**Simplification Questions: **A strong grasp of fundamental mathematical concepts taught in 9th and 10th grade is frequently vital for competitive exams.
Simplification, in particular, carries significant importance in the Quant section, where emphasis is placed on basic questions.
Candidates preparing for different examinations will come across numerous scoring questions in the Quant section.
It is crucial for candidates to possess a clear comprehension of the concept and engage in regular practice to solve such questions effectively.

In the space below, you will find basic concepts related to Simplification questions, as well as a variety of example questions frequently asked in examinations.
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**Table of Contents**

**Classification of Simplification**

**Simplification Rules**

**Tips to Solve Simplification Questions**

**Simplification Questions for Competitive Exams**

__Classification of Simplification__

There are two types of Simplification:
__Classification of Simplification__

- The first kind of simplification question is 'Finding the missing number,' and you must be familiar with both types.
- 'The relation between the numbers and simplifying the numbers using the principles of simplification' is the second type of simplification issue.

__Simplification Rules__

The rules of simplification which should be known to all the candidates are as follows:
__Simplification Rules__

V |
Vinculum |

B |
Remove Brackets - in the order ( ) , { }, [ ] |

O |
Of |

D |
Division |

M |
Multiplication |

A |
Addition |

S |
Subtraction |

**Tips & Tricks to Solve Simplification/ Approximation Questions**

Several fundamental tips and tactics may be employed to tackle the approximation and simplification problems to guarantee that the candidate does not lose marks in this area.
Source: safalta.com

Take a look at the following suggestions:- Always use the BODMAS rule to answer approximation or simplification issues.
- A rounded-off value is used for values that are supplied in a decimal format. For example, 45.62 may be read as 46, 22.10 as 22, and so on.
- Learning tables up to 20 may be quite beneficial to applicants and can help them save time.
- Remember the following fundamental formulas that might be utilized in such a situation:
- (a+b)
^{2}= a^{2}+ b^{2}+ 2ab - (a-b)
^{2}= a^{2}+ b^{2}– 2ab - a
^{2}– b^{2}= (a+b) (a-b) - a
^{3}+ b^{3}= (a+b) (a^{2}– ab + b^{2}) - (a+b)
^{3}= a^{3 }+ b^{3}+ 3ab (a+b) - (a-b)
^{3}= a^{3}– b^{3}– 3ab (a-b) - Do not overcomplicate the problems, and make sure that any lengthy computations are ignored to complete the equations in the allotted time.

Also, practice questions from the following topics:

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**Simplification of Important Questions For Competitive Exams**

Here we have compiled a list of questions on Simplification which can be practiced by candidates. The solutions to these questions have been provided as well.

Q1.
(42)2 – (?)2 = 3563 – 2055

18

28

36

42

16

Q2.
? = 5.8 × 2.5 + 0.6 × 6.75 + 139.25

157.30

157.80

158.40

160.30

None of these

Q3.
3889 + 12.952 – ? = 3854.002

47.095

47.752

47.932

47.95

None of these

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Q4.
138.009 + 341.981 – 146.305 = 123.6 + ?

120.085

120.85

220.085

124.125

None of these

Q5.
832.58 – 242.31 = 779.84 – ?

179.57

199.57

295.05

198.125

None of these

Q6.
(25)2 + (16)2 – (18)2 – (4)2 + (√4)2 – (√121) = ?

534

544

540

542

None of these

Q7.
(√196 + √225 + √961)÷3 + 15 - 5 = ?

34

44

40

42

30

Q8.
(17)2 + √441 + (6)3 – (8)2 + 38

450

500

400

550

300

Q9.
17 × 8 + 18/3 - √361 + √196/7 + 4 × 19

205

200

201

208

191

Q10.
100 + 25 × 2.5 – 160 = ? + 40

220

240

200

250

225

Q11.
125 ÷ 2.50 + x2 - 42 = 129

7

5

9

11

8

Q12.
20% of 450 + 30% of 300 = ? × 3

58

68

60

54

48

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Q13.
× 120% × 50% × 200 = ? × 112.5

4

6

2

5

2

Q14.
190 + 170 – 219 + ? = 278

112

124

110

108

137

Q15.
(45 × 20÷10 + 21) ÷ 3 =?

900

1369

961

1264

1225

Q16.
3600 ÷ 72 × 4 + 574 – 378 =?

596

498

496

898

449

Q17.
0.006 × 0.02 × 0.0036 ÷ (0.06 × 0.004) = x

0.018

0.0018

0.18

1.8

18

Q18.
of (418 – 394) + 762 = x + 247

662

695

643

638

613

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Q19.
(3.03 + 7.07)2 – x = 5 × 1.04 × 6.8

66.65

65.66

61.13

72.17

59.15

Q20.
× 20 = x

940

952

960

950

980

Q21. What approximate value will come in the place of question mark (?) in the following question? 5.997 × 21.659 + 369.2502 = ?

500

655

625

502

575

Q22. What approximate value will come in the place of question mark (?) in the following question? 39.093% of 304.806 + 51.0025% of 510.357 – 173.76 = ?

326

192

251

203

119

Q23. What should come in the place of question mark (?) in the following questions? 84368+65466−72009−13964=?

61481

62921

63861

64241

None of these

Q24. What should come in the place of question mark (?) in the following questions?

?/52 9 = 324/ ?

404

408

410

414

416

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Q25. What should come in the place of question mark (?) in the following questions? 33^7.8 × 33^1.2 ÷ 33^5 = 33 × 33?

2.8

3

3.2

4

6

Q26. What should come in the place of question mark (?) in the following questions? 12% 𝑜𝑓 555+15% 𝑜𝑓 666=?

166.5

167.5

168.5

169.5

None of these

Q27. What should come in the place of question mark (?) in the following questions? 7/5 𝑜𝑓 58 + 3/8 𝑜𝑓 139.2=?

133.4

137.2

127.8

131.6

None of these

Q28. What approximate value will come in the place of question mark (?) in the following question? (32.298 × 10.025÷ 15.012 + 31.99) ÷ 2.26 =√?

784

689

676

729

900

Q29. What approximate value will come in the place of question mark (?) in the following question? (15.0159/ 8.167) × 104.0102% × 49.9025% × 240.0125 = ? × 12.158

14

16

21

15

18

Q30. What approximate value will come in the place of question mark (?) in the following question? 24.0423% of 449.759 + 31.9025% of 300.0234 = ? × 3.010

58

68

63

54

48

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Q31. What approximate value will come in the place of question mark (?) in the following question? 124.856 ÷ 1.25 +?^2 -42.0156 = 139.0235

7

5

9

11

8

Q32. What approximate value will come in the place of question mark (?) in the following question? 499.998 + 12.003 × 13.5 – 160.365 = ? + 54.023

438

437

548

448

540

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Q33. What approximate value will come in the place of question mark (?) in the following question? of 5*1/8 of (5471.926 – 5408.002) + 762.985 = x + 246.886

762

795

843

892

913

Q34. What approximate value will come in the place of question mark (?) in the following question? (20.13)^2 + (12.96)^2 – (19.11)^2 = ?

203

213

208

218

212

Q35. What approximate value will come in the place of question mark (?) in the following question? ( ?/ 4 )+ 42.01 + 129.99 = 68.09 + 229. 01 + 76.99

860

920

790

808

735

**Solutions:**

Q1.
Answer: 5 Solution:

(42)2 – (?)2 = 3563 – 2055

1764 - (?)2 = 1508

(?)2 = 1764 – 1508

(?)2 = 256

? = 16

Q2.
Answer:2 Solution:

5.8 × 2.5 + 0.6 × 6.75 + 139.25

14.50 + 4.05 + 139.25

157.80

Q3.
Answer:4 Solution:

3889 + 12.952 – ? = 3854.002

? = 3889 + 12.952 – 3854.002

? = 3901.952 – 3854.002

? = 47.95

Q4.
Answer:5 Solution:

138.009 + 341.981 – 146.305 = 123.6 + x x = (138.009 + 341.981) – (146.305 + 123.6)

479.99 – 269.905

210.085

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Q5.
Answer: 5 Solution:

832.58 – 242.31 = 779.84 – x x = (779.84 + 242.31) – 832.58

1022.15 – 832.58

189.57

Q6.
Answer:1 Solution:

(25)2 + (16)2 – (18)2 – (4)2 + (√4)2 – (√121) = ?

625 + 256 – 324 – 16 + 4 – 11

534

Q7.
Answer:5 Solution:

(√196 + √225 + √961)÷3 + 15 - 5 = ?

20 + 15 – 5

30

Q8.
Answer:2 Solution:

289 + 21 + 216 – 64 + 38

310 + 152 + 38

Q9.
Answer:3 Solution:

17 × 8 + 18/3 - √361 + √196/7 + 4 × 19

136 + 6 – 19 + 2 + 76

142 – 19 + 78

220 – 19

201

Q10.
Answer:3 Solution:

100 + 25 × 2.5 – 160 = x + 40

100 + 300 – 160 =x + 40

400 – 160 = x + 40 240 = x + 40 x = 240 – 40 x= 200

Q11.
Answer: 4 Solution:

125 ÷ 2.50 +x2 -42 = 129

X2 = 129 - 8

X2 = 121

X =√121

X = 11

Q12.
Answer: 3 Solution:

20% of 450 + 30% of 300 = X × 3 20/100 × 450 + 30/100 × 300 = X × 3

90 + 90 = X × 3

X= 180 / 3

X = 60

Q13.
Answer: 5 Solution:

× 120% × 50% × 200 = x × 112.5

× 200 = x × 112.5

X = 2

Q14.
Answer: 5 Solution:

190 + 170 – 219 + x = 278

360 – 219 + x = 278

141 + x = 278

X = 278 – 141

X = 137

Q15.
Answer: 2 Solution:

(45 × 20÷ 10 + 21)/3 =

( 90 + 21)/3 =

X = 372 X = 1369

Q16.
Answer : 3

3600 ÷ 72 × 4 + 574 – 378 = ?

3600

× 4 + 574 – 378

200 + 574 – 378

2276 – 378

496

Q17.
Answer: 2

0.006 × 0.02 × 0.0036 ÷ (0.06 × 0.004) = x

= x

X = 0.0018

Q18.
Answer: 4

of (418 – 394) + 762 = x + 247

× 24 + 762 = x + 247

123 + 762 = x + 247

X = 885 – 247

X = 638

Q19.
Answer:1

(3.03 + 7.07)2 – x = 5 × 1.04 × 6.8

(10.1)2 – x = 35.36

102.01 – x = 35.36

X = 102.01 – 35.36

X = 66.65

Q20.
Answer:3

× 20 = x

× 20 = x

X = 960

Q21. Answer: 502

Explanation:

Writing the approximate values to the nearest integer ⇒6 × 22 + 370 = ? ⇒132 + 370 = ? ⇒502

Q22. Answer: 203

Explanation: Writing the approximate values to the nearest integer

⇒40/100 × 305 + 50 /100 × 510 – 174 = ?

⇒122 + 255 – 174 =?

⇒203

Q23. Answer: 63861

Explanation: 149834−85973=63861

Q24. Answer: 414

Q25. Answer: 3

Q26. Answer: 166.5

Explanation:

66.6+99.9=166.5

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Q27. Answer: 133.4

Explanation: 81.2+52.2=133.4

Q28. Answer: 729

Explanation: Writing the approximate values to the nearest integer

⇒ (33 × 10÷ 15 + 32) ÷ 2 =

⇒ (22 + 32) / 2 =

⇒54/2=

⇒X = 27

⇒X = 729

Q29. Answer: 18

Explanation: Writing the approximate values to the nearest integer

⇒15/8 × 104% × 50% × 240 = x × 13

⇒15/8 × 104/100 × 50/100 × 240 = x × 13

⇒234 = x × 13

⇒X = 234/13

⇒X = 18

Q30. Answer: 68

Explanation:

Writing the approximate values to the nearest integer

⇒24% of 450 + 32% of 300 = X × 3

⇒24/100 × 450 + 32/100 × 300 = X × 3

⇒108 + 96 = X × 3

⇒204 = X × 3

⇒X= 204 / 3

⇒X = 68

Q31. Answer: 9

Explanation:

Writing the approximate values to the nearest integer

⇒125 ÷ 1.25 +x -42 = 139

⇒125/1.25=100

⇒100 + x – 42 = 139

⇒X = 139 + 42 – 100

⇒X =181 – 100

⇒X = 81

X = √81

⇒X = 9

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Q32. Answer: 448

Explanation:

Writing the approximate values to the nearest integer

⇒500 + 12 × 13.5 – 160 = x + 54

⇒500 + 162 – 160 =x + 54

⇒662 – 160 = x + 54

⇒502 = x + 54

⇒x = 502 – 54

⇒x= 448

Q33. Answer: 843

Explanation:

Writing the approximate values to the nearest integer ⇒

5*1/8 of (5472 – 5408) + 762 = x + 247

⇒41/8 × 64 + 762 = x + 247

⇒328 + 762 = x + 247

⇒X = 1090 – 247

⇒X = 843

Q34. Answer: 208

Explanation:

Writing the approximate values to the nearest integer

⇒ (20)^2 + (13)^2 – (19)^2 = ?

⇒400 + 169 – 361 = ?

⇒208

Q35. Answer: 808

Explanation:

Writing the approximate values to the nearest integer

⇒?/4 + 42 + 130 = 68 + 229 + 77

⇒?/4 + 172 = 374

⇒?/4 = 374 – 172

⇒202 × 4

⇒ 808

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## What are simplification questions?

## Why are simplification questions important?

## What are some tricks and tips for solving simplification questions?

- Understand the order of operations (PEMDAS/BODMAS) to perform calculations correctly.
- Utilize the commutative, associative, and distributive properties to manipulate expressions effectively.
- Break down complex expressions into smaller parts and simplify each part individually.
- Look for common factors, cancel out terms, and combine like terms to reduce complexity.
- Practice regularly to improve speed and accuracy.