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# What arithmetic should I memorize?

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Re: What arithmetic should I memorize? [#permalink]  16 Mar 2012, 17:17
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]  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]  07 Oct 2012, 09:06
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Re: What arithmetic should I memorize? [#permalink]  03 Nov 2012, 01:09
1
KUDOS
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]  29 Nov 2012, 10:10
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]  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]  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]  26 Dec 2012, 18:19
1
KUDOS
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]  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]  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]  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]  09 May 2013, 14:42
bb,
you are great!
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Re: What arithmetic should I memorize? [#permalink]  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] 09 May 2013, 16:15
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