Quantitative Techniques Shortcut.

✓Method to multiply 2-digit number.

(i)AB × CD = AC / AD + BC / BD

35 × 47 = 12 / 21 + 20 / 35 

= 12 / 41 / 35 

= 1645

(ii)AB × AC = A2 / A (B + C) / BC

74 × 76 = 72 / 7(4 + 6) / 4 × 6

= 49 / 70 / 24 = 49 / 70 / 24 = 5624

(iii)AB × CC = AC / (A + B)C / BC

= 35 × 44 = 3 × 4 / (3 + 5) × 4 / 5 × 4

= 12 / 32 / 20 

 = 15402.

✓Method to multiply 3-digit no.

ABC × DEF = 

AD / AE + BD / AF + BE + CD / BF + CE / CF

456 × 234 = 

4 × 2 / 4 × 3 + 5 × 2 / 4 × 4 + 5 × 3 + 6 × 2 / 5 × 4 + 6 × 3 / 6 × 4

= 8 / 12 + 10 / 16 + 15 + 12 / 20 + 18 / 24

= 8 / 22 /43 / 38 / 24 = 1067043.

✓If in a series all number contains repeating 7. To find their sum, we start from the left multiply 7 by 1, 2, 3, 4, 5 & 6. 

Look at theexample below.

777777 + 77777 + 7777 + 777 + 77 + 7 = ?

= 7 × 1 / 7 × 2 / 7 × 3 / 7 × 4 / 7 × 5 / 7 × 6= 7 / 14 / 21 / 28 / 35 / 42 = 8641924.

✓To find the sum of those number in which one number is repeated after decimal, then first write the number in either increasingor decreasing order. Then -find the sum by using the below method.

0.5555 + 0.555 + 0.55 + 0.5= 

5 × 4 / 5 × 3 / 5 × 2 / 5 × 1

= 20 / 15 / 10 / 5 = 2.16055

✓Those numbers whose all digits are 3.

(33)^2 = 1089

Those number. in which all digits are number is 3 two or more than 2 times repeated, to find the square ofthese number, we repeat 1 and 8 by 

(n – 1) time. 

Where n →Number of times 3 repeated.

(333)^2 = 110889

(3333)^2 = 111088896.

Those number whose all digits are 9.

(99)^2 = 9801

(999)^2 = 998001

(9999)^2 = 99980001

(99999)^2 = 9999800001.

Those number whose all digits are 1.

A number whose one’s, ten’s, hundred’s digit is 1 i.e., 11, 111, 1111, ....In this we count number of digits. We write 1, 2, 3, ..... in their square the digit in the number, then write in decreasing order up to1.

(11)^2 = 121

(111)^2 = 12321

(1111)^2 = 1234321