum (thankfully after only being 1 week into studying). I genuinely am surprised to see such great resources on here and I'm feeling more confident, even after just discovering gmatclub, that I'll get a good score.

I have a question about the downloadable sheet. I'm kind of confused with how it's ordered and why some of the items are included. Why are some fractions and some exponents on here, but others aren't? Is there a reason for these particular ones to be remembered? When a fraction or percentage is listed, should we be memorizing the decimal, percentage and fraction versions of each of them?

For the last three lines, why is it important to know the multiples of 12, 15 and 8 over other ones?
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Re: What arithmetic should I memorize? [#permalink]

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17 Mar 2012, 01:28
tkaelle wrote:
I know this post is quite old, but I'm just discovering this forum (thankfully after only being 1 week into studying). I genuinely am surprised to see such great resources on here and I'm feeling more confident, even after just discovering gmatclub, that I'll get a good score.

I have a question about the downloadable sheet. I'm kind of confused with how it's ordered and why some of the items are included. Why are some fractions and some exponents on here, but others aren't? Is there a reason for these particular ones to be remembered? When a fraction or percentage is listed, should we be memorizing the decimal, percentage and fraction versions of each of them?

For the last three lines, why is it important to know the multiples of 12, 15 and 8 over other ones?

The doc gives some arithmetics which one will frequently need while solving the GMAT questions. Though I agree that some useful staff is missing and presence of some other things is debatable.

As for the percentages, it's good to know fractional as well as decimal representation of some of them.
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Re: What arithmetic should I memorize? [#permalink]

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07 Oct 2012, 09:06
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Re: What arithmetic should I memorize? [#permalink]

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03 Nov 2012, 01:09
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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.
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Re: What arithmetic should I memorize? [#permalink]

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29 Nov 2012, 10:10
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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.

Hope this helps.
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Re: What arithmetic should I memorize? [#permalink]

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01 Dec 2012, 23:04
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!

This is awesome 'AtifS' ......!!! Great time saving...
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Re: What arithmetic should I memorize? [#permalink]

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01 Dec 2012, 23:22
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!

Well,this can be directly seen whether last three digits of any no. are divisible by 8.
EG : for same no : 1936, 936/8=117 => 1936 is divisible by 8

Let's take another no 7992, 992/8=124 => 7992 is divisible by 8.

So,you're getting your answer in 1 step and I think you don't need to memorize a lot for it
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Re: What arithmetic should I memorize? [#permalink]

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26 Dec 2012, 18:19
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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!
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Re: What arithmetic should I memorize? [#permalink]

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26 Dec 2012, 19:56
Good one imk... Kudos man...!

Hope it'll work out for all the relevant aspects for the series of even/odd Consecutive integers with Even no. of elements of course!

Btw, if you know any other shortcuts, could you please come up with those & help the Club..!
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Re: What arithmetic should I memorize? [#permalink]

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14 Apr 2013, 12:58
bb wrote:
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.

I am wondering if there is an error with the file that I downloaded. It just had random fractions and percentages, with no solutions to memorize! Why do I have the feeling I am missing something really obvious?
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Re: What arithmetic should I memorize? [#permalink]

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15 Apr 2013, 00:26
sns wrote:
bb wrote:
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.

I am wondering if there is an error with the file that I downloaded. It just had random fractions and percentages, with no solutions to memorize! Why do I have the feeling I am missing something really obvious?

Yes, answers are not given. You can get them yourself and memorize, though not everything in this doc is worth memorizing.
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Re: What arithmetic should I memorize? [#permalink]

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09 May 2013, 14:42
bb,
you are great!
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Re: What arithmetic should I memorize? [#permalink]

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09 May 2013, 16:15
sns wrote:
bb wrote:
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.

I am wondering if there is an error with the file that I downloaded. It just had random fractions and percentages, with no solutions to memorize! Why do I have the feeling I am missing something really obvious?

This is intended as a test - can you answer them right off the bat or quickly.... or are you wasting your time on these every day simple calculations.
This was my personal list and it may be slightly different for you. Bunuel seems to have his own - I'd love to see it
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Re: What arithmetic should I memorize? [#permalink]

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05 Dec 2013, 07:35
You know what, we have the same problem, I search it on the internet that's why I ended up here in you post.And Im very glad because I found the answer from the comments.
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Re: What arithmetic should I memorize? [#permalink]

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28 Dec 2013, 01:26
Well, I have been looking at some vedic maths and thought of putting it for everyone here..

Starting with multiplying.....We all know what is 40*50 ie. 2000. Now what s 55 *45....we need time correct...there is easier way for such question type where the unit digit is 5 and ten's digit are consecutive nos..For ex 1,2, or 3, 4 or 4,5 etc

Coming back to current problem.... 55*45
Step 1 : Keep as the last 2 nos of the product XX75
Step 2: Square the larger of the 2 ten's digit no.
In this case it is 5 and square is 25.
Step 3: Subtract 1 from 25 = 24
Ans will be 2475

Try any nos for eg. 25*35 will be 875 by same logic. For practice try these 95*85 or 65*75 or 135*125 (You can figure out the answers by calculator) and if you a problem, please post it here.

Similarly for squares of nos upto 60 can be easily calculated. ( I assume you know squares from 30-40 and obviously before 30) and using this method you can find squares of nos from 40 to 60 easily...Beyond this it is all about practice.

okay------->
Lets start...what is 53^2
Now we can always do it by making (50+3)^2 and simplify....Well I give another trick and you can figure out in less than 15 seconds

Step 1: 53 is 3 more than 50 and so the unit digit will be 3^2 which is 09
XX09

Step 2: Now 5^2 + unit digit will be the first 2 digits of this number. In this case it will be 28

2809

Consider another problem 58^2. Lets apply the same steps

1. 8^2 = 64 so we have XX64 because 58 is 8 more than 50
2. 5^2 +8= 33 so we have 3364

You can do it same way for nos greater than 60 also find it. For ex 65^2

1. 65 -----------> 65 is 15 more than 50 so 15^2 = 225.......keep the last 2 digits only xx25
2. Now 5^2 =25+15= 40
3. Add 2 from 225 and we get 4225

Try these nos 56^2 or 67^2
For nos less than 50...

What is the square of of 46^2

Step 1: Now 46 is 4 less than 50 so the nos will be XX16
Step 2: Now 5^ 2 is 25 and subtracting 4 from 25 we get 21.
So 46^2 will be 2116

What is 39^2 ??

Step 1: Square of 11(Cause 39 is 11 less than 50) is 121 and so Last 2 digits will 21 and so we have XX 21
Step 2: 5^2 -11 (Because 39 is 11 less than 50) we get 14 and add 1
We get 1521.....

try 43^2 or 48^2, 37^2

I hope you find them useful...Will put one on finding square of larger nos such as 101, 109, 119 etc.....

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

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02 Jan 2014, 02:48
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!

if you just check whether the last 3 digits are divisible by 8 would become more easier rather then dividing it twice.
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Re: What arithmetic should I memorize? [#permalink]

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05 Jan 2014, 23:40
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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
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What arithmetic should I memorize? [#permalink]

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24 Jul 2014, 14:01
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I found this post a little too late but agree with bb that there are set number of things that everyone must know, out cold, by test day. This can save valuable time and give you opportunity to spend more time analyzing and solving questions rather than doing mundane computations.

Till 2 weeks back, I only knew tables up to to 10. The day and age we live in, I never felt the need. I either have excel or a calculator handy on my smart phone. These are habits one has to develop so I started putting together a Brain Dump sheet. I have roughly 30 print-outs on my desk, and first thing I do when I get to work is take 5 minutes to fill them out. Initially it will be difficult, but start by breaking them down into smaller sections till you have average proficiency.

You might want to add first 100 prime numbers to the list attached.

2 3 5 7
11 13 17 19
23 29
31 37
41 43 47
53 59
61 67
71 73 79
83 89
97

Learning aid:
2x, 5x and 8x are similar.
3x, 6x are similar
4x and 7x are similar.

bb wrote:
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

File comment: Quant Braindump
Quant Braindump 3.PDF [226.68 KiB]

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What arithmetic should I memorize? [#permalink]

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25 Jul 2014, 04:46
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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]

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What arithmetic should I memorize? [#permalink]

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14 Dec 2014, 03:09
hubahuba wrote:
I found this post a little too late but agree with bb that there are set number of things that everyone must know, out cold, by test day. This can save valuable time and give you opportunity to spend more time analyzing and solving questions rather than doing mundane computations.

Till 2 weeks back, I only knew tables up to to 10. The day and age we live in, I never felt the need. I either have excel or a calculator handy on my smart phone. These are habits one has to develop so I started putting together a Brain Dump sheet. I have roughly 30 print-outs on my desk, and first thing I do when I get to work is take 5 minutes to fill them out. Initially it will be difficult, but start by breaking them down into smaller sections till you have average proficiency.

You might want to add first 100 prime numbers to the list attached.

2 3 5 7
11 13 17 19
23 29
31 37
41 43 47
53 59
61 67
71 73 79
83 89
97

Learning aid:
2x, 5x and 8x are similar.
3x, 6x are similar
4x and 7x are similar.

bb wrote:
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.

A very good way to remember the prime numbers.
Tens digit of each 'similar' series differ from each other by 3.
The difference between highest and lowest prime number in each series is 6 (exception - 7x, where in 79-71=8)
Note: 4x and 7x are similar: Although the number of primes is 3 within the series, numbers with highlighted x are different.
What arithmetic should I memorize?   [#permalink] 14 Dec 2014, 03:09

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