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# What arithmetic should I memorize?

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Joined: 09 Sep 2013
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Re: What arithmetic should I memorize? [#permalink]

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21 Dec 2015, 03:00
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Location: India
GMAT 1: 730 Q50 V38
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Re: What arithmetic should I memorize? [#permalink]

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07 Feb 2016, 17:39
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!

There's a pattern that numbers which are powers of 2 follow (2,4,8,16, and so on).

Here, if I were to check if 1936 is divisible by 8, I just need to know that 8=2^3.

Since 8 is 2 raised to the power of 3, for any number under consideration, I just need to check if the last 3 digits of the number are divisible by 8 or not (Here, 936=8*117). If the last 3 digits are divisible by 8, the entire number will be divisible by 8, irrespective of the number of digits in that number.

Another example:

Check if 1000032 is divisible by 16.

Now you know that 16=2^4, and the last four digits of the number quoted above (0032) are divisible by 16. Hence, the number is divisible by 16.

The same rule applies to 5. You can easily check divisibility by 5,25,125,625, etc. using the same rule!
Intern
Joined: 11 Sep 2016
Posts: 1
Re: What arithmetic should I memorize? [#permalink]

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12 Sep 2016, 09:33
Hi to everyone!

Want to share very useful tip on how to multiply integers that are both in 10<x<20 range.
Example 1:
13x15 = (13+5)x10+3x5 = 180+15 = 195
or
13x15 = (15+3)x10+3x5 = 180+15 = 195

Example 2:
18x19 = (18+9)x10+8x9 = 270+72 = 342

Such technic could save you 5-10 sec (depends on practice) per each computation
Intern
Joined: 10 Jun 2016
Posts: 12
Re: What arithmetic should I memorize? [#permalink]

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31 Mar 2017, 08:43
Thank you very much!
Director
Joined: 02 Sep 2016
Posts: 786
What arithmetic should I memorize? [#permalink]

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04 Apr 2017, 00:21
2
This post was
BOOKMARKED
Though its important to understand the concept well but knowing few tricks (VEDIC MATHS) can speed up the process of solving questions under timed conditions.

Few tricks are:

(1) Squaring a number which ends in 5.
Square 25

Step 1: Write last two digits of the final answer: 5^5= 25
Step 2: multiple the first digit by the next bigger digit. 2*3=6

(2) This can be used for elimination: if a number ends in 2,3,7, and 8 at unit's place, then that number won't be a perfect square.

(3) The common squares are:
2^2=4
3^2=9
4^2=16
5^2=25
6^2=36
7^2=49
8^2=64
9^2=81
10^2=100
11^2=121
12^2=144
13^2=169
14^2=196
15^2=225
16^2=256
17^2= 289
18^2= 324
19^2= 361
20^2= 200

Its better to know these squares but not necessary. Like I said knowing these can speed up the process of solving a question.

(4) Common cubes:
2^3= 8
3^3=27
4^3=64
5^3=125
6^3=216
7^3=343
8^3=512
9^3=729

(5) Square root of 0 is 0
Sq. root of 1 is 1
Sq. root of 2 is approx 1.41
Sq. root of 3 is approx.1.73

(6) Dividend= Divisor*Quotient+Remainder
0<=Remainder<Divisor

(7) Non-negative integers are 0,1,2,3,4,5,........
(8) 2 and 3 are the only consecutive prime nos.
And 2 is the only even prime no.

1 is not a prime no. as a prime no. has two factors 1 and itself. (1 has only one factor i.e. 1)

(9) Sum and product of three consecutive integers is always divisible by 3.
For example, 2,3,4
Product= 24 (3*8=24)
Sum= 9 (3*3=9)

(10) LCM(a,b)* GCD(a,b)= a*b
In LCM, we take the highest powers of the prime factors.
For example, LCM (2 and 4)
2= 2^1
4=2^2

We will take the higher power of 2 i.e. 2. The LCM is 4.

In GCD, we take the lowest power of the prime factors that are common.
For example, GCD (3,9)
3=3^1
9=3^2

GCD= 3

GCD is always less than or equal to the nos.

(11) Even nos. can be represented as 2n, 2n+2, 2n+4, and so on.
Odd nos. can be represented as 2n+1, 2n+3, 2n+5, and so on.

(12) 1 is the smallest divisor/factor of all the integers. Whereas 0 is the smallest multiple of every integer.

(13) Mean=Median of n consecutive integers.
For example, n, (n+1), (n+2), (n+3), and (n+4)
Sum= 5n+10
Mean= sum/n
=[5(n+2)]/5
=n+2

Median is the no. in the middle of the series.
If n is even, then take an average of the two middle terms.
If n is odd, take the middle term.

Here the median is (n+2).

(14) Always read the language of the question carefully as it can include important words such as inclusive, exclusive, distinct, positive integer, negative integer, factors, prime factors, and so on.
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Joined: 30 Jul 2014
Posts: 6
Re: What arithmetic should I memorize? [#permalink]

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10 Dec 2017, 04:18
enfinity wrote:
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

Hi!

Is this method applicable to all the squares? For example - how will you solve 89*89?
Math Expert
Joined: 02 Sep 2009
Posts: 43828
Re: What arithmetic should I memorize? [#permalink]

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10 Dec 2017, 04:24
prateetchhatwal wrote:
enfinity wrote:
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

Hi!

Is this method applicable to all the squares? For example - how will you solve 89*89?

This is only applicable for those which end with units digit of 5.
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Re: What arithmetic should I memorize?   [#permalink] 10 Dec 2017, 04:24

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