QUICK TRICKS

SURPRISING NUMBER PATTERNS

1 . 1 = 111 . 11 = 121

111 . 111 = 123211111 . 1111 = 1234321

11111 . 11111 = 123454321111111 . 111111 = 12345654321

1111111 . 1111111 = 123456765432111111111 . 11111111 =

123456787654321111111111 . 111111111 =

12345678987654321

12345679 . 9 = 111111111

12345679 . 18 = 222222222

12345679 . 27 = 333333333

12345679 . 36 = 444444444

12345679 . 45 = 555555555

12345679 . 54 = 666666666

12345679 . 63 = 777777777

12345679 . 72 = 888888888

12345679 . 81 = 999999999

987654321 . 9 = 08 888 888 889

987654321 . 18 = 17 777 777 778

987654321 . 27 = 26 666 666 667

987654321 . 36 = 35 555 555 556

987654321 . 45 = 44 444 444 445

987654321 . 54 = 53 333 333 334

987654321 . 63 = 62 222 222 223

987654321 . 72 = 71 111 111 112

987654321 . 81 = 80 000 000 001

999999 . 1 = 0999999999999 . 2 = 1999998999999 . 3 = 2999997999999 . 4 = 3999996999999 . 5 = 4999995999999 . 6 = 5999994999999 . 7 = 6999993999999 . 8 = 7999992999999 . 9 = 8999991

999999 . 10 = 9999990

9 . 9 = 8199 . 99 = 9801

999 . 999 = 9980019999 . 9999 = 99980001

99999 . 99999 = 9999800001999999 . 999999 = 999998000001

9999999 . 9999999 = 99999980000001

0 . 9 + 1 = 1 1 . 9 + 2 = 11

12 . 9 + 3 = 111123 . 9 + 4 = 1111

1234 . 9 + 5 = 1111112345 . 9 + 6 = 111111

123456 . 9 + 7 = 11111111234567 . 9 + 8 = 11111111

12345678 . 9 + 9 = 111111111

1 . 8 + 1 = 9 12 . 8 + 2 = 98

123 . 8 + 3 = 987 1234 . 8 + 4 = 9876

12345 . 8 + 5 = 98765 123456 . 8 + 6 = 987654

1234567 . 8 + 7 = 9876543 12345678 . 8 + 8 = 98765432

123456789 . 8 + 9 = 987654321

MULTIPLICATION

MULTIPLICATION

MULTIPLICATION

SQUARE OF NOS ENDING IN 5

2 DIGIT MULTIPLY BY 11

SPEED MULTIPLYING BY 21, 31, 41

To multiply by 21: Double the number, then multiply by 10 and add the original number.

For example: To multiply 37 by 21, Double 37 yields 74,multiply by 10 to get 740 and then add the original number 37 to get 777.

To multiply by 31: Triple the number, then multiply by 10 and add the original number.

For example: To multiply 43 by 31, Triple 43 yields 129,multiply by 10 to get 1,290 and then add the original number 43 to get 1,333.

To multiply by 41: Quadruple the number, then multiply by 10 and add the original number.

For example: To multiply 47 by 41, Quadruple 47 yields 188,multiply by 10 to get 1,880 and then add the original number 47 to get 1,927.

BY THE DEFICIENCY - BY WHATEVER THE DEFICIENCY, LESSEN IT FURTHER BY THAT MUCH AND SETUP THE SQUARE THEREOF

• A number is divisible by ‘2’ if it ends in zero or in a digit which is a multiple of ‘2’i.e. 2,4, 6, 8.

• A number is divisible by ‘3’, if the sum of the digits is divisible by ‘3’.

• A number is divisible by ‘4’ if the number formed by the last two digits, i.e. tens and units are divisible by 4.

• A number is divisible by ‘5’ if it ends in zero or 5.

• A number is divisible by ‘6’ if it divisible by ‘2’ and ‘3’.

• A number is divisible by ‘8’ if the number formed by the last three digits, is divisible by ‘8’.

• A number is divisible by ‘9’ if the sum of its digit is divisible by ‘9’.

• A number is divisible by ‘10’ if it ends in zero.

• A number is divisible by ‘11’ if the difference between the sums of the digits in the even and odd places is zero or a multiple of ‘11’.

TIME AND WORK

• A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :A. 1/4B. 1/10 C. 7/15 D. 8/15

2. A and B can finish a work in 16 days, while A alone can do the same work in 24 days. In how many days, B alone can finish the same work?

1. If 12 men can do a piece of work in 36 days. In how many days 18 men can do the same work?

If 6 men dig 100 meters in 20 days working 8 hours, how many men are required to dig 200 meters in 10 days working 4 hours?

If 20 men cut 40 trees working 8 hours each day in 10 days. Find out how many trees will be cut by 30 men working 4 hours a day for 20 days?

• A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

• P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

• X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?