Speed Maths | Reasoning for competitive exams

  

SPEED MATHS

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5 Number TRICKS:  

When a number is multiplied by 5 = Half of the number × 10

Formula: x×5=Half ofx×10

1. Example:

18×5=90

*Half of 18=9×10=90 1

2Example:

 7×5=85 

*Half of 17=8.5×10=853 

3 Example: 

6×5=180

 *Half of 36=18×10=1802

4 Example:

36×5=1180 

*Half of 236=118×10=11801

5 Example: 

364×5=6820 

*Half of 1364=682×10=68205

 6 Example:

 82×5=2910 

*Half of 582=291×10=2910

(Try yourself 5 digit short tricks with us)  

When a number is multiplied by 25 = 1/4 of the number × 100

Formula: x×25=(x×1/4)×100

Example:

 1.18×25=450

*1/4 of the 18=18×14 100=450

 2.120×25=3000

 *1/4 of the 120=120×14 100=3000

 3.249×25=6225

 *1/4 of the 249=249×14 100=6225

 4.1364×25=34100 

*14 of the 1364=1364×14 100=34100

 

(Try Yourself another number with 25) 

When a number is multiplied by 125 = 18 of the number × 1000

     Formula x×125=(x×1/8)×1000

Example:    

1. 5 × 125 = 625 

*18 of the 5 = 5 × 1/8 × 1000 = 625

2. 18 × 125=18 × 1/8 ×1000

=2.25 × 1000

=2250

3. 400 × 125=400 × 1/8 ×1000

=50 × 1000

=50000

4. 289 × 125 = 289 × 1/8 × 1000

= 36.125 × 1000

= 36123

Multiplication by 11

Tricks 1.

33 × 11 = 363

Tricks 2:

38 × 11 = 418

52 × 11=572 (Same as example 1)

Tricks 3.

3 or <3 digit number 

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Calendar Test :

1 week - 7 days

1 year - 52 weeks + 1 ordinary days ( ordinary year )

Leap year - 52 weeks+ 2 odd days.

Ordinary year - 28th February.

Leap year - 29 th February.

Days code : 

Sunday - 0

Monday - 1

Tuesday - 2

Wednesday - 3

Thursday - 4

Friday - 5

Saturday - 6

Months code :

January - 0

February - 3

March - 3

April - 6

May - 1

June - 4

July - 6

August - 2

September - 5

October - 0

November - 3

December - 5

Years Code :

1600 to 1699 : code number is 6

1700 to 1799 : 4

1800 to 1899 : 2

1900 to 1999 : 0

2000 to  2099 : 6

Exercise:

Q. 1. What was the day of the week on 26th January 1947 ?

Solution:

Step 1. Last two digit of the year - 47.
Step 2. Above digit is divided by 4 : 47/4= 11 (using this method)
Step 3. Take the Date - 26
Step 4 . Take the code for the month - 00 (for January )
Step 5 . Take the code for year : 00 ( for 1900 to 1999 is 0)
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Sum = 84
Step 5. - sum/7=84/7=7*12+0 now remaining number is Zero.
Therefore, code "0" is referes to Sunday. So, 26th January 1974 was on Sunday {alertSuccess}

 

 

Q. 2. What was the day of the week on 5th October 2016 ?

Solution: 

Step 1. Last two digits of the year - 16

Step 2. Divided by 4 - 04

Step 3. Take the date - 05

Step 4. Take the code for month ( October ) - 00

Step 5. Take the code for year ( 2016 ) - 06

Step 6. Sum/7=31/7=7*4+3

Code 3 refers to wednesday.

So, 5th October 2016 on Wednesday. {alertSuccess}

 

Condition for Leap Year:

Q. 3. What was the day of the week on 24 February 2012 ?

Solution:

Last two digits of the year - 12.

Divided by 4 - 03

Take date - 29

Code for month - 03

Code for year - 06

Sum = 53

Now, Sum/7 = 53/7= 7×7+4

In case of leap year, code for the date= Reminder - 1 =4-1=3

Code 3 represents Wednesday.

So 29th February 2012 was on Wednesday. {alertSuccess}