Aptiiude Maths

1 : 35 33 29 23 15...............
» you didn't select an answer.
The answer is :5

2 : 8 15 24 35 48 63
» you didn't select an answer.
The answer is :80

3 : 2 4 10 24 54 .............
» you didn't select an answer.
The answer is :116

4 : 19 17 18 16...........
»you answered : , which is correct

5 : 19 17 18 16..........
» you didn't select an answer.
The answer is :17

6 : 96 48 52 26 30.......
» you didn't select an answer.
The answer is :15

7 : 20 10 22 9 24 8 26............
» you didn't select an answer.
The answer is :7

8 : 1 7 2 6 3 5 4...........
» you didn't select an answer.
The answer is :4

9 : 2 4 12 48................
» you didn't select an answer.
The answer is :240

10 : 12 23 34 45...........
» you didn't select an answer.
The answer is :56

11 : 7 35 28 140 133..........
» you didn't select an answer.
The answer is :665

12 : if 3*2=46 2*5=104 4*3=68 then 4*7=?
» you didn't select an answer.
The answer is :148

13 : 6 9 14 21 30....................... 54
» you didn't select an answer.
The answer is :41

14 : 5 6 11 66 9 7 16............
» you didn't select an answer.
The answer is :102

15 : 4 196 16 144 36 100 64...............
» you didn't select an answer.
The answer is :64

16 : 3 8 4 6 5 4 6..............
» you didn't select an answer.
The answer is :2

17 : 7 8 49 64....................... 512
» you didn't select an answer.
The answer is :333

18 : 1 1 2 4 7 11..........
» you didn't select an answer.
The answer is :16

19 : 2 3 4 9............... 81
» you didn't select an answer.
The answer is :16

20 : 10................. 16 17 22 23 28
» you didn't select an answer.
The answer is :11

Mental Math with Tricks and Shortcuts (continued)

Mental Math with Tricks and Shortcuts (continued)

Cube Roots the Long Way

(636056)^1/3

What number cubed is less than 636 = 8. Put 8 down as first part of answer

Square 8 for 64 and multiply by 300 = 19200. Divide into 114056 = 6, add the 8 and 6 = 14

Multiply 14 x 30 = 420, add 420 to 19200 = 19620, square the 6 and add to 19620 = 19656

If 6 x 19656 is less than 124056, then it is not necessary to use lower number.

636 056 = 86³

512

19656)124056

117936

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7120

USE ESTIMATES

Use estimates to check your answers. Get in the habit of doing this for all calculations.

NOTE: Considerable care has been taken to eliminate errors in this document, but the author does not

guarantee that the document is error free by implication or in fact.

Mental Maths with Tricks and Shortcuts

Mental Math with Tricks and Shortcuts

11 if the number has an even number of digits that are all the same: 33, 4444, 777777, and etc.

11 if, beginning from the right, subtracting the smaller of the sums of the even digits and odd digits

results in a number equal to 0 or divisible by 11:

406857/11 Even = 15 Odd = 15 = 0

1049807/11 Even = 9 Odd = 20 = 11

12 if test for divisibility by 3 & 4 work

15 if test for divisibility by 3 & 5 work

Others by using tests above in different multiplication combinations

SQUARE ROOTS Examples

Separate the number into groups of 2 digits or less beginning from the right

(66049)1/2 6 60 49

What number can be squared and be less than 6 = 2 with a reminder of 2

Bring down the second group of digits next to the remainder to give 260

Double the first part of the answer to get 4, divide into 26 of the 260 to get 6 as a trial number

Use 4 & 6 to get 46 and multiply by 6 to equal 276 which is larger than 260, therefore try 5

Use 4 & 5 to get 45, 45 x 5 = 225, 260 – 225 = 35, bring down the 49 to get 3549

Double the 25 to get 50, divide 50 into 354 to get 7 as a trial second part of divisor

Use 50 & 7 to get 507 and multiply 507 x 7 to get 3549 with no remainder.

See complete calculations below:

6 60 49 (257 = Answer

4

45)260

225

507)3549

3549

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0

CUBE ROOTS

Memorize the following:

Cube of 1 = 1, 2 = 8, 3 = 27, 4 = 64, 5 = 125, 6 = 216, 7 = 343, 8 = 512, 9 = 729

Note: no result ends in the same digit

(300763)1/3 Divide in to groups of 3 from right = 300 763

Note: the number ends in a 3. Last digit of cube will be 7 if this is a cube without a remainder

Since 7 cubed = 343 and 6 cubed = 216, the left most group of 300 is between them and we must use

the smaller, or 6.

The answer is 67 This method works up to 1,000,000 for true cubes

Maths Tricks and Shortcuts : SUBTRACTION

Mental Math with Tricks and Shortcuts

SUBTRACTION

Techniques:

1) Learn to calculate from left to right: 1427 – 698 = (800 – 100) + (30 – 10) + 9 = 729

2) Think in terms of what number added to the smaller equals the larger: 785 – 342 = 443 (left to right)

3) Add a number to the larger to round to next highest 0; then add same number to the smaller and subtract:

496 – 279 = (496 + 4) – (279 + 4) = 500 – 283 = 217 (left to right)

4) Add a number to the smaller to round to the next highest 10, 100, 1000 and etc.; then subtract and add

the same number to the result to get the answer: 721 – 587 = 721 – (587 + 13) = (721 – 600) + 13 = 134

5) Subtract a number from each number and then subtract: 829 – 534 = 795 – 500 = 295

DIVISION

Techniques: Examples

Divide by parts of divisor one at a time: 1344/24 = (1344/6)/4 = 224/4 = 56

Method of Short Division 340 Remainders (3, 4, and 0 during calculations) 7)1792

-------------

256 ßAnswer

Divide both divisor and dividend by same number to get a short division problem

10

972/27 divide both by 9 = 3)108

--------

36

Dividing by 5, 50, 500, and etc.: Multiply by 2 and then divide by 10, 100, 1000, and etc.

365/5 = 730/10 = 73

Dividing by 25, 250, 2500, and etc.: Multiply by 4 and divide by 100, 1000, 10000, and etc.

Dividing by 125: Multiply by 8 and then divide by 1000

36125/125 = 289000/1000 = 289

It can be divided evenly by:

2 if the number ends in 0, 2, 4, 6, and 8

3 if the sum of the digits in the number is divisible by 3

4 if the number ends in 00 or a 2 digit number divisible by 4

5 if the number ends in 0 or 5

6 if the number is even and the sum of the digits is divisible by 3

7 sorry, you must just try this one

8 if the last three digits are 000 or divisible by 8

9 if the sum of the digits are divisible by 9

10 if the number ends in 0