Simplification Questions and Answers, Tricks and Tips to solve simplification related questions

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. Join our Free Course of Reasoning for All Competitive Exams! 

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:

• 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.

Let's look at several cases with detailed explanations:

Simplification Rules

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

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. 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 = a² + b² + 2ab
• (a-b)² = a² + b² – 2ab
• a² – b² = (a+b) (a-b)
• a³ + b³ = (a+b) (a² – ab + b²)
• (a+b)³ = a³ + b³ + 3ab (a+b)
• (a-b)³ = a³ – b³ – 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:

Blood Relations	Click Here
Syllogism	Click Here
Coding-Decoding	Click Here
Inequality	Click Here

 

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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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Mastering simplification techniques boosts problem-solving skills. Understanding the order of operations, manipulating expressions, and breaking them down simplifies complex equations. Practice, stay updated, and be confident in approaching simplification questions for success.

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