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![Page 1: Quick tricks](https://reader033.fdocuments.in/reader033/viewer/2022061209/548c5983b47959b6398b4765/html5/thumbnails/1.jpg)
QUICK TRICKS
![Page 2: Quick tricks](https://reader033.fdocuments.in/reader033/viewer/2022061209/548c5983b47959b6398b4765/html5/thumbnails/2.jpg)
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
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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
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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
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999999 . 1 = 0999999999999 . 2 = 1999998999999 . 3 = 2999997999999 . 4 = 3999996999999 . 5 = 4999995999999 . 6 = 5999994999999 . 7 = 6999993999999 . 8 = 7999992999999 . 9 = 8999991
999999 . 10 = 9999990
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9 . 9 = 8199 . 99 = 9801
999 . 999 = 9980019999 . 9999 = 99980001
99999 . 99999 = 9999800001999999 . 999999 = 999998000001
9999999 . 9999999 = 99999980000001
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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
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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
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MULTIPLICATION
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MULTIPLICATION
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MULTIPLICATION
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SQUARE OF NOS ENDING IN 5
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2 DIGIT MULTIPLY BY 11
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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.
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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.
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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.
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BY THE DEFICIENCY - BY WHATEVER THE DEFICIENCY, LESSEN IT FURTHER BY THAT MUCH AND SETUP THE SQUARE THEREOF
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• 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’.
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TIME AND WORK
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• 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
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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?
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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?
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• 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?
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• 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?
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• 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?