Simplifications are very important in Bank Exams. In Quantitative Aptitude /Numerical Ability section, about 40 − 50% of questions in clerical exam and about 20 − 25% of questions in Probationary Officers exam will be of simplifications.
All simplification questions are to be solved based on BODMAS rule only.
B − Bracket
O − Of
D − Division
M − Multiplication
A − Addition
S − Subtraction
When there are more brackets in the given expression, simplification should be started from inner most bracket to the outer most bracket.
Some Important Identities
* (a + b)2 = a2 + b2 + 2ab
* (a − b)2 = a2 + b2 − 2ab
* (a + b) (a − b) = a2 − b2
* (a + b)3 = a3 + b3 + 3a2 b + 3ab2
* (a − b)3 = a3 − b3 − 3a2 b + 3ab2
* a3 + b3 = (a + b) (a2 − ab + b2)
* a3 − b3 = (a − b) (a2 + ab + b2)
* (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
* a3 + b3 + c3 − 3abc = (a + b + c) (a2 + b2 + c2 − ab − bc − ac)
Laws of Indices
Squares and Cubes of numbers are very useful in simplification questions. Following table gives squares and cubes of 25 numbers
Model Questions
1. 368 × 247 − 564 + 324 = ? + 124
a) 90533 b) 90532 c) 89549 d) 89546
Sol: If we can observe the options the last digit varies so just we can find the last digit and choose the option so we can do the calculation only to unit’s place digit.
Ans: b
2.1272 × 48 + 2436 = 407 × ?
a) 156 b) 192 c) 134 d) 121
Sol: If we can observe the options the last digit varies so just we can find the last digit and choose the option so we can do the calculation only to unit's place digit.
Ans: a
3. 528 × 79 = ? − 127
a) 12345 b) 41839 c) 42345 d) 42347
Sol: If we can observe the options the last digit varies so just we can find the last digit and choose the option so we can do the calculation only to unit's place digit
Ans: b
4. 4368 + 2158 − 596 − ? = 3421 + 1262
a) 1247 b) 1066 c) 1174 d) 1384
Sol: If we can observe the options the last digit varies so just we can find the last digit and choose the option so we can do the calculation only to unit's place digit.
Ans: a
5. 7960 + 2965 − 8050 + 4028 = ?
a) 6903 b) 6904 c) 6905 d) 6907
Sol: If we can observe the options the last digit varies so just we can find the last digit and choose the option so we can do the calculation only to unit's place digit.
Ans: a
6. 7962 + 8463 + 9643 − 10467 = ?
a) 15601 b) 15611 c) 15521 d) 15531
Sol: If we can observe the options the last digit is same but ten's place digit varies so just we can find the ten’s place digit and choose the option.
Ans: a
7. 68.742 − 34.206 + 52.477 − 21.541 = ?
a) 48.252 b) 65.472 c) 81.292 d) 61.382
Sol: If we can observe the options the last digit is same but ten's place digit varies so just we can find the ten’s place digit and choose the option.
Ans: b
8. 
a) 658 b) 126 c) 124 d) 149
Sol: If we can observe the options the last digit varies so just we can find the last digit and choose the option so we can do the calculation only to unit's place digit.
Ans: b
9. 85793 − ? + 151 = 77477
a) 8677 b) 8467 c) 8487 d) 8997
Sol: If we can observe the options the last digit is same but ten's place digit varies so just we can find the ten’s place digit and choose the option.
Ans: b
10. 12.9 × 14.6 × 42.7 = ?
a) 8042.118 b) 8016.482
c) 8047.228 d) 8012.422
Sol: We can add the all digits of the number and multiply.
Then we can get the resultant number. The resultant number also we can add the all digits to convert a single digit.
Which option will satisfy the digit sum of the question that option should be the answer.
12.9 × 14.6 × 42.7 = x
3 × 2 × 4 = x
24 = x 
6 = x
Option ‘a’ digit sum is also 6 so the option ‘a’ is the solution.
Ans: a
11. 20111 × 21 × 11 = ?
a) 4645611 b) 4645641 c) 4645621 d) 4111141
Sol: We can add the all digits of the number and multiply. Then we can get the resultant number. The resultant number also we can add the all digits to convert a single digit. Which option will satisfy the digit sum of the question that option should be the answer.
20111 × 21 × 11 = x
5 × 3 × 2 = x
30 = x 
3 = x
Option ‘b’ digit sum is also 3 so the option ‘b’ is the solution
Ans: b
12. 40% of 400 + ?% of 300 = 250
a) 40 b) 36 c) 25 d) 30
Sol:
Ans: d
13. 
a) 185 b) 187 c) 183 d) 184
Sol:
Ans: c
14. 
a) 600 b) 250 c) 200 d) 400
Sol:
Ans: d
15. (48% of 625) ÷ 0.75 = ?
a) 800 b) 405 c) 400 d) 500
Sol:
Ans: c
16. 80% of (1.5 × 4 + ?) = 24
a) 30 b) 36 c) 24 d) 28
Sol:
Ans: c
17. 
a) 6 b) 16 c) 8 d) 4
Sol:
Ans: d
18. 
a) 64 b) 60 c) 68 d) 56
Sol:
Ans: a
19. 
a) 14 b) 13 c) 15 d) 18
Sol:
Ans: b
20. 
a) 8 b) 5 c) 15 d) 13
Sol:
Ans: b
21. (360 − 225) × 6 − 210 = ? × 12
a) 100 b) 50 c) 80 d) 20
Sol:
Ans: b
22. (45 × 8) − 16% of 2000 = ? − 260
a) 100 b) 250 c) 300 d) 450
Sol:
Ans: c
23. 24% of 500 + 900 = ? × 51
a) 35 b) 20 c) 15 d) 25
Sol:
Ans: b
24. 
a) 100 b) 180 c) 150 d) 200
Sol:
Ans: d
25. 50% of 1200 − 320 = ? + 12% of 1500
a) 100 b) 120 c) 150 d) 80
Sol:
Ans: a
